Recent zbMATH articles in MSC 76https://zbmath.org/atom/cc/762021-01-08T12:24:00+00:00WerkzeugA new mixed finite volume element method for solving one-dimensional porous medium problems.https://zbmath.org/1449.652182021-01-08T12:24:00+00:00"Chen, Guofang"https://zbmath.org/authors/?q=ai:chen.guofang"Hei, Yuanyuan"https://zbmath.org/authors/?q=ai:hei.yuanyuan"Lv, Junliang"https://zbmath.org/authors/?q=ai:lv.junliangSummary: For the one-dimensional porous medium problem, the wave front of the numerical solution could not propagate forward when the standard mixed finite volume element method was used to solve them, we propose a new mixed finite volume element method for solving the degradation problem, in which the flux variable only includes the derivative of the original variable to the spacial variable. The results show that the method can avoid the phenomenon that the wave front of the numerical solution can not propagate forward, and can capture the interface of numerical solution well. The validity of the method is verified by numerical experiments.Existence and uniqueness of solutions for a class of steady-state incompressible non-Newtonian Boussinesq equations.https://zbmath.org/1449.760052021-01-08T12:24:00+00:00"Yang, Hui"https://zbmath.org/authors/?q=ai:yang.hui.1"Wang, Changjia"https://zbmath.org/authors/?q=ai:wang.changjiaSummary: We considered the first boundary value problems for a class of steady-state incompressible non-Newtonian Boussinesq equations in a three-dimensional smooth bounded domain \(\Omega\). Under the conditions that the external force term was appropriately small, we proved the existence and uniqueness of regular solutions for the problem when the exponent \(p \in (1, 2)\) by using the iterative method.Boundary layer flow due to the vibration of a sphere.https://zbmath.org/1449.760022021-01-08T12:24:00+00:00"Sadiq, Muhammad Adil"https://zbmath.org/authors/?q=ai:sadiq.muhammad-adilSummary: Boundary layer flow of the Newtonian fluid that is caused by the vibration of inner sphere while the outer sphere is at rest is calculated. Vishik-Lyusternik (Nayfeh refers to this method as the method of composite expansions) method is employed to construct an asymptotic expansion of the solution of the Navier-Stokes equations in the limit of high-frequency vibrations for Reynolds number of \(O(1)\). The effect of the Stokes drift of fluid particles is also considered.Magnetoviscous potential flow analysis of Kelvin-Helmholtz instability with heat and mass transfer.https://zbmath.org/1449.760262021-01-08T12:24:00+00:00"Asthana, Rishi"https://zbmath.org/authors/?q=ai:asthana.rishi"Awasthi, Mukesh Kumar"https://zbmath.org/authors/?q=ai:awasthi.mukesh-kumar"Agrawal, G. S."https://zbmath.org/authors/?q=ai:agrawal.g-s.1Summary: A linear analysis of the Kelvin-Helmholtz instability of interface between two viscous and magnetic fluids has been carried out where there was heat and mass transfer across the interface while the fluids have been subjected to a constant magnetic field parallel to the streaming direction. The viscous potential flow theory has been used for the investigation. A dispersion relation has been obtained and a stability criterion is given by a critical value of relative velocity as well as the critical value of magnetic field. The resulting plots show the effect of various physical parameters such as wave number, viscosity ratio, ratio of magnetic permeabilities and heat transfer coefficient. It has been observed that heat and mass transfer has a destabilizing effect whereas the horizontal magnetic field stabilizes the system.MARS: theoretical framework and numerical algorithms for a new approach of interface tracking in simulating multiphase flows.https://zbmath.org/1449.760672021-01-08T12:24:00+00:00"Zhang, Qinghai"https://zbmath.org/authors/?q=ai:zhang.qinghaiSummary: Interface tracking (IT) is one of the most fundamental problems in the study of multiphase flows. In current IT methods, geometric and topological problems are avoided by converting them to numerically solving partial differential equations. In contrast, we tackle geometric and topological problems with tools in geometry and topology. This review paper is a brief summary of the MARS theory and associated numerical algorithms, including (1) the Yin space as a model of continua, (2) Boolean algebra on the Yin space, (3) homological analysis on topological changes of a flow phase, (4) the theory of donating regions for classifying fluxing points and calculating Lagrangian flux in the context of scalar conservation laws, (5) numerical analysis on the convergence rates of VOF methods, (6) the cubic MARS methods for fourth-order interface tracking, and (7) the HFES method for estimating curvature and normal vectors with fourth- and higher-order accuracy. Results of classical benchmark tests show that the cubic MARS method and the HFES method are advantageous over current IT methods in terms of both accuracy and efficiency.Verification of a new CFD compressible segregated and multi-phase solver with different flux updates-equations sequences.https://zbmath.org/1449.760012021-01-08T12:24:00+00:00"Payri, Raúl"https://zbmath.org/authors/?q=ai:payri.raul"Ruiz, Santiago"https://zbmath.org/authors/?q=ai:ruiz.santiago"Gimeno, Jaime"https://zbmath.org/authors/?q=ai:gimeno.jaime"Martí-Aldaraví, Pedro"https://zbmath.org/authors/?q=ai:marti-aldaravi.pedroSummary: A new solver capable of calculating liquid and/or gas problems has been developed, verified and validated. Compressible solvers in Computational Fluid Dynamics use both mass flux and volumetric fluxes through the cell surface to calculate derivative terms. These fluxes depend on density and velocity fields, therefore the stability of the solver is affected by ``how'' and ``where'' density and velocity are calculated or updated. In addition to verification and validation, this paper deals with how different flux updates-equations sequences change the computational solution, reaching the conclusion that for mono-phase solvers no extra-updates should be used in order to minimize computational cost, but for multi-phase solvers with high density gradients an extra-update should be implemented to improve the stability of the solver.State-space estimation with a Bayesian filter in a coupled PDE system for transient gas flows.https://zbmath.org/1449.760452021-01-08T12:24:00+00:00"Uilhoorn, Ferdinand E."https://zbmath.org/authors/?q=ai:uilhoorn.ferdinand-evertSummary: The accuracy of the first-principle models describing the evolution of gas dynamics in pipelines is sometimes limited by the lack of understanding of the gas transport phenomena. In this paper, a stochastic filtering approach is proposed based on a sequential Monte Carlo method to provide real-time estimates of the state in gas pipelines. After constructing a state-space model of the compressible single-phase flow based on the laws of conservation of mass and momentum, the optimal sequential importance resampling filter (SIR) is implemented. The state variables are updated with simulated measurements. The two-step Lax-Wendroff method is used for the discretization of the partial differential equations describing the gas model in both space and time to obtain finite-dimensional discrete-time state-space representations. The system states are then combined into an augmented state vector. The resulting nonlinear state-space model is used for the design of the particle filter that provides real-time estimations of the system states. Simulation results for a coupled PDE system describing an unsteady isothermal gas flow demonstrate the effectiveness of the proposed method. A sensitivity analysis is conducted to examine the performance of the filter for different model and observation error covariances and observation intervals.CFD simulation of deflagration-detonation processes using vector- and parallel computing systems.https://zbmath.org/1449.760422021-01-08T12:24:00+00:00"Rehm, W."https://zbmath.org/authors/?q=ai:rehm.warren-s|rehm.wolfgang"Gerndt, M."https://zbmath.org/authors/?q=ai:gerndt.michael"Jahn, W."https://zbmath.org/authors/?q=ai:jahn.walter"Semler, F."https://zbmath.org/authors/?q=ai:semler.f"Jones, I."https://zbmath.org/authors/?q=ai:jones.ian-p|jones.i-a|jones.ian-gordon|jones.ian-s-f|jones.ilenna-simoneSummary: In this paper, we describe the state of computational fluid dynamics simulations (CFD) of deflagration and detonation processes in hydrogen-air mixtures, using vector- and parallel computing systems, which have been provided in the Institute for Safety Research and Reactor Technology (ISR) at the Forschungszentrum Jülich (FZJ). The R\&D work is performed within the scope of an EC project on hydrogen safety that is addressed to the verification of models and criteria for the prediction of Deflagration-to-Detonation Transition (DDT) in hydrogen-air-steam systems under severe accident conditions. Particularly, we report on the present state and recent progress made in the establishment of the CRAY hardware cluster (T90, T3E, J90) with vector and parallel processing capabilities, as well as on the current achievement of the CFD software cluster (CFX, ERCO, DET, IFSAS), including test cases for verification and validation, with some illustrating examples. Emphasis is put on the multi-dimensional simulation of fast turbulent hydrogen flames, for instance, using the general purpose field code CFX from AEA. The numerical results are compared with experimental results, which have been obtained for various conditions in the Russian large scale RUT test facility. Specifically, we outline deflagration-detonation processes concerning the numerical resolution of reacting flows in complex geometries, applying mesh refinement or massively parallel processing. First test cases indicate that our modern field code cluster (MFCC) with high-performance supercomputer networking (HPCN) will be a suitable constellation to resolve DDT processes in safety enclosures of innovative nuclear reactor containments or other industrial plants, e.g. solar hydrogen demonstration facilities.Modeling of the fluid filtration for hydraulic fracture conditions.https://zbmath.org/1449.760532021-01-08T12:24:00+00:00"Astaf'ev, V. I."https://zbmath.org/authors/?q=ai:astafev.vladimir-ivanovich"Fedorchenko, G. D."https://zbmath.org/authors/?q=ai:fedorchenko.g-dSummary: We research the process of fluid filtration to bore under the hydraulic fracture conditions. This fracture is presented as the thin ellipsis crossing the bore. Use the theory of complex-valued functions allows finding the accurate solution of this problem and obtaining the analytic expression for the skin factor value which shows the influence of hydraulic fracture on well efficiency. In conclusion we introduce the simple formulation of this problem, when the hydraulic fracture is presented as zero-thickness notch having the finite conductivity.Solitary waves in a thick walled elastic tube.https://zbmath.org/1449.740872021-01-08T12:24:00+00:00"Demiray, Hilmi"https://zbmath.org/authors/?q=ai:demiray.hilmi"Dost, Sadik"https://zbmath.org/authors/?q=ai:dost.sadikSummary: In the present work, we studied the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible inviscid fluid. The efects of wall inertia and shear deformation are taken into account in determining the inner pressure-inner cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly nonlinear waves in the long wave approximation is investigated and the Korteweg-de Vries equation is obtained as the evolution equation. Due to dependence of the coefficients of the governing Korteweg-de Vries equation on the initial deformation, the material parameters and the thickness ratio, it is observed that the solution profile changes with these parameters. The numerical calculations indicate that for engineering materials (small \(\alpha)\)) the wave profile gets steepened with increasing thickness ratio, whereas for soft biological tissues the wave profile is not so sensitive to the thickness ratio but it is quite sensitive to the material nonlinearity characterized by the coefficient \(\alpha\). This shows that for biological tissues the material nonlinearity is more important than the geometrical nonlinearity.Modelling and analysis of variable geometry exhaust gas systems.https://zbmath.org/1449.760462021-01-08T12:24:00+00:00"Bartlett, H."https://zbmath.org/authors/?q=ai:bartlett.harry"Whalley, R."https://zbmath.org/authors/?q=ai:whalley.richard-dSummary: This paper presents the modelling and analysis of variable geometry, exhaust gas systems. An automotive example is considered whereby the pulsating exhausts gas flow through an exhaust pipe and silencer are considered over a wide range of speeds. Analytical procedures are outlined enabling the general analysis and modelling of variable geometry, exhaust gas systems. Simulation results show the effect of pulsating gas streams through a vehicle exhaust and silencer confirming thereby the calculated results.A comparison of one-dimensional and three-dimensional models for the simulation of gas-solids transport systems.https://zbmath.org/1449.760642021-01-08T12:24:00+00:00"Mason, David J."https://zbmath.org/authors/?q=ai:mason.david-j"Levy, Avi"https://zbmath.org/authors/?q=ai:levy.aviSummary: This paper compares the use of one-dimensional (1-D) and a three-dimensional (3-D) models to simulate the flow of a gas-solids mixture through a pipeline. Both models solve steady flow conservation equations for mass, momentum and energy. The implementation of each model is presented in terms of the changes made to the generic model in order to describe this type of flow. Performance data was obtained for a pneumatic conveying system used to convey pulverised fuel ash (PFA) in a power station. Each model was used to simulate the behaviour of this ash transfer line.Two-level penalty method for the steady incompressible Stokes equations.https://zbmath.org/1449.653222021-01-08T12:24:00+00:00"Li, Shishun"https://zbmath.org/authors/?q=ai:li.shishun"Qi, Fenfen"https://zbmath.org/authors/?q=ai:qi.fenfen"Shao, Xinping"https://zbmath.org/authors/?q=ai:shao.xinpingSummary: In this paper, we present a two-level penalty method for the steady incompressible Stokes equations by employing two finite element spaces. This method involves solving one small Stokes equation on the coarse space and two penalty equations on the fine space (the linear systems with same symmetric and positive coefficient matrices). The convergence shows that the coarse space can be chosen very small. Moreover, the penalty parameter is only dependent on the coarse mesh size and the regularity of the problem. Therefore, the resulting solution still achieves asymptotic optimal accuracy when the penalty parameter is chosen ``not very small''. The numerical results confirm the convergence analysis, and the numerical comparison also shows that this method is efficient for solving the steady incompressible Stokes equations.The INTERNODES method for non-conforming discretizations of PDEs.https://zbmath.org/1449.653442021-01-08T12:24:00+00:00"Gervasio, Paola"https://zbmath.org/authors/?q=ai:gervasio.paola"Quarteroni, Alfio"https://zbmath.org/authors/?q=ai:quarteroni.alfio-mSummary: INTERNODES is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into two or several disjoint subdomains. It exploits two intergrid interpolation operators, one for transfering the Dirichlet trace across the interfaces, and the other for the Neumann trace. In this paper, in every subdomain the original problem is discretized by either the finite element method (FEM) or the spectral element method (SEM or \(hp\)-FEM), using a priori non-matching grids and piecewise polynomials of different degrees. Other discretization methods, however, can be used. INTERNODES can also be applied to heterogeneous or multiphysics problems, that is, problems that feature different differential operators inside adjacent subdomains. For instance, in this paper we apply the INTERNODES method to a Stokes-Darcy coupled problem that models the filtration of fluids in porous media. Our results highlight the flexibility of the method as well as its optimal rate of convergence with respect to the grid size and the polynomial degree.On gradient calculation in flux correction method.https://zbmath.org/1449.652392021-01-08T12:24:00+00:00"Bakhvalov, P. A."https://zbmath.org/authors/?q=ai:bakhvalov.pavel-aSummary: Flux Correction method is a family of edge-based schemes for solving hyperbolic systems on unstructured meshes. The cruical operation there is a nodal gradient calculation of physical variables with at least second order of accuracy. There are two well-known procedures meeting this condition. One is based on Least Squares method and the other one is based on spectral elements. In this paper we compare resulting schemes and discuss their problems.On the global existence and stability of 3-D viscous cylindrical circulatory flows.https://zbmath.org/1449.353422021-01-08T12:24:00+00:00"Yin, Huicheng"https://zbmath.org/authors/?q=ai:yin.huicheng"Lin, Zhang"https://zbmath.org/authors/?q=ai:lin.zhangThe main result in this paper is a global existence and uniqueness theorem of cylindrical symmetric circulatory flows for the three-dimensional compressible Navier-Stokes equations. It is also shown that the flow is globally stable in time when the corresponding initial states are perturbed suitably small. The proof follows from the local existence result of classical solutions, continuity arguments, and is essentially based on uniform weighted energy estimates.
Reviewer: Radu Precup (Cluj-Napoca)Continuous method for calculating the transport equations for a multicomponent heterogeneous system on fixed Euler grids.https://zbmath.org/1449.760352021-01-08T12:24:00+00:00"Zhang, Ch."https://zbmath.org/authors/?q=ai:zhang.changqin|zhang.chun-zao|zhang.chengyi.1|zhang.chaobi|zhang.chicheng|zhang.changze|zhang.chengjie|zhang.changda|zhang.chongqun|zhang.chaoyan|zhang.changcheng|zhang.changyao|zhang.chungou|zhang.chunwei|zhang.chendong|zhang.chaunzeng|zhang.chuanke|zhang.chunying|zhang.chunfang|zhang.chunfeng|zhang.chiyuan|zhang.chengshan|zhang.changqing|zhang.chuntian|zhang.chengqian|zhang.chao.4|zhang.changgeng|zhang.chenggong|zhang.chao.3|zhang.chaofan|zhang.changguang|zhang.chuangliang|zhang.chiong|zhang.chongjie|zhang.changrong|zhang.changbin|zhang.chenxia|zhang.chunyao|zhang.chaomin|zhang.chunze|zhang.chengcui|zhang.chenglong|zhang.chunkai|zhang.chenliang|zhang.chengguo|zhang.chuhan-h|zhang.chun-lian|zhang.changjuan|zhang.chuanqian|zhang.chenyan|zhang.chidong|zhang.chaoying|zhang.chengliang|zhang.chaoli|zhang.chaoyuan|zhang.chuanzeng|zhang.chuanfang|zhang.changming|zhang.chengxiang|zhang.changwang|zhang.chenbin|zhang.chaozhu|zhang.chao|zhang.chaoqun|zhang.chunshu|zhang.chichen|zhang.chengke|zhang.chengfu|zhang.chunmei|zhang.chaoyi|zhang.chen-jun|zhang.chuhua|zhang.changbo|zhang.chuanjing|zhang.chongfu|zhang.chihao|zhang.chengcheng|zhang.chaoxian|zhang.chenghu|zhang.chengcai|zhang.chong|zhang.chengfen|zhang.chaohua|zhang.chunqing|zhang.chengjin|zhang.chuanjun|zhang.chang-yue|zhang.chenming|zhang.chao.7|zhang.changsheng|zhang.cheng-jun|zhang.changxue|zhang.shunyan|zhang.chaolong|zhang.chengzhao|zhang.chuanmin|zhang.chengchun|zhang.chenghui|zhang.chengdian|zhang.chengheng|zhang.chaowei|zhang.chuang|zhang.chaoen|zhang.chaonan|zhang.chenyang|zhang.chuncao|zhang.chenling|zhang.changzhu|zhang.chenglin|zhang.chiqun|zhang.chenyu|zhang.chundi|zhang.chaowen|zhang.chengrui|zhang.chengwen|zhang.chaojin|zhang.chao.5|zhang.chunrei|zhang.chu-xu|zhang.changli|zhang.chunhui|zhang.chengtang|zhang.chaolun|zhang.chiping|zhang.chunmiao|zhang.chengpeng|zhang.chenlu|zhang.chun-lai|zhang.chuanrong|zhang.chuanfu|zhang.chuanli|zhang.chengye|zhang.chunlin|zhang.chuanqing|zhang.changshui|zhang.chengqi|zhang.chenli|zhang.chuncheng|zhang.chao.8|zhang.chenyi|zhang.chuting|zhang.chenzi|zhang.chengyuan|zhang.chenhua|zhang.chunru|zhang.changyong|zhang.changsuo|zhang.chuangyuan|zhang.chengxi|zhang.chuan|zhang.chuhan|zhang.chenying|zhang.chong-gao|zhang.changquan|zhang.chi|zhang.christophe|zhang.chongming|zhang.chen-rong|zhang.chaojun|zhang.chenghong|zhang.chenguang|zhang.chisheng|zhang.chenfu|zhang.chengxiao|zhang.chunzhi|zhang.chonghui|zhang.chengwu|zhang.chen|zhang.chun-ye|zhang.cheng-jie|zhang.changkuang|zhang.charles-x|zhang.chunjin|zhang.chaogui|zhang.chunrui|zhang.chu|zhang.chenchen|zhang.chaoyong|zhang.chune|zhang.chenghao|zhang.chunting|zhang.chunli|zhang.chengchuang|zhang.chuanlin|zhang.chuanzhi|zhang.chuanni|zhang.chunhua|zhang.chunming-m|zhang.chuck|zhang.chengchang|zhang.chuanyi|zhang.chao.9|zhang.chengyang|zhang.chun-qi|zhang.chibin|zhang.chunhong|zhang.chuangang|zhang.chengning|zhang.chuanwu|zhang.chencheng|zhang.chunqin|zhang.chengyong|zhang.chengyu|zhang.chuanjie|zhang.chunbo|zhang.chunyu|zhang.chunyang|zhang.chunming|zhang.chunnan|zhang.chun|zhang.chang-de|zhang.chenren|zhang.chengyao|zhang.chaoning|zhang.chunlu|zhang.chunxia|zhang.chunsai|zhang.chaohui|zhang.chao.6|zhang.chonglin|zhang.chunsheng|zhang.changyun|zhang.chongqi|zhang.chaoquan|zhang.changfan|zhang.chenmei|zhang.chunxi|zhang.chongshan|zhang.chuhu|zhang.chunliang|zhang.chengzhi|zhang.chaoran|zhang.chubing|zhang.chuanbao|zhang.chongwei|zhang.chengyun|zhang.chuntao|zhang.chongwu|zhang.chunyong|zhang.changyou|zhang.chao.1|zhang.chunguo|zhang.chong-long|zhang.changjiang|zhang.cha|zhang.chensong|zhang.chunpu|zhang.changhua|zhang.chenxi|zhang.chaoxia|zhang.cheng|zhang.chunling|zhang.chao.2|zhang.chaojie|zhang.chunping|zhang.chuanzhou|zhang.changgui|zhang.cheng-en|zhang.chunxiao|zhang.chengping|zhang.changwen|zhang.chun-yi|zhang.chang|zhang.chengxue|zhang.changnian|zhang.chaoming|zhang.chubin|zhang.chunyue|zhang.chaoyang|zhang.changhai|zhang.chunmin|zhang.chenhao|zhang.chengwei|zhang.chengli|zhang.chaopeng|zhang.chunyuan|zhang.chaofeng|zhang.changchun|zhang.chuanding|zhang.chunjie|zhang.chuanmei|zhang.chengbin|zhang.chuanhao|zhang.chengmin|zhang.chenfei|zhang.chunjiang|zhang.chanbao|zhang.changrui|zhang.chongyan|zhang.chungang|zhang.chunlei|zhang.changkuan|zhang.chaoliang|zhang.chengguang|zhang.chuanbin"Men'shov, I. S."https://zbmath.org/authors/?q=ai:menshov.igor-sSummary: A new numerical method for solving the transport equations of a multicomponent heterogeneous system on fixed Eulerian grids is considered. The system consists of an arbitrary number of components. Any two components are separated by a boundary (interface). Each component is characterized by a characteristic function -- the volume fraction, which is transported in a given velocity field and determines the instantaneous distribution of the component in space. The feature of this system is that it requires two conditions to be satisfied. First, the volume fraction of each component should be in the interval \([0,1]\), and, secondly, any partial sum of volume fractions should not exceed unity. To ensure these conditions, we introduce special characteristic functions instead of volume fractions and propose to solve the transport equations with respect to them. We prove that this approach ensures the fulfillment of the above conditions. The method is compatible with various TVD schemes (MINMOD, Van Leer, Van Albada, Superbee) and interface-sharpening methods (Limited downwind, THINC, Anti-diffusion, Artifical compression). The method is verified in the calculation of a number of test problems, using all the above schemes. Numerical results show the accuracy and reliability of the proposed method.Inhibition or enhancement of chaotic convection via inclined magnetic field.https://zbmath.org/1449.760512021-01-08T12:24:00+00:00"Jawdat, J. M."https://zbmath.org/authors/?q=ai:jawdat.j-m"Momani, S."https://zbmath.org/authors/?q=ai:momani.shaher-m"Hashim, I."https://zbmath.org/authors/?q=ai:hashim.ishakSummary: In this paper, we investigate the onset of convection in a horizontal layer of fluid which is heated from the underside. An inclined magnetic field is applied to the layer. The Galerkin truncated approximations were used to obtain a Lorenz-like model. The nonlinear system was solved by the fourth-order Runge-Kutta method. The results show that the Hartmann number and the angle of inclination of the magnetic field could inhibit or enhance the onset of chaotic convection.Cabaret difference scheme with improved dispersion properties.https://zbmath.org/1449.651622021-01-08T12:24:00+00:00"Sukhinov, A. I."https://zbmath.org/authors/?q=ai:sukhinov.alexander-i"Chistyakov, A. E."https://zbmath.org/authors/?q=ai:chistyakov.alexander-eSummary: Difference scheme for the advection transport equation has been constructed as the linear combination of ``cabaret'' scheme and the scheme with the central differences. The research of stability and dispersion properties of the scheme is conducted. It is shown that the constructed scheme has the best dispersion properties for high harmonicas in case of small numbers of Courant in comparison with the known scheme of ``cabaret'' for advection transport equation. Comparison of errors of this scheme and two-parameter difference scheme of the third order of accuracy on the basis of numerical experiments on sets of test tasks used earlier is carried out. It has been showed, that developed scheme has smaller errors in grid space \(L_1\) in comparison of mentioned above scheme. Additionally the developed scheme uses more compact set of nodes (when calculating \(i\)-go of knot values of the hubs \(i-1, i, i+1\) are used), and requires smaller number of arithmetic operations.On the study of oscillating viscous flows by using the Adomian-Padé approximation.https://zbmath.org/1449.760412021-01-08T12:24:00+00:00"Liu, Chi-Min"https://zbmath.org/authors/?q=ai:liu.chi-minSummary: The Adomian-Padé technique is applied to examine two oscillating viscous flows, the Stokes' second problem and the pressure-driven pulsating flow. Main purposes for studying oscillating flows are not only to verify the accuracy of the approximation solution, but also to provide a basis for analyzing more problems by the present method with the help of Fourier analysis. Results show that the Adomian-Padé approximation presents a very excellent behavior in comparison with the exact solution of Stokes' second problem. For the pulsating flow, only the Adomian decomposition method is required to perform the calculation as the fluid domain is finite where the Padé approximant may not provide a better solution. Based on present results, more problems can be mathematically solved by using the Adomian-Padé technique, the Fourier analysis, and powerful computers.On the influence of a layer of a viscous compressible fluid on the surface instability of the incompressible elastic half-plane exposed to finite initial deformations.https://zbmath.org/1449.760232021-01-08T12:24:00+00:00"Bagno, A. M."https://zbmath.org/authors/?q=ai:bagno.a-mSummary: The problem of propagation of harmonic waves in the pre-deformed incompressible elastic half-space that interacts with a layer of an viscous compressible fluid is considered. The study is based on the three-dimensional linearized equations of theory of elasticity of finite deformations for the incompressible elastic half-space and the three-dimensional linearized Navier-Stokes equations for a layer of a viscous compressible fluid. The approach based on the utilization of representations of general solutions of the linearized equations for an elastic solid and a fluid is applied. A dispersion equation, which describes propagation of harmonic waves in a hydroelastic system, is obtained. The dispersion curve for surface waves over a wide range of frequencies is constructed. The effects of finite initial deformations of the elastic half-space and of the thickness of the layer of a viscous compressible fluid on the phase velocities, attenuation coefficients, dispersion of the surface waves, and surface instability of a hydroelastic waveguide are analyzed. The numerical results are presented in the form of graphs, and their analysis is given.Secondary instability of the three-dimensional nonequilibrium compressible boundary layer.https://zbmath.org/1449.760302021-01-08T12:24:00+00:00"Zavershinskiĭ, I. P."https://zbmath.org/authors/?q=ai:zavershinskii.igor-petrovich"Knestyapin, V. N."https://zbmath.org/authors/?q=ai:knestyapin.v-nSummary: We research the stability of the non-linear spatial waves (secondary instability) which propagate in the compressible nonequilibrium supersonic boundary layer of the plain plate at an angle to the main flow. The increment of the growth of the secondary instability of motion is determined.Lie group analysis on Brownian motion and thermophoresis effect on free convective boundary-layer flow on a vertical cylinder embedded in a nanofluid-saturated porous medium.https://zbmath.org/1449.760392021-01-08T12:24:00+00:00"Ferdows, Mohammad"https://zbmath.org/authors/?q=ai:ferdows.mohammad"Hamad, Mohammed Abdul Ali"https://zbmath.org/authors/?q=ai:hamad.mohammed-abdul-ali"Ali, Mohamed"https://zbmath.org/authors/?q=ai:ali.mohamed-m|ali.mohamed-e|ali.mohamed-afsar|ali.mohamed-s-s|ali.mohamed-rSummary: Natural convective boundary-layer flow of a nanofluid on a heated vertical cylinder embedded in a nanofluid-saturated porous medium is studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. Lie groups analysis is used to get the similarity transformations, which transform the governing partial differential equations to a system of ordinary differential equations. Two groups of similarity transformations are obtained. Numerical solutions of the resulting ordinary differential systems are obtained and discussed for various values of the governing parameters.New numerical studies for Darcy's problem coupled with the heat equation.https://zbmath.org/1449.353492021-01-08T12:24:00+00:00"Dib, Dayana"https://zbmath.org/authors/?q=ai:dib.dayana"Dib, Séréna"https://zbmath.org/authors/?q=ai:dib.serena"Sayah, Toni"https://zbmath.org/authors/?q=ai:sayah.toniSummary: In this article, we consider the heat equation coupled with Darcy's law by a nonlinear viscosity depending on the temperature. We recall two numerical schemes and introduce a new non-stabilized one, we show the existence and uniqueness of the solutions and we establish an a priori error estimates using the Brezzi-Rappaz-Raviart theorem. Numerical investigations are preformed and showed.A new formulation for extrapolation of seismic wave field response and its derivatives.https://zbmath.org/1449.860042021-01-08T12:24:00+00:00"Moradpouri, Farzad"https://zbmath.org/authors/?q=ai:moradpouri.farzad"Moradzadeh, Ali"https://zbmath.org/authors/?q=ai:moradzadeh.ali"Pestana, Reynam Cruz"https://zbmath.org/authors/?q=ai:pestana.reynam-cruz"Monfared, Mehrdad Soleimani"https://zbmath.org/authors/?q=ai:monfared.mehrdad-soleimaniSummary: The aim of this study is to present a new symplectic integrator for the case of spatially varying velocity based on Leapfrog (L) and Rapid Expansion Methods (REM). First of all, approximation of the wave field at each time step has been considered using rapid expansion method. Then the wave equation is rewrite as Hamiltonian system. It can provide an accurate solution for the acoustic wave equation to simulate the wave field response at each time. After that, for much more accurate and stable solution to extrapolate the wave field and its derivative, a new formulation based on leapfrog and rapid expansion methods has been presented. The obtained results of simple model indicate that this new formulation provides a very high level of accuracy and stability for estimation of wave field response and its derivatives.Identification of piecewise constant Robin coefficient for the Stokes problem using the Levenberg-Marquardt method.https://zbmath.org/1449.653072021-01-08T12:24:00+00:00"Khayat, Faten"https://zbmath.org/authors/?q=ai:khayat.fatenSummary: In this work, we prove the quadratic convergence of the Levenberg-Marquardt method for the inverse problem of identifying a Robin coefficient for the Stokes system, where we suppose that this parameter is piecewise constant on some non-accessible part of the boundary and under the assumption that on this part, the velocity of a given reference solution stays far from zero.Theoretical understanding of unsteady flow separation for shear flow past three square cylinders in vee shape using structural bifurcation analysis.https://zbmath.org/1449.652982021-01-08T12:24:00+00:00"Kumar, Atendra"https://zbmath.org/authors/?q=ai:kumar.atendra"Ray, Rajendra K."https://zbmath.org/authors/?q=ai:ray.rajendra-kSummary: The unsteady flow separation of two-dimensional (2-D) incompressible shear flow past three identical square cylinders arranged in vee shape is studied in this paper, using theoretical structural bifurcation analysis based on topological equivalence. Through this analysis, the exact location and time of occurrence of bifurcation points (flow separation points) associated with secondary and tertiary vortices on all cylinders are studied. The existence of saddle points is also studied during primary flow separation. Different gap ratios between the downstream cylinders, \(s/d = 0.6-3.0\) (where \(s\) is the gap between cylinders, \(d\) is the length of cylinder side) with fixed gap \(2d\) between upstream and downstream cylinders for different shear parameter \((K)\) values ranging from \(K=0.0\) to 0.4 are considered at Reynolds number (Re) 100. In this process, the instantaneous vorticity contours and streakline patterns, center-line velocity fluctuation, phase diagram, lift and drag coefficients are studied to confirm the theoretical results. Computations are carried out by using higher order compact finite difference scheme. Present study mainly investigates the effect of \(K\) and gap ratio on unsteady flow separation and vortex-shedding phenomenon. All the computed results very efficiently and very accurately reproduce the complex flow phenomenon. Through this study, many noticeable and interesting results are reported for the first time for this problem.The 3D compressible Euler equations with damping in the general unbounded domain.https://zbmath.org/1449.353462021-01-08T12:24:00+00:00"Yang, Jiaqi"https://zbmath.org/authors/?q=ai:yang.jiaqi"Yuan, Meng"https://zbmath.org/authors/?q=ai:yuan.mengSummary: In this paper, the authors consider the 3D damped compressible Euler equations in the general unbounded domain with slip boundary condition. The authors obtain the global existence and uniqueness when the initial data are near the equilibrium. Meanwhile, they also investigate the decay rates of the system in the half space. The authors show that the classical solution decays in the \({L^2}\)-norm to the constant background state at the rate of \( (1+t)^{-\frac{3}{4}}\).An influence of the false bottom on the nonlinear dynamics of the water freezing process.https://zbmath.org/1449.860022021-01-08T12:24:00+00:00"Nizovtseva, Irina Gennad'evna"https://zbmath.org/authors/?q=ai:nizovtseva.irina-gennadevna"Alexandrov, Dmitriĭ Valer'evich"https://zbmath.org/authors/?q=ai:aleksandrov.dmitrii-valerevichSummary: The current paper casts the light on the processes of structural-phase transitions during the freezing salt water, including the false bottom effects. A nonlinear mathematical model of heat and mass transfer was obtained. It takes into account the presence of three moving boundaries of phase transition and turbulent fluid flows from the ocean side by the surface of the false bottom. The exact analytical solutions of the nonlinear model were obtained -- in their turn, they takes into account the time dependence of temperature and salinity at the depth and fluctuations of friction velocity. The distribution of temperature and salinity, the concentration of solids, the laws of motion of the boundaries of the phase transition, ``salt water -- the two-phase zone'', ``two-phase zone -- melted water'' and ``melt-water -- ice'' were found. The heat flux at the lower boundary of a false bottom was specified. The latter can change its direction at the time oscillations of the sea water temperature and friction velocity. Also it was shown, that structural transitions in the ice thickness are strictly associated with the processes of evolution of a false bottom.Element-free Galerkin method for confined steady flow of unhomogeneous problems.https://zbmath.org/1449.760342021-01-08T12:24:00+00:00"Zhou, Deliang"https://zbmath.org/authors/?q=ai:zhou.deliang"Li, Yue"https://zbmath.org/authors/?q=ai:li.yue"Wang, Zonghui"https://zbmath.org/authors/?q=ai:wang.zonghuiSummary: A coupling algorithm of element-free Galerkin (EFG) method and point collocation method is established to solve confined steady flow of unhomogeneous problems in groundwater, and transmissibility coefficient of aquifer is defined by slice constants. Based on the compatible conditions of head and flow rate, the equations at the nodes of different partition boundaries are established by using point collocation method. The EFG equations are established on the subregion of each partition without dividing lines. Coupled equations for numerical solution of head function are obtained simultaneously. The example results show that the method has a good calculation precision.On the influence of finite initial deformations on the wave process in the system consisting of an elastic half-space and a layer of a viscous compressible fluid.https://zbmath.org/1449.760222021-01-08T12:24:00+00:00"Bagno, A. M."https://zbmath.org/authors/?q=ai:bagno.a-mSummary: The problem of the propagation of acoustic waves in a previously deformed incompressible elastic half-space interacting with a layer of a viscous compressible fluid is considered. The study was carried out on the basis of three-dimensional linearized equations of the theory of elasticity of finite deformations for an incompressible elastic half-space and three-dimensional linearized Navier-Stokes equations for a layer of a viscous compressible fluid. The formulation of the problem and the approach based on the use of representations of general solutions of the linearized equations for an elastic body and fluid are used. A dispersion equation describing the propagation of harmonic waves in a hydroelastic system is obtained. Dispersion curves of surface waves are constructed in a wide frequency range. The effect of the finite initial deformations of the elastic half-space and the thickness of a layer of a viscous compressible fluid on the phase velocities, attenuation coefficients, and dispersion of surface waves in hydroelastic waveguides is analyzed. The numerical results are presented in the form of graphs, and their analysis is given.Optimal control problem for 3D micropolar fluid equations.https://zbmath.org/1449.490052021-01-08T12:24:00+00:00"Mallea-Zepeda, Exequiel"https://zbmath.org/authors/?q=ai:mallea-zepeda.exequiel"Medina, Luis"https://zbmath.org/authors/?q=ai:medina.luis-a|medina.luis-quintanar|medina.luis-carlosSummary: In this paper we study an optimal control problem related to strong solutions of 3D micropolar fluid equations. We deduce the existence of a global optimal solution with distributed control and, using a Lagrange multipliers theorem, we derive first-order optimality conditions for local optimal solutions.Structural stability on boundary reaction terms in a porous medium of Brinkman-Forchheimer type.https://zbmath.org/1449.350542021-01-08T12:24:00+00:00"Li, Yuanfei"https://zbmath.org/authors/?q=ai:li.yuanfei"Guo, Lianhong"https://zbmath.org/authors/?q=ai:guo.lianhongSummary: A saturated porous medium of Brinkman-Forchheimer type with an exothermic reaction occurring on the domain boundary is studied. The continuous dependence of the equation on the boundary reaction term and Soret coefficient is obtained by using energy estimation, differential inequality technique and the prior bounds of velocity, temperature and salt concentration.Modeling of temperature dependencies in the problem of hydrogen permeability.https://zbmath.org/1449.760542021-01-08T12:24:00+00:00"Bormatova, Elena Pavlovna"https://zbmath.org/authors/?q=ai:bormatova.elena-pavlovnaSummary: Processes of hydrogen transfer through the membrane with a presence of desorption are considered. The temperature dependencies of outlet flux and permeability factor, that are based on the relations between the rates of diffusion and surface processes, are modeled.The Riemann problem with delta initial data for Chaplygin nonsymmetric Keyfitz-Kranzer system with a source term.https://zbmath.org/1449.353382021-01-08T12:24:00+00:00"Song, Yun"https://zbmath.org/authors/?q=ai:song.yun"Guo, Lihui"https://zbmath.org/authors/?q=ai:guo.lihuiSummary: This paper is concerned with the Riemann problem with delta initial data for Chaplygin nonsymmetric Keyfitz-Kranzer system with a Coulomb-like friction term. It is interesting to see that the source term makes the Riemann solutions no longer self-similar. Delta contact discontinuities appear in some situations. Under generalized Rankine-Hugoniot conditions and entropy condition, we obtain the propagation speed, position and strength of delta shock wave. Furthermore, under delta initial data, stability of generalized solutions are obtained.Mathematical modeling of the undetachable filtration of a water suspension with changing the flow direction.https://zbmath.org/1449.760592021-01-08T12:24:00+00:00"Polyakov, V. L."https://zbmath.org/authors/?q=ai:polyakov.v-lSummary: A theoretical study of the clarifying effect at a rapid filter when changing the direction of the suspension flow in its medium during the filter run (descending to ascending or vice versa) is performed. As an instrument for research, mostly exact analytical methods have been used. In the technological process of filtration, two stages are conventionally distinguished - before and after changing the place of a suspension supply. The theoretical analysis is based on a mathematical model of undetachable nonlinear filtration. The composition and amount of a dispersed contamination in the initial suspension are stable, and the filter medium is initially clean (first stage) or already contains a large amount of a deposition mainly near the outlet (second stage). The suspension flow in the contaminated medium obeys the linear law with hydraulic conductivity, which is an empirical function of the concentration of deposited particles. The exact solution in implicit form of the corresponding mathematical problem is presented in relation to the first stage of filtration, which allows us to specify the physico-chemical picture in the medium layer as far as the beginning of the second stage. An arbitrary form of the functional filtration coefficient is allowed, which requires the use of numerical methods to solve this problem in the second stage. The initial system of ordinary differential equations in the canonical form and the procedure for calculating the most important filtration characteristics based on the data array thus obtained are presented. A special case of a linear form of the filtration coefficient is analyzed separately by strict analytical methods. In a number of examples with typical initial data, the derived calculation equations and dependencies are used to establish the effect due to a sharp change in the direction of the suspension flow during one filter run. It is shown that, in this way, the quality of the filtrate is deteriorated minimally. However, due to the active participation in the suspension clarification of the virtually entire volume of the filter medium, it is possible to achieve a more uniform distribution of the deposition in it and, as a result, a very significant reduction in head losses. Thus, based on the calculations of the technological time (the maximum permissible head losses are achieved), there is a real opportunity to extend the continuous operation time of rapid filters by 25 pct. or more. The nonlinear problem of transfer and deposition of ferric iron in the layer of a fast filter bed is formulated with regard for the oxidation of ferrous iron and definitely solved. The equations for the calculation of changes over time and over the height of the bed in the concentrations of suspended and deposited particles of iron hydroxide and the increase of a head loss in it are constructed. The forecast of the concentration of iron hydroxide in the filtrate and deposited form is done on examples. The possibility of a reliable substantiation of technological and constructive parameters based on the obtained solutions is shown.Analysis solution of lattice Boltzmann model for complex Ginzburg-Landau equation.https://zbmath.org/1449.354052021-01-08T12:24:00+00:00"Zhang, Jianying"https://zbmath.org/authors/?q=ai:zhang.jianying"Yan, Guangwu"https://zbmath.org/authors/?q=ai:yan.guangwu"Li, Ting"https://zbmath.org/authors/?q=ai:li.tingSummary: By using the method of Chapman analysis in the lattice Boltzmann model, we gave the general forms of a series of partial differential equations and Chapman polynomials. By solving the equilibrium distribution functions for complex Ginzburg-Landau equation, we gave the expressions of distribution functions on different time scales, and then obtained analysis solutions of the lattice Boltzmann for complex Ginzburg-Landau equation.Propagation of traveling wave solutions for nonlinear evolution equation through the implementation of the extended modified direct algebraic method.https://zbmath.org/1449.351482021-01-08T12:24:00+00:00"Yaro, David"https://zbmath.org/authors/?q=ai:yaro.david"Seadawy, Aly"https://zbmath.org/authors/?q=ai:seadawy.aly-r"Lu, Dian-chen"https://zbmath.org/authors/?q=ai:lu.dianchenSummary: In this work, different kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional (3-D) nonlinear evolution equations (NEEs) through the implementation of the modified extended direct algebraic method. Bright-singular and dark-singular combo solitons, Jacobi's elliptic functions, Weierstrass elliptic functions, constant wave solutions and so on are attained beside their existing conditions. Physical interpretation of the solutions to the 3-D modified KdV-Zakharov-Kuznetsov equation are also given.Convective layered flows of a vertically whirling viscous incompressible fluid. Velocity field investigation.https://zbmath.org/1449.760272021-01-08T12:24:00+00:00"Burmasheva, Natal'ya Vladimirovna"https://zbmath.org/authors/?q=ai:burmasheva.natalya-vladimirovna"Prosviryakov, Evgeniĭ Yur'evich"https://zbmath.org/authors/?q=ai:prosviryakov.evgenii-yurevichSummary: This article discusses the solvability of an overdetermined system of heat convection equations in the Boussinesq approximation. The Oberbeck-Boussinesq system of equations, supplemented by an incompressibility equation, is overdetermined. The number of equations exceeds the number of unknown functions, since non-uniform layered flows of a viscous incompressible fluid are studied (one of the components of the velocity vector is identically zero). The solvability of the non-linear system of Oberbeck-Boussinesq equations is investigated. The solvability of the overdetermined system of non-linear Oberbeck-Boussinesq equations in partial derivatives is studied by constructing several particular exact solutions. A new class of exact solutions for describing three-dimensional non-linear layered flows of a vertical swirling viscous incompressible fluid is presented. The vertical component of vorticity in a non-rotating fluid is generated by a non-uniform velocity field at the lower boundary of an infinite horizontal fluid layer. Convection in a viscous incompressible fluid is induced by linear heat sources. The main attention is paid to the study of the properties of the flow velocity field. The dependence of the structure of this field on the magnitude of vertical twist is investigated. It is shown that, with nonzero vertical twist, one of the components of the velocity vector allows stratification into five zones through the thickness of the layer under study (four stagnant points). The analysis of the velocity field has shown that the kinetic energy of the fluid can twice take the zero value through the layer thickness.On the influence of a layer of the ideal compressible fluid on the surface instability of the incompressible elastic halfspace exposed to finite initial deformations.https://zbmath.org/1449.760472021-01-08T12:24:00+00:00"Bagno, A. M."https://zbmath.org/authors/?q=ai:bagno.a-mSummary: The problem of propagation of normal waves in the predeformed incompressible elastic half-space that interacts with a layer of an ideal compressible fluid is considered. The study is based on the three-dimensional linearized equations of the theory of elasticity of finite deformations for the incompressible elastic half-space and the three-dimensional linearized Euler equations for a layer of the ideal compressible fluid. The problem formulation and the approach based on the utilization of representations of general solutions of the linearized equations for an elastic solid and the fluid are applied. A dispersion equation, which describes the propagation of harmonic waves in a hydroelastic system is obtained. The dispersion curve for a surface wave over a wide range of frequencies is constructed. The effect of finite initial deformations of the elastic half-space and the thickness of the layer of the ideal compressible fluid on the phase velocities, dispersion of surface waves, and surface instability of a hydroelastic waveguide is analyzed. The numerical results are presented in the form of graphs, and their analysis is given.3D dynamic Green's functions in a multilayered poroelastic half-space.https://zbmath.org/1449.760622021-01-08T12:24:00+00:00"Zheng, Pei"https://zbmath.org/authors/?q=ai:zheng.fei"Ding, Boyang"https://zbmath.org/authors/?q=ai:ding.boyang"Zhao, She-Xu"https://zbmath.org/authors/?q=ai:zhao.shexu"Ding, Ding"https://zbmath.org/authors/?q=ai:ding.dingSummary: The complete 3D dynamic Green's functions in the multilayered poroelastic media are presented in this study. A method of potentials in cylindrical coordinate system is applied first to decouple the Biot's wave equations into four scalar Helmholtz equations, and then, general solutions to 3D wave propagation problems are obtained. After that, a three vector base and the propagator matrix method are introduced to treat 3D wave propagation problems in the stratified poroelastic half-space disturbed by buried sources. It is known that the original propagator algorithm has the loss-of-precision problem when the waves become evanescent. At present, an orthogonalization procedure is inserted into the matrix propagation loop to avoid the numerical difficulty of the original propagator algorithm. At last, the validity of the present approach for accurate and efficient calculating 3D dynamic Green's functions of a multilayered poroelastic half-space is confirmed by comparing the numerical results with the known exact analytical solutions of a uniform poroelastic half-space.Dynamics of sedimentation of particle in a viscous fluid in the presence of two flat walls.https://zbmath.org/1449.760202021-01-08T12:24:00+00:00"Martynov, S. I."https://zbmath.org/authors/?q=ai:martynov.sergei-ivanovich"Pronkina, T. V."https://zbmath.org/authors/?q=ai:pronkina.t-v"Dvoryaninova, N. V."https://zbmath.org/authors/?q=ai:dvoryaninova.n-v"Karyagina, T. V."https://zbmath.org/authors/?q=ai:karyagina.t-vIn the paper the motion of a rigid spherical particle in a fluid in presence of two flat planes is explored. The angle between the planes may be arbitrary; it is supposed that the Stokes approximation is valid. The linearity of the governing equations allows to represent the particle's motion as the combination of its motion between two parallel and between two perpendicular planes. The planes themselves are modelled by a system of fictitous mirror-placed particles. To describe the pressure and velocity fields near the particles, multipole expansions are used. The sedimentation of the spherical particle in presence of two planes is examined as an example of the general theory built earlier in the paper.
Reviewer: Aleksey Syromyasov (Saransk)Analytical investigations of temperature effects on creep strain relaxation of biomaterials using homotopy perturbation and differential transform methods.https://zbmath.org/1449.800082021-01-08T12:24:00+00:00"Adeleye, Olurotimi"https://zbmath.org/authors/?q=ai:adeleye.olurotimi"Abdulkareem, Olakanla"https://zbmath.org/authors/?q=ai:abdulkareem.olakanla"Yinusa, Ahmed"https://zbmath.org/authors/?q=ai:yinusa.ahmed-a"Sobamowo, Gbeminiyi"https://zbmath.org/authors/?q=ai:sobamowo.gbeminiyi-mSummary: In this paper, the effect of temperature on relaxation of creep strain in biomaterials is modeled and analyzed with homotopy perturbation and differential transform methods. Polymeric biomaterials used as implants undergo both geometric and material nonlinear deformation when subjected to different loading conditions. The present study is concerned with the effects of temperature on the geometric nonlinear deformation of the relaxation of creep strain in these materials. Polymeric biomaterials exhibit time dependent response as observed in viscoelastic materials and this is represented by a one-dimensional rheological material model with constant material parameters. This model is then extended to capture the effects of temperature and the resulting final governing model is a nonlinear differential equation which cannot be easily solved by the standard analytic techniques. Here, two efficient special nonlinear analytic techniques, the homotopy perturbation and differential transform methods, are applied to obtain the solution of the developed nonlinear differential equation. The obtained analytical solutions are validated with the fourth-order Runge-Kutta numerical method. An error analysis shows that good agreement exists between the solutions obtained with these methods. The effects of some parameters on the model were investigated. As observed from the study, it can be shown that an increase in thermal conductivity and viscosity resulted in an increase in resistance to deformation of the material, while an increase in the material stiffness resulted in an increase in the rate of deformation and relaxation.An improved algorithm for fluid free surface simulation.https://zbmath.org/1449.760432021-01-08T12:24:00+00:00"Wang, Huanhuan"https://zbmath.org/authors/?q=ai:wang.huanhuan"Zhu, Xiaolin"https://zbmath.org/authors/?q=ai:zhu.xiaolin"Yin, Jingcun"https://zbmath.org/authors/?q=ai:yin.jingcunSummary: Simulation of fluid free surface based on smoothed particle hydrodynamics method requires generation of air particles near the fluid free surface to ensure simulation accuracy. The distribution of air particles generated by the traditional method is not uniform and smooth, which affects the simulation effect and has a large amount of calculation. In this paper, the traditional method of adding air particles to the free surface simulation of fluid in continuum surface force model is improved. Firstly, the bilayer air particles are generated dynamically on the normal direction of the free surface of the fluid, and then the tangential force is applied to the generated air particles, so that the air particles are uniformly distributed and therefore the simulation accuracy of the free surface of the fluid is improved. Since the simulated time step is very short and the position of the air particle changes very little under the unit time step, the air particles in the previous step can be considered as the air particles in the next step in a short period of time. Based on this consideration, an adaptive interval step method is proposed to regenerate air particles, which reduces the amount of calculation and improves the efficiency of simulation.Accurate solution for sliding Burger fluid flow.https://zbmath.org/1449.353592021-01-08T12:24:00+00:00"Zubair, Muhammad"https://zbmath.org/authors/?q=ai:zubair.muhammad"Hayat, Tasawar"https://zbmath.org/authors/?q=ai:hayat.tasawarSummary: This article addresses the influence of partial slip condition in the hydromagnetic flow of Burgers fluid in a rotating frame of reference. The flows are induced by oscillation of a boundary. Two problems for oscillatory flows are considered. Exact solutions to the resulting boundary value problems are constructed. Analysis has been carried out in the presence of magnetic field. Physical interpretation is made through the plots for various embedded parameters.Weak and strong convergence of solutions to linearized equations of low compressible fluid.https://zbmath.org/1449.351622021-01-08T12:24:00+00:00"Gusev, Nikolaĭ Anatol'evich"https://zbmath.org/authors/?q=ai:gusev.nikolai-anatolevichSummary: Initial-boundary value problem for linearized equations of viscous barotropic low compressible fluid in a bounded domain is considered. Convergence of solutions of this problem at withincompressible limit approaching to zero is studied. Sufficient conditions for the weak and strong convergence of this problem for uncompressible liquid are given.Evaporation of unstable polymer jet in electrospinning.https://zbmath.org/1449.760682021-01-08T12:24:00+00:00"Sal'kovskiĭ, Yuriĭ Evgen'evich"https://zbmath.org/authors/?q=ai:salkovskii.yurii-evgenevichSummary: This study is focused on mathematical modeling of drying unstable polymer electrospun jet. The developed model includes nonuniformity of polymer concentration over the jet cross-section due to the evaporation. The parametric study for influence of mass transfer coefficient on jet motion and fiber deposition is performed.Computing of throwing ability of the explosives at cylindric front tossing of metal.https://zbmath.org/1449.760442021-01-08T12:24:00+00:00"Reut, Igor' Igorevich"https://zbmath.org/authors/?q=ai:reut.igor-igorevich"Krivchenko, Aleksandr L'vovich"https://zbmath.org/authors/?q=ai:krivchenko.aleksandr-lvovichSummary: Calculation methods of copper plate relative front tossing speed by equivalent mass method and the widening speed calculation methods for the copper cylindric confinement are offered. The calculation results were compared with experimental data. The mean-square deviation is less than 3,5 percent.Serrin-type blowup criterion of three-dimensional nonhomogeneous heat conducting magnetohydrodynamic flows with vacuum.https://zbmath.org/1449.353582021-01-08T12:24:00+00:00"Zhou, Ling"https://zbmath.org/authors/?q=ai:zhou.lingSummary: We consider an initial boundary value problem for the nonhomogeneous heat conducting magnetohydrodynamic flows. We show that for the initial density allowing vacuum, the strong solution exists globally if the velocity field satisfies Serrin's condition. Our method relies upon the delicate energy estimates and regularity properties of Stokes system and elliptic equations.The generalized Riemann problem for chromatography equations with delta shock wave.https://zbmath.org/1449.353372021-01-08T12:24:00+00:00"Pan, Lijun"https://zbmath.org/authors/?q=ai:pan.lijun"Han, Xinli"https://zbmath.org/authors/?q=ai:han.xinli"Li, Tong"https://zbmath.org/authors/?q=ai:li.tongSummary: This paper is concerned with the generalized Riemann problem for the nonlinear chromatography equations, where the delta shock wave occurs in the corresponding Riemann solution. It is quite different from the previous generalized Riemann problems which focus on classical elementary waves. We constructively solve the generalized Riemann problem in a neighborhood of the origin on the \(x-t\) plane. In solutions, we find that the generalized Riemann solutions have a structure similar to the solution of the corresponding Riemann problem for most of cases. However, a delta shock wave in the corresponding Riemann solution may turn into a shock wave followed by a contact discontinuity, which provides us with a detailed method for analyzing the internal mechanism of a delta shock wave.Numerical method for MHD flows of fractional viscous equation.https://zbmath.org/1449.652112021-01-08T12:24:00+00:00"Zhang, Jun"https://zbmath.org/authors/?q=ai:zhang.jun.1|zhang.jun|zhang.jun.7|zhang.jun.5|zhang.jun.3|zhang.jun.9|zhang.jun.2|zhang.jun.6|zhang.jun.10Summary: In this paper, the numerical approximation of fractional viscosity MHD equation is discussed. We present an efficient numerical scheme for solving this equation and analyze its stability and error estimates. We prove that the scheme is unconditionally stable and the convergence order of the scheme is \(2 - \beta\) in time and spectral accuracy in space. Finally, numerical examples are given to verify the theoretical results.Ultrasonic researches of acoustic relaxation in propyl acetate.https://zbmath.org/1449.820052021-01-08T12:24:00+00:00"Kononenko, V. S."https://zbmath.org/authors/?q=ai:kononenko.v-s"Savichev, V. V."https://zbmath.org/authors/?q=ai:savichev.v-v"Tiranin, V. E."https://zbmath.org/authors/?q=ai:tiranin.v-eSummary: For the first time dependences \(\alpha/f^2\) are obtained on the frequency of ultrasound in wide temperature and frequency ranges, where \(\alpha \)-absorption of ultrasound propyl acetate allows to calculate relaxation and thermodynamic parameters of the acoustic relaxation caused by internal rotation of groups in molecules under the influence of a ultrasonic wave.Numerical study of the stability of breakwater built on a sloped porous seabed under tsunami loading.https://zbmath.org/1449.860032021-01-08T12:24:00+00:00"Jianhong, Ye"https://zbmath.org/authors/?q=ai:jianhong.ye"Dongsheng, Jeng"https://zbmath.org/authors/?q=ai:dongsheng.jeng"Ren, Wang"https://zbmath.org/authors/?q=ai:ren.wang"Changqi, Zhu"https://zbmath.org/authors/?q=ai:changqi.zhuSummary: Strong earthquake induced huge tsunami has occurred for three times in Pacific ocean in recent ten years; for example, the tsunami triggered by the Sumatra earthquake in 2004, Chile earthquake in 2010 and Tohoku earthquake (Japan) in 2011. Tsunami carrying huge energy always would bring high risks to the population living near to coastline. Breakwater is widely used to dissipate the wave energy, and protect coastline and ports. However, they are vulnerable when being attacked by tsunami wave. At present, the interaction mechanism between tsunami, breakwater and its seabed foundation is not fully understood. In this study, the dynamics and stability of a breakwater under the attacking of tsunami wave is investigated by adopting an integrated model PORO-WSSI 2D, in which the VARANS equation for wave motion, and the Biot's dynamic equation for soil are used. Based on the numerical results, it is found that offshore breakwater interacts intensively with tsunami wave when it overtopping and overflowing over a breakwater. The impact force on the lateral side of breakwater applied by tsunami wave is huge. The shear failure is likely to occur in the seabed foundation of breakwater. The liquefaction is unlikely to occur due to the fact that there is basically no upward seepage force in seabed foundation in the process of tsunami wave passing through the breakwater.Modelling the impact of dam failure scenarios on flood inundation using SPH.https://zbmath.org/1449.760112021-01-08T12:24:00+00:00"Prakash, Mahesh"https://zbmath.org/authors/?q=ai:prakash.mahesh"Rothauge, Kai"https://zbmath.org/authors/?q=ai:rothauge.kai"Cleary, Paul W."https://zbmath.org/authors/?q=ai:cleary.paul-wSummary: Flooding resulting from collapse of a dam is a highly destructive event. It is important to accurately predict the flow behaviour so that potential mitigation strategies can be investigated for disaster management planning. The meshless SPH method has previously been able to model this class of extreme flow events. In this paper, we extend the method to include modelling of dam wall fragments. Collisions between dam wall fragments, between fragments and terrain and full two-way coupling between fragments and the free surface water flow is included. This gives a method that can specifically investigate the impact of the dam wall failure scenario on the subsequent inundation. The historical St. Francis dam failure is used to demonstrate the impact of including the dam fragments. It also provides a means of quantitatively investigating their effect in terms of arrival time and water height at a downstream power station. The scenario with multiple independently timed failures of different parts of the wall (which closely matches the historical failure) gives excellent agreement with the observed data and gives the best match of all failure scenarios. Traditionally such modelling is performed by solving the two dimensional shallow water equations which is not able to capture the three dimensional nature of the flow in earlier stages of dam flooding. We specifically investigate the three dimensional nature of flow structures and formation of multiple downstream hydraulic jumps. These strongly influence water height and therefore control the extent of flooding of tributary valleys.Regularity criteria for the NS and MHD equations in terms of horizontal components.https://zbmath.org/1449.351392021-01-08T12:24:00+00:00"Zhang, Hui"https://zbmath.org/authors/?q=ai:zhang.hui.9|zhang.hui.7|zhang.hui.3|zhang.hui.5|zhang.hui|zhang.hui.2|zhang.hui.6|zhang.hui.8|zhang.hui.1|zhang.hui.11|zhang.hui.10|zhang.hui.4"Xu, Juan"https://zbmath.org/authors/?q=ai:xu.juan.1|xu.juanSummary: In this paper, we consider the regularity of weak solutions to the incompressible Navier-Stokes (NS) equations and MHD equations in the Triebel-Lizorkin space and multiplier space respectively. By using Littlewood-Paley decomposition and energy estimate methods, we proved that if horizontal velocity \(\tilde u = ({u_1}, {u_2}, 0)\) satisfies \[{\nabla_h}\tilde u \in {L^p} (0,T;\dot F_{q, \frac{{2q}}{3}}^0 (\mathbb{R}^3)),\;\;\; \frac{2}{p} + \frac{3}{q} = 0,\;\;\; \frac{3}{2} < q \le \infty,\] then the weak solution is actually the unique strong solution on \([0,T)\). For MHD equations, we prove that if horizontal velocity and magnetic field satisfy \[ (\tilde u, \tilde b) \in L^{\frac{2}{1-r}} (0,T;{\dot X}_r), r \in [0,1),\] or horizontal gradient satisfies \[ ({\nabla_h}\tilde u, {\nabla_h}\tilde b) \in L^{\frac{2}{2-r}} (0, T;{\dot X}_r), r \in [0,1),\] then the weak solution is actually unique strong solution on \([0,T)\).Global regularity for 3D generalized Oldroyd-B type models with fractional dissipation.https://zbmath.org/1449.351402021-01-08T12:24:00+00:00"Zhang, Qiuyue"https://zbmath.org/authors/?q=ai:zhang.qiuyueSummary: In this paper, we consider the 3D generalized Oldroyd-B type models with fractional Laplacian dissipation \( (-\Delta)^{\eta_1}u\) and \( (-\Delta)^{\eta_2}\tau\) in the corotational case. By using energy method, for \({\eta_1} \ge \frac{5}{4}\) and \({\eta_2} \ge \frac{5}{4}\), we obtain the global regularity of classical solutions when the initial data (\({u_0}, {\tau_0}\)) are sufficiently smooth.A lattice Boltzmann model for Maxwell's equations.https://zbmath.org/1449.760382021-01-08T12:24:00+00:00"Liu, Yanhong"https://zbmath.org/authors/?q=ai:liu.yanhong-a"Yan, Guangwu"https://zbmath.org/authors/?q=ai:yan.guangwuSummary: In this paper, a lattice Boltzmann model for the Maxwell's equations is proposed by taking separate sets of distribution functions for the electric and magnetic fields, and a lattice Boltzmann model for the Maxwell vorticity equations with third order truncation error is proposed by using the higher-order moment method. At the same time, the expressions of the equilibrium distribution function and the stability conditions for this model are given. As numerical examples, some classical electromagnetic phenomena, such as the electric and magnetic fields around a line current source, the electric field and equipotential lines around an electrostatic dipole, the electric and magnetic fields around oscillating dipoles are given. These numerical results agree well with classical ones.Weak solutions for the systems of multifluid flows.https://zbmath.org/1449.351672021-01-08T12:24:00+00:00"Liu, Shujun"https://zbmath.org/authors/?q=ai:liu.shujunSummary: In this paper, we study the weak solutions for the systems of multifluid flows, which include the system of isentropic gas dynamics in Eulerian coordinates and a system arising from river flows. There are more linearly degenerate fields compared with single-component system, and singularities in these linearly degenerate fields emerge when considering the corresponding vanishing viscosity system. we obtain the existence of global solutions for the system of multifluid flows by analyzing the uniform BV estimates in linearly degenerate fields, coupled with the compensated compactness method and the vanishing viscosity method.Estimates in Morrey-Campanato spaces of a suitable weak solution of the Navier-Stokes equations, satifying an extra-condition.https://zbmath.org/1449.760162021-01-08T12:24:00+00:00"Mauro, Jmmy Alfonso"https://zbmath.org/authors/?q=ai:mauro.jmmy-alfonsoIn this paper the non-stationary Navier-Stokes equations with unit viscosity and zero body force are studied. The regularity of suitable weak solutions of the Cauchy problem satisfying a suitable extra-condition is investigated. To do this the author applies the theory of Morrey-Campanato spaces and obtains suitable estimates.
Reviewer: Angela Slavova (Sofia)Mathematical modelling of processes occurring in power cylinders of hydraulic press during its decompression.https://zbmath.org/1449.932082021-01-08T12:24:00+00:00"Korchak, Elena Sergeevna"https://zbmath.org/authors/?q=ai:korchak.elena-sergeevnaSummary: The main ways of decompression used in modern control systems and mathematical modelling of processes occurring in power cylinders under hydraulic press during its decompression are considered. Mechanism of fluid column oscillations in power cylinders is described. Oscillating effects in power cylinders while decompression is analyzed, its mathematical description is given. By means of numerical analysis on the basis of hydraulic forging press with active force of 60 MN peculiarities of typical process of power cylinders decompression are shown. Practical recommendations concerning different decompressing valves using and its influence on maintenance properties of presses are given.Convergence analysis of the lowest nonconforming mixed finite element for nonlinear Sobolev-Galpern type equations of moisture migration.https://zbmath.org/1449.653302021-01-08T12:24:00+00:00"Zhang, Houchao"https://zbmath.org/authors/?q=ai:zhang.houchao"Wang, An"https://zbmath.org/authors/?q=ai:wang.anSummary: Based on the nonconforming linear triangular finite element, the lowest nonconforming mixed finite element approximate scheme is established for nonlinear Sobolev-Galpern type equations of moisture migration. The existence and uniqueness of approximation solution are proved. At the same time, without the conventional Ritz projection, the optimal error estimates of exact solution \(u\) in \({H^1}\)-norm and intermediate variable \(\boldsymbol{P} = - (a (u)\nabla {u_t} + b (u)\nabla u)\) in \({L^2}\)-norm are deduced by some special properties of the elements.Pressure distribution in a porous squeeze film bearing lubricated by a Vočadlo fluid.https://zbmath.org/1449.760032021-01-08T12:24:00+00:00"Walicka, A."https://zbmath.org/authors/?q=ai:walicka.anna"Jurczak, P."https://zbmath.org/authors/?q=ai:jurczak.pSummary: The influence of a wall porosity on the pressure distribution in a curvilinear squeeze film bearing lubricated by a lubricant being a viscoplastic fluid of a Vočadlo type is considered.
After general considerations on the flow of viscoplastic fluid (lubricant) in a bearing clearance and in a porous layer a modified Reynolds equation for the curvilinear squeeze film bearing with a Vočadlo lubricant is given. The solution of this equation is obtained by a method of successive approximation. As a result one obtains a formula expressing the pressure distribution. The example of squeeze film in an axial bearing (modeled by two parallel disks) is discussed in detail.Tear film dynamics with evaporation, osmolarity and surfactant transport.https://zbmath.org/1449.920092021-01-08T12:24:00+00:00"Siddique, J. I."https://zbmath.org/authors/?q=ai:siddique.javed-i"Braun, R. J."https://zbmath.org/authors/?q=ai:braun.richard-jSummary: In this article we develop a model for the evaporation and rupture of the tear film. The tear film is generally considered a multi-layer structure which we simplify to a single layer in our modeling. We examine how well the floating lipid layer can be approximated by a mobile insoluble surfactant monolayer in the context of lubrication theory with film rupture ``breakup'' in the tear film literature. This model includes the effects of surface tension, insoluble surfactant monolayer transport, solutal Marangoni effects, evaporation, osmolarity transport, osmosis and wettability of corneal surface. Evaporation is hypothesized to be dependent on pressure, temperature and surface concentration at the surface of the film. A focus of this paper is to study the competition between the effect of increasing surfactant concentration to (1) slowing down evaporation and (2) lowering surface tension. The solutal Marangoni effect, for local increases in surfactant concentration, can induce local thinning and this effect always seems to dominate the reduction in thinning rate due to evaporation in our model. It also seems to eliminate any localized area of increased evaporation due to reduced surfactant concentration. Osmolarity in the tear film increases because water lost to the average evaporation rate and to a lesser extent by flow inside the film. The presence of van der Waals conjoining pressure is only significant when osmosis is very small or absent. The model predicts that the Marangoni effect coupled with evaporation can determine the location of first breakup; it also agrees with another model of breakup that predicts elevated osmolarity when breakup occurs.Complex evolution of a multi-particle system.https://zbmath.org/1449.370072021-01-08T12:24:00+00:00"Machado, J. A. Tenreiro"https://zbmath.org/authors/?q=ai:machado.jose-antonio-tenreiroSummary: This paper studies a discrete dynamical system of interacting particles that evolve by interacting among them. The computational model is an abstraction of the natural world, and real systems can range from the huge cosmological scale down to the scale of biological cell, or even molecules. Different conditions for the system evolution are tested. The emerging patterns are analysed by means of fractal dimension and entropy measures. It is observed that the population of particles evolves towards geometrical objects with a fractal nature. Moreover, the time signature of the entropy can be interpreted at the light of complex dynamical systems.On a homogenous thermoconvection model of the non-compressible viscoelastic Kelvin-Voight fluid of the non-zero order.https://zbmath.org/1449.354572021-01-08T12:24:00+00:00"Sukacheva, Tamara Gennad'evich"https://zbmath.org/authors/?q=ai:sukacheva.tamara-gennadevich"Matveeva, Ol'ga Pavlovna"https://zbmath.org/authors/?q=ai:matveeva.olga-pavlovnaSummary: The homogeneous thermoconvection problem of the non-compressible viscoelastic Kelvin-Voight fluid of the non-zero order is considered. The conducted research is based on the results of the semilinear Sobolev type equations theory, because the first initial value problem for the corresponding system of the differential equations in private derivatives is reduced to the abstract Cauchy problem for the specified equation. The concepts of the \(p\)-sectorial operator and the resolving semigroup of operators of the Cauchy problem for the corresponding linear homogeneous Sobolev type equation are used. The existence and uniqueness theorem of the solution which is a quasi-stationary semi-trajectory is proved. The complete description of the phase space is obtained.Incipient sediment transport for non-cohesive landforms by the discrete element method (DEM).https://zbmath.org/1449.760322021-01-08T12:24:00+00:00"Bravo, R."https://zbmath.org/authors/?q=ai:bravo.raquel-s-f|bravo.rafael"Ortiz, P."https://zbmath.org/authors/?q=ai:ortiz.paloma|ortiz.patricio-f|ortiz.pablo|ortiz.philip"Pérez-Aparicio, J. L."https://zbmath.org/authors/?q=ai:perez-aparicio.jose-lSummary: We introduce a numerical method for incipient sediment transport past bedforms. The approach is based on the discrete element method (DEM) [the third and the first author, ``Discrete elements'', in: Practical applications using computational contact mechanics Vol. 2 (2006)], simulating the micro-mechanics of the landform as an aggregate of rigid spheres interacting by contact and friction. A continuous finite element approximation [the second author et al., Int. J. Numer. Methods Eng. 66, No. 10, 1569--1586 (2006; Zbl 1110.76318)] predicts the boundary shear stress field due to the fluid flow, resulting in drag and lift forces acting over the particles. Numerical experiments verify the method by reproducing results by \textit{A. Shields} [Application of similarity principles and turbulence research to bed-load movement. Techn. Rep., California Institute of Technology (1936)] and other authors for the initiation of motion of a single grain. A series of experiments for sediments with varying compacity and constituting piles yields enhanced relationships between threshold shear stress and friction Reynolds number, to define incipient sediment transport criterion for flows over small-scale bed morphologies.A note on three-dimensional axisymmetric flow.https://zbmath.org/1449.760212021-01-08T12:24:00+00:00"Shu, Xiaozhen"https://zbmath.org/authors/?q=ai:shu.xiaozhen"Hu, Chunhua"https://zbmath.org/authors/?q=ai:hu.chunhua"Wang, Chengqiang"https://zbmath.org/authors/?q=ai:wang.chengqiangSummary: The fourth-order differential equation describing the three dimensional axisymmetric flow can be converted to an equivalent integral equation. Utilizing some special analytic techniques, an equivalent integral equation related to the fourth-order nonlinear differential equation is obtained. An exact solution is given and the properties of the solution are obtained.Mathematical model of copper corrosion.https://zbmath.org/1449.741652021-01-08T12:24:00+00:00"Clarelli, F."https://zbmath.org/authors/?q=ai:clarelli.fabrizio"De Filippo, B."https://zbmath.org/authors/?q=ai:de-filippo.b"Natalini, R."https://zbmath.org/authors/?q=ai:natalini.robertoSummary: A new partial differential model for monitoring and detecting copper corrosion products (mainly brochantite and cuprite) is proposed to provide predictive tools suitable for describing the evolution of damage induced on bronze specimens by sulfur dioxide (\(\mathrm{SO}_{2}\)) pollution. This model is characterized by the movement of a double free boundary. Numerical simulations show a nice agreement with experimental result.Non-stationary crystallization of water with a mushy layer in the turbulent and non-turbulent boundary conditions.https://zbmath.org/1449.800182021-01-08T12:24:00+00:00"Nizovtseva, Irina Gennad'evna"https://zbmath.org/authors/?q=ai:nizovtseva.irina-gennadevna"Aleksandrov, Dmitriĭ Valer'evich"https://zbmath.org/authors/?q=ai:aleksandrov.dmitrii-valerevichSummary: In the present work, we develop a mathematical model of the solidification processes from a cooling by arbitrary law boundaries in the presence of mushy layer for non-isothermal solution (sea water), both in the absence and presence of turbulence in the liquid at the boundary between the mushy layer and liquid phase of the system. The distribution of temperature, impurity concentration and the solid phase fraction in all regions of the process, and also the law of motion of the solid phase-mushy layer boundary are found. We consider two scenarios of the process: with no solid phase (which describes the solidification with some needle-shaped crystals) and with some portion of the solid phase (which describes the solidification of a blunt-end crystals) at the boundary of mushy layer and liquid. The results of the developed theory are in good agreement with observations.On the global well-posedness of 3-D Navier-Stokes equations with vanishing horizontal viscosity.https://zbmath.org/1449.353472021-01-08T12:24:00+00:00"Abidi, Hammadi"https://zbmath.org/authors/?q=ai:abidi.hammadi"Paicu, Marius"https://zbmath.org/authors/?q=ai:paicu.mariusSummary: We study, in this paper, the axisymmetric 3-D Navier-Stokes system where the horizontal viscosity is zero. We prove the existence of a unique global solution to the system with initial data in Lebesgue spaces.Volumetric flow rate reconstruction in great vessels.https://zbmath.org/1449.920132021-01-08T12:24:00+00:00"Lovas, Attila"https://zbmath.org/authors/?q=ai:lovas.attila"Nagy, Róbert"https://zbmath.org/authors/?q=ai:nagy.robert"Sótonyi, Péter"https://zbmath.org/authors/?q=ai:sotonyi.peter"Szilágyi, Brigitta"https://zbmath.org/authors/?q=ai:szilagyi.brigittaSummary: We present a new algorithm to reconstruct the volumetric flux in the aorta. We study a simple 1D blood flow model without viscosity term and sophisticated material model. Using the continuity law, we could reduce the original inverse problem related to a system of PDEs to a parameter identification problem involving a Riccati-type ODE with periodic coefficients. We implemented a block-based optimization algorithm to recover the model parameters. We tested our method on real data obtained using CG-gated CT angiography imaging of the aorta. Local flow rate was calculated in 10cm long aorta segments which are located 1cm below the heart. The reconstructed volumetric flux shows a realistic wave-like behavior, where reflections from arteria iliaca can also be observed. Our approach is suitable for estimating the main characteristics of pulsatile flow in the aorta and thereby contributing to a more accurate description of several cardiovascular lesions.Global regularity of the 3D generalized MHD equations with only velocity dissipation.https://zbmath.org/1449.760142021-01-08T12:24:00+00:00"Cai, Xiaojing"https://zbmath.org/authors/?q=ai:cai.xiaojing"Liu, Bingyu"https://zbmath.org/authors/?q=ai:liu.bingyuSummary: In this paper, we consider the global regularity of the three-dimensional (3D) generalized magnetohydrodynamic (MHD) equations with only velocity dissipation in terms of fractional Laplacians. By the Galerkin approximation methods, the compactness and the energy method, we give a refined proof of the correlation theorem and prove the global existence and uniqueness of the strong solutions for any \(\alpha \ge 5/2\).Lie symmetry analysis for the space-time fractional porous medium equations.https://zbmath.org/1449.350172021-01-08T12:24:00+00:00"Yang, Ying"https://zbmath.org/authors/?q=ai:yang.ying"Wang, Lizhen"https://zbmath.org/authors/?q=ai:wang.lizhenSummary: In this paper, we study the space-time fractional porous medium equation, the space-time fractional porous medium equation with a nonlinear convection term, the space-time fractional dual porous medium equation using Lie symmetry analysis. The corresponding symmetry groups of these three types of porous medium equations are obtained. Based on the above results we perform the similarity reduction and obtain the group-invariant solutions to these equations.Global dissipative solutions of the Dullin-Gottwald-Holm equation with a forcing.https://zbmath.org/1449.352852021-01-08T12:24:00+00:00"Li, Bin"https://zbmath.org/authors/?q=ai:li.bin.1|li.bin"Zhu, Shihui"https://zbmath.org/authors/?q=ai:zhu.shihuiSummary: Based on the new characteristic method, by exploiting the balance law and some estimates, we prove the existence of global dissipative solutions for the Dullin-Gottwald-Holm equation with a forcing term in \({H^1} (\mathbb{R})\).Asymptotic stability of self-similar solutions for dissipative systems modeling electrohydrodynamics.https://zbmath.org/1449.353572021-01-08T12:24:00+00:00"Zhao, Jihong"https://zbmath.org/authors/?q=ai:zhao.jihong"Li, Xiurong"https://zbmath.org/authors/?q=ai:li.xiurongSummary: The authors consider a dissipative system of nonlinear and nonlocal equations modeling the flow of electrohydrodynamics in the whole space \({\mathbb{R}^n}\), \(n \ge 3\). By making use of the generalized \({L^p}\)-\({L^q}\) heat semigroup estimates in the Lorentz spaces and the generalized Hardy-Littlewood-Sobolev inequality, the authors first prove the global existence and uniqueness of the self-similar solutions in the Lorentz spaces, then establish the asymptotic stability of the self-similar solutions as time goes to infinity. Since the authors cope with the initial data in the Lorentz spaces, the global existence and asymptotic stability of the self-similar solutions corresponding to the initial data are small homogeneous functions.A robust hybrid Roe Riemann solver.https://zbmath.org/1449.760402021-01-08T12:24:00+00:00"Hu, Lijun"https://zbmath.org/authors/?q=ai:hu.lijun"Yuan, Li"https://zbmath.org/authors/?q=ai:yuan.li"Zhai, Jian"https://zbmath.org/authors/?q=ai:zhai.jianSummary: Numerical shock instabilities will occur near strong shock waves when using Roe scheme to compute multidimensional flow problems. The HLLEC scheme with shear viscosity can not only resolve contact discontinuities, but also show good stability in numerical computation. We combine the Roe scheme and the HLLEC scheme to eliminate the numerical shock instabilities. In the vicinity of strong shock waves, the switching function is defined by the angle between the normal directions of the shock front and the cell interface, so that the numerical flux is switched to the HLLEC scheme in the transverse direction of the shock front. In other places, numerical flux is still evaluated by the Roe scheme. Numerical experiments show that the hybrid scheme proposed here can not only eliminate the shock instabilities of Roe scheme, but also reduce the shear dissipation brought by the HLLEC scheme to the greatest extent, preserving the advantage of high resolution of Roe scheme.A unified boundary condition based on the halfway bounce-back scheme in lattice Boltzmann method.https://zbmath.org/1449.760372021-01-08T12:24:00+00:00"Ling, Fengru"https://zbmath.org/authors/?q=ai:ling.fengru"Zhang, Chaoying"https://zbmath.org/authors/?q=ai:zhang.chaoying"Chen, Yanyan"https://zbmath.org/authors/?q=ai:chen.yanyan"Qin, Zhangrong"https://zbmath.org/authors/?q=ai:qin.zhangrongSummary: The lattice Boltzmann method can effectively simulate the fluid flow in complex flow fields. However, the reliability of the simulation results strongly depends on the selected boundary treatment methods. Based on the halfway bounce-back scheme, a unified treatment for the curved wall is proposed by improving the curved boundary condition scheme of interpolation. Results from tests are in good agreement with the exact solutions. Compared with several curved boundary condition schemes commonly used in lattice Boltzmann simulation, this method exhibits high accuracy and numerical stability of the complex boundary. The novel method provides a reliable way to solve the common problem of mass leakage in the curved boundary condition, satisfying the mass conservation constraint.On the regularity criteria for 3-D liquid crystal flows in terms of the horizontal derivative components of the pressure.https://zbmath.org/1449.351412021-01-08T12:24:00+00:00"Zhao, Lingling"https://zbmath.org/authors/?q=ai:zhao.lingling"Li, Fengquan"https://zbmath.org/authors/?q=ai:li.fengquanSummary: This paper is devoted to investigating regularity criteria for the 3-D nematic liquid crystal flows in terms of horizontal derivative components of the pressure and gradient of the orientation field. More precisely, we mainly proved that the strong solution \( (u, d)\) can be extended beyond \(T\), provided that the horizontal derivative components of the pressure \({\nabla_h}P = ({\partial_{x_1}}P, {\partial_{x_2}}P)\) and gradient of the orientation field satisfy \[{\nabla_h}P \in {L^s} (0, T; {L^q} (\mathbb{R}^3)),\; \frac{2}{s} + \frac{3}{q} \le \frac{5}{2},\; \frac{18}{13} \le q \le 6\] and \[\nabla d \in {L^\beta} (0, T; {L^\gamma} (\mathbb{R}^3)),\; \frac{2}{\gamma} + \frac{3}{\beta} \le \frac{3}{4},\; \frac{36}{7} \le \beta \le 12.\]A new moving mesh method for solving the two-dimensional Navier-Stokes equation.https://zbmath.org/1449.653412021-01-08T12:24:00+00:00"Duan, Xianbao"https://zbmath.org/authors/?q=ai:duan.xianbao"Cao, Qinqin"https://zbmath.org/authors/?q=ai:cao.qinqin"Tan, Hongxia"https://zbmath.org/authors/?q=ai:tan.hongxiaSummary: In order to reduce the computational cost of solving partial differential equation (PDE), whose solution has strong singularity or drastic change in a small local area, a moving mesh method based on equation solution is proposed and applied to solve the two-dimensional incompressible Navier-Stokes equations. Different from the most existing moving mesh methods, the moving distance of the nodes is obtained by solving a variable-coefficient diffusion equation, which avoids regional mapping and does not need to smooth the monitoring function, so the algorithm is easier to program and implement. Numerical examples show that the proposed algorithm can refine the mesh in the position where the gradient of the solution changes drastically, which can save a lot of computation time on the premise of improving the resolution of the numerical solution. Due to the typicality of the Navier-Stokes equations, the proposed algorithm can be generalized to solve many similar partial differential equations numerically.A finite element variational multiscale method based on Crank-Nicolson scheme for the unsteady Navier-Stokes equations.https://zbmath.org/1449.652642021-01-08T12:24:00+00:00"Xue, Jufeng"https://zbmath.org/authors/?q=ai:xue.jufeng"Shang, Yueqiang"https://zbmath.org/authors/?q=ai:shang.yueqiangSummary: The incompressible viscous flows are fluid movements that do not change in density. They are used to describe many important physical phenomena such as weather, ocean currents, flow around airfoil, and blood flow within the arteries. The Navier-Stokes equations are the basic equations for incompressible viscous flows. Therefore, the numerical method for solving Navier-Stokes equations has been paid more and more attention in recent decades. In this paper, we mainly study a two-level fully discrete finite element variational multiscale method based on Crank-Nicolson scheme for the unsteady Navier-Stokes equations. The method is carried out in two steps. A stabilized nonlinear Navier-Stokes system is solved on a coarse grid at the first step, and the second step is that a stabilized linear problem is solved on a fine grid to correct the coarse grid solution. Error estimate of the velocity which is derived via the two-level finite element variational multiscale method is of second-order in time. Numerical experiments show that the method of this paper can save a lot of computation time compared with the finite element variational method which uses a one-level grid directly on the fine grid in the case of coarse grid matching.An efficient two-level method for solving incompressible Navier-Stokes equations.https://zbmath.org/1449.652882021-01-08T12:24:00+00:00"Du, Binbin"https://zbmath.org/authors/?q=ai:du.binbin"Huang, Jianguo"https://zbmath.org/authors/?q=ai:huang.jianguoSummary: This paper proposes a two-level Arrow-Hurwicz (A-H) method (simply called the \(m\)-A-H-1-Oseen method) for solving incompressible Navier-Stokes (N-S)equations. The incompressible N-S equations are first solved by the A-H method to obtain a numerical solution on a coarse mesh. Next, the desired numerical solution is obtained by solving the Oseen scheme, which is derived on a fine mesh by linearizing the original equations using the coarse solution, leading to the required two-level method. The convergence analysis is developed systematically.Integrated geological and hydrodynamic modeling in the management system of oil and gas production.https://zbmath.org/1449.760602021-01-08T12:24:00+00:00"Popkov, V. I."https://zbmath.org/authors/?q=ai:popkov.v-i.1"Shakshin, V. P."https://zbmath.org/authors/?q=ai:shakshin.v-pSummary: The most important research results based on innovational solutions in the oil and gas industry for hydrodynamic modeling are presented. A formally logical approach to definition of the system in category theory terms and final results for the facial modeling of the fields are presented. In addition approaches for development of existing knowledge system about oil and gas production into a unified model-conception of the field system.Model of blood flow along the arterial bed, taking into account the bioactivity of the vessel wall.https://zbmath.org/1449.760712021-01-08T12:24:00+00:00"Solovĭova, O. M."https://zbmath.org/authors/?q=ai:soloviova.o-m"Kizilova, N. M."https://zbmath.org/authors/?q=ai:kizilova.n-mSummary: The modification of a two-dimensional model of incompressible viscous fluid motion along a deformed thick-walled tube from viscoelastic bioactive material is proposed in connection to the modeling of blood flow along the arterial bed is proposed. The motion of a viscous incompressible fluid is described by a system of equations including the Navier-Stokes equations and the continuity equation. The behavior of the tube wall material is described by a 5-element rheological model with one active element. The solution of the problem is solved setting boundary conditions on the interface of the two media, the outer surface of the tube is considered as non-moving. At the end of the tube, a zero-dimensional Frank model with regulation is considered, as a model of the microcirculatory bed. The dispersion equation for the propagation of wave velocity is obtained for the case of active properties of tube, the amplitudes of fluid velocities, wall displacements, and fluid and tube pressures. Numerical computations have been carried out for the model parameters corresponded to the normal and pathological arterial wall.Displacement shallow water internal solitary wave.https://zbmath.org/1449.760122021-01-08T12:24:00+00:00"Wu, Feng"https://zbmath.org/authors/?q=ai:wu.feng"Yao, Zheng"https://zbmath.org/authors/?q=ai:yao.zheng"Sun, Yan"https://zbmath.org/authors/?q=ai:sun.yan"Zhong, Wanxie"https://zbmath.org/authors/?q=ai:zhong.wanxieSummary: This paper studies the internal solitary wave in a water system, which consists of two layers of constant-density incompressible inviscid water. By using the Lagrange coordinate and Hamilton principle, an internal wave equation for shallow water displacement of the two-water system and the corresponding internal solitary displacement wave (DISW) solution are derived. The numerical tests show good agreement between the DISW and the classical KdV solitary wave, which means that it is effective to use the Lagrange coordinate and Hamilton principle to analyze the internal wave problem, and hence a way to develop the symplectic method is provided for it.Critical curves and non-extinction condition for non-Newtonian filtration equations coupled via boundary sources.https://zbmath.org/1449.352622021-01-08T12:24:00+00:00"Ling, Zhengqiu"https://zbmath.org/authors/?q=ai:ling.zhengqiuSummary: This paper is concerned with the critical curves and non-extinction condition of the solutions for a non-Newtonian polytropic filtration equation coupled via nonlinear boundary sources in \(\mathbb{R}^N\). The critical global existence curve and the critical Fujita curve are given by means of various self-similar supersolutions and subsolutions. In particular, it is shown that the above two critical curves depend not only on the parameters in the problem, but also the dimension \(N\) of space. This differs greatly from the known results for dimension \(N = 1\). In addition, the non-extinction conditions of solutions for this problem are given.Resonant steady-state sloshing in upright tanks performing a three-dimensional periodic motion.https://zbmath.org/1449.760102021-01-08T12:24:00+00:00"Timokha, A. N."https://zbmath.org/authors/?q=ai:timokha.alexander-n"Tkachenko, E. M."https://zbmath.org/authors/?q=ai:tkachenko.e-mSummary: Analytical approaches to hydrostatic capillary (meniscus) problem in infinite horizontal channel and axisymmetric container are developed. For these geometric cases, finding the capillary menisci reduces to freeboundary problems for special systems of ordinary differential equations. Their solutions describe capillary curves, which appear as intersections of the capillary menisci and (depending on the container type) either crosssection or meridional plane. Further studies on capillary waves require to know analytical approximations of these capillary curves in the \(\mathbb{C}^n, n \geq 3,\) metrics. An objective may consists of constructing analytical approximate solutions of the corresponding systems of ordinary differential equations. The present paper focuses on limits of applicability of the Taylor polynomial and Padé approximations, which were proposed for this class of capillary problems in 1984 by Barnyak and Timokha.Steady-state sloshing in an orbitally-forced square-base tank.https://zbmath.org/1449.760092021-01-08T12:24:00+00:00"Timokha, A. N."https://zbmath.org/authors/?q=ai:timokha.alexander-n"Lahodzinskyi, O. E."https://zbmath.org/authors/?q=ai:lahodzinskyi.o-eSummary: The paper conducts a series of analytical studies on the resonant steady-state sloshing in a rigid square base container, which have been originated by \textit{O. M. Faltinsen} et al. [J. Fluid Mech. 487, 1--42 (2003; Zbl 1053.76006)] who derived and applied the Narimanov-Moiseev-type nonlinear modal equations for investigation in the sloshing problem. The modal equations, which consist on nine-dimensional system of ordinary differential equations, should be applicable for sway/pitch/surge/roll periodic excitations but, due to, basically, mathematical difficulties, the previous papers exclusively concentrated on the reciprocating (longitudinal, oblique and diagonal) motions of the container. This article is showed that the steady-state waves caused by this kind of forcing are asymptotically identical to those occurring when the tank performs horizontal orbital motions. We generalize the previous results by \textit{O. M. Faltinsen} et al. [J. Fluid Mech. 487, 1--42 (2003; Zbl 1053.76006)] to classify the steady-state wave regimes versus the semi-axes ratio of the forcing ellipse in the tank which is filled by a liquid with a finite depth.About general solutions of Euler and Navier-Stokes equations.https://zbmath.org/1449.760172021-01-08T12:24:00+00:00"Rozumnyuk, V. I."https://zbmath.org/authors/?q=ai:rozumnyuk.vyacheslav-iSummary: Constructing a general solution to the Navier-Stokes equation is a fundamental problem of current fluid mechanics and mathematics due to nonlinearity occurring when moving to Euler variables. A new transition procedure is proposed without appearing nonlinear terms in the equation, which makes it possible constructing a general solution to the Navier-Stokes equation as a combination of general solutions to Laplace and diffusion equations. Existence, uniqueness, and smoothness of the solutions to Euler's and Navier-Stokes equations are found out with investigating solutions to the Laplace and diffusion equations well-studied.Steady-state resonant sloshing in upright cylindrical tank due to elliptical forcing.https://zbmath.org/1449.760082021-01-08T12:24:00+00:00"Raynovs'kyĭ, I. A."https://zbmath.org/authors/?q=ai:raynovskyi.i-aSummary: The nonlinear Narimanov-Moiseev multimodal equations are used to study the swirling-type resonant sloshing in a circular base container occurring due to an orbital (rotary) tank motion in the horizontal plane with the forcing frequency close to the lowest natural sloshing frequency. These equations are equipped with linear damping terms associated with the logarithmic decrements of the natural sloshing modes. The surface tension is neglected. An asymptotic steady-state solution is constructed and the response amplitude curves are analyzed to prove their hard-spring type behavior for the finite liquid depth (the mean liquid depth-to-the-radius ratio). For the orbital forcing only swirling occurs. This behavior type is supported by the existing experimental data. Phase lags, which are piecewise functions along the continuous amplitude response curves in the undamped case, become of the non-constant character when the damping matters. The wave elevations at the vertical wall are satisfactory predicted except for a frequency range where the model test observations reported wave breaking and/or mean rotational flows.Thermal creep flow in the rarefied gas.https://zbmath.org/1449.760492021-01-08T12:24:00+00:00"Huang, Feimin"https://zbmath.org/authors/?q=ai:huang.feiminSummary: The usual heat flow moves along the direction from high temperature place to the low one, as often observed in the daily life. However, when the gas is very rarefied, the gas may move along a different way, that is, the so-called thermal creep flow moves along the direction from the low temperature place to the high one. In this note, we survey our recent mathematical works on this topic.Structural stability in resonant penetrative convection in a Brinkman fluid interfacing with a Darcy fluid.https://zbmath.org/1449.760252021-01-08T12:24:00+00:00"Li, Yuanfei"https://zbmath.org/authors/?q=ai:li.yuanfei"Guo, Zhanwei"https://zbmath.org/authors/?q=ai:guo.zhanweiSummary: In this paper, we consider the structural stability of two porous media fluids in a bounded region. Their governing equations are Brinkman equation and Darcy equation, respectively, and there is a heat source or sink in Brinkman fluid. When considering the thermal convection in a plane infinite layer, resonance may occur between the inner layers of the fluid which maybe lead to instability. In this paper, the continuous dependence of the fluid on the heat source or sink is analyzed by deducing a prior temperature bound. The second study is to assume that the system satisfies Newton's cooling law at the boundary of the region. We also obtain the continuous dependence of the model on the cooling coefficient.Application of the finite element-differences method for modeling of filtration processes.https://zbmath.org/1449.760562021-01-08T12:24:00+00:00"Lubkov, M. V."https://zbmath.org/authors/?q=ai:lubkov.m-vSummary: We consider modeling and geophysical interpretation of the obtained results in the oil and gas production problems. For solving these practical problems, we use combined finite element-differences method of resolving piezoconductivity problem with calculation of heterogeneous filtration parameters distribution of oil and gas productive reservoirs and oil-gas penetration conditions in the borders of the reservoirs. At that, we consider the main factors, which influence on the intensity of filtration processes near oil production well and gas production well respectively. These factors are important for effective supporting in practice high level of the oil and gas production. On the base of computer modeling, we have showed that intensity of filtration process near the acting oil and gas production wells mainly depends on oil phase and respectively gas phase permeability, as in close zone of well acting so in remote zone. The viscosity and reservoir porosity parameters in close and remote zones of the well action have little direct effect on filtration process near the acting well. However, these parameters can influence on the filtration process implicitly via direct acting on the respective phase permeability. We also have carried out analysis of the pumping well influence on the filtration process near production well in different practical cases.Analysis of reservoir mass influence on the system free surfaced liquid and spherical reservoir.https://zbmath.org/1449.760072021-01-08T12:24:00+00:00"Limarchenko, O. S."https://zbmath.org/authors/?q=ai:limarchenko.oleg-s"Slyusarchuk, Yu. A."https://zbmath.org/authors/?q=ai:slyusarchuk.yu-aSummary: Within the framework of combined motion the effect of ratio of masses of reservoir and liquid on the behavior of a free surface of liquid in the reservoir of spherical shape is studied. We suppose that liquid is ideal and it fills partially the reservoir. Mathematical modelling is done on the basis of the model, which takes into account combined character of nonlinear dynamics of liquid and the reservoir. Examples were done based on mathematical model of combined motion of liquid in spherical reservoir and free-surfaced liquid under harmonic force disturbance in horizontal direction. Two cases of the ratio of masses in the system are considered. First, the mass of the reservoir is 5 times less than the mass of the liquid; the mass of the reservoir is 5 times greater than the mass of the liquid. In order to identify specific features of the system behavior, the results were compared with the results for liquid behavior in cylindrical and conical reservoirs. It was ascertained that mass increasing has no tendency of converging to a steady mode of motion, which was confirmed experimentally. Distinctions of manifestation of nonlinear processes for the below-resonance, near-resonance and above-resonance modes are shown. We note manifestation of nonlinear effects such as modulation, the presence of high-frequency normal modes of oscillations, antiresonance and drift of the mean of oscillations.Well-posedness for the 2D non-autonomous incompressible fluid flow in Lipschitz-like domain.https://zbmath.org/1449.760152021-01-08T12:24:00+00:00"Yang, Xinguang"https://zbmath.org/authors/?q=ai:yang.xinguang"Wang, Shubin"https://zbmath.org/authors/?q=ai:wang.shubinSummary: This paper is concerned with the global well-posedness and regularity of weak solutions for the 2D non-autonomous incompressible Navier-Stokes equation with a inhomogeneous boundary condition in Lipschitz-like domain. Using the estimate for governing steady state equation and Hardy's inequality, the existence and regularity of global unique weak solution can be proved. Moreover, these results also hold for 2D Navier-Stokes equation with Rayleigh's friction and Navier-Stokes-Voigt flow, but invalid for three dimension.Control of a reservoir partially filled with liquid based on Gauss's principle of least constraint (deceleration task).https://zbmath.org/1449.760062021-01-08T12:24:00+00:00"Konstantinov, O. V."https://zbmath.org/authors/?q=ai:konstantinov.o-v.1Summary: The task of constructing control for the motion of a given reservoir -- a liquid with a free surface mechanical system is provided in the presence of constant perturbations -- the oscillations of the free surface of the liquid. To construct the control, the principle of the least coaxing of Gauss was used, which allows to minimize the control load and implement the given laws of the software movement. The control calculation was carried out on the basis of a simplified linear model with two degrees of freedom, which allowed the control function to be obtained in analytical form for various software laws (including nonlinear) movement of the reservoir and free surface of the liquid. The tank partially filled with a liquid, which initially moves evenly at a given speed, must be completely stopped at a given time. The control, constructed for the implementation of linear software laws of motion, can be used only to provide ``comfortable'' movements of the reservoir, that is, in the absence of large disturbances of the free surface of the liquid. In order to ensure the movement of the reservoir in the presence of highly intense loads, it is necessary to introduce nonlinear software motion laws for obtaining and using a nonlinear control law.Productivity analysis of doubly periodic systems of production wells.https://zbmath.org/1449.760612021-01-08T12:24:00+00:00"Roters, Pavel Vyacheslavovich"https://zbmath.org/authors/?q=ai:roters.pavel-vyacheslavovichSummary: The article presents a mathematical model, which allows to analyze the productivity of systems of production wells. System of wells is modeled by a flat infinite doubly periodic lattice of point sinks of equal power. Also an analytic representation for the Dietz's shape factor is presented, which agrees with numerical calculations by the method of imaginary producing wells.Features of heat and mass exchange in laminar flows of micro and nanofluids in tubes and channels.https://zbmath.org/1449.760662021-01-08T12:24:00+00:00"Kizilova, N. M."https://zbmath.org/authors/?q=ai:kizilova.n-m"Tkachenko, Ye.D."https://zbmath.org/authors/?q=ai:tkachenko.ye-dSummary: In recent years, high efficiency of using suspensions of nanoparticles for cooling of the operating systems compared to a homogeneous liquid has been shown, and the parameters of suspensions effective for various specific devices have been selected in experiments. A brief review of the relevant experimental data as well as mathematical models of the flow of micro- and nanofluids, based on the incompressible Navier Stokes equations with boundary conditions accounting for tangential momentum transfer of the particles an temperature jump due to diffuse reflection at rough walls, are presented. For the case of a laminar flow between infinite parallel plates with constant heat fluxes through the plates, an analytical solution is obtained for the velocity and temperature fields. Numerical calculations showed that with an increase in the momentum transfer coefficients at the plates, the flow accelerates significantly, which contributes to an increase in volumetric flow with the same pressure drop across the channel due to a decrease in the shear stress at the wall. Correspondingly, the heat transfer through the plates and the heat removal with the fluid flow increase. Based on the obtained analytical relationships, it is possible to select the parameters of the plate surfaces in such a way as to optimize the system, for example, to reduce the energy loss due to viscous and thermal dissipation or to obtain uniform temperature distributions in the liquid with asymmetric heat flows through the plates.Modeling of blood microcirculation, heat and mass transfer in human tissues.https://zbmath.org/1449.760692021-01-08T12:24:00+00:00"Kizilova, N. M."https://zbmath.org/authors/?q=ai:kizilova.n-m"Korobov, A. M."https://zbmath.org/authors/?q=ai:korobov.a-mSummary: A mathematical model of the structure of the blood vessels system which provides blood microcirculation in the superficial tissues of human, namely the skin, to provide blood supply as a fluid, which heats/cools, and determines thermoregulation in changes of ambient temperature and overheating supercooling is proposed. The model is based on data from current studies of the structure of microcirculatory beds based on microCT technologies. The microvascular system is modeled as a fractal binary tree optimized for uniform supply of a nutrient fluid (blood for biological tissues) due to the homogeneous distribution of capillaries, optimal values for diameters, lengths and branching angles in bifurcations of tubes that provide flow distribution with minimal energy costs. The model has been developed to use in computer-based monitoring systems for the planning of physiotherapy procedures for different diseases.Acoustic radiation force effect on a spherical drop placed in the vicinity of an ideal liquid free surface.https://zbmath.org/1449.760502021-01-08T12:24:00+00:00"Zhuk, O. P."https://zbmath.org/authors/?q=ai:zhuk.o-p"Zhuk, Ya. O."https://zbmath.org/authors/?q=ai:zhuk.ya-oSummary: Acoustic radiation force effect on a liquid spherical drop placed in the vicinity of an ideal liquid free surface is studied. The problem of determination of the radiation forces acting on an obstacle in ideal liquid is formulated with respect to the Lagrange coordinate system. Thus, the radiation pressure is defined as time-averaged value of the acoustic pressure over the obstacle surface. This approach is adequate if, at determining of the acoustic pressure in a fluid, the deviation of the pressure from the harmonic law in time domain is taken into account in the obstacle vicinity. An action of the acoustic radiation force on a spherical drop of ideal liquid placed in turn in a liquid by its free plane surface is studied here for the case of the incident plane sound wave propagating perpendicularly to the liquid boundary. As a result, the liquid sphere is appeared to be located in the standing sound wave of pressure which has its displacement node at the free surface. Problem solution is obtained as a three step procedure. Initially, solution of the problem of an incident wave scattering at the drop is derived. With making use of the results obtained, the second step encompasses determining of hydrodynamic forces acting on the liquid spherical drop with their subsequent averaging over the suitable time interval at the third step. It is found there frequencies of the incident wave exist that provide zero radiation force acting on the drop which is immobile in this case. These equilibrium positions of the spherical drop could be stable or unstable with respect to the incident wave frequency variation.Modeling of stress state of a perforated cement sheath in a well with hydraulic fracture.https://zbmath.org/1449.760552021-01-08T12:24:00+00:00"Kireev, Timur Faritovich"https://zbmath.org/authors/?q=ai:kireev.timur-faritovich"Bulgakova, Guzel' Talgatovna"https://zbmath.org/authors/?q=ai:bulgakova.guzel-talgatovnaSummary: Modeling of stress state of a perforated cement sheath in a well with hydraulic fracture is performed. The incompressible fluid flow model is used to calculate the pore pressure of a fluid. The linear-elastic body model and finite volume method with multipoint stress approximation are used to calculate the stress state of the cement sheath and production casing. The numerical model was verified by comparing the calculation results with a calculation in the Fenics open-source computing platform. It is shown that the maximum value of von Mises stress falls on the perforation zone at the junction of the cement sheath and the production casing. The presence of a hydraulic fracture can reduce the stress of the cement sheath.Non-helical exact solutions to the Euler equations for swirling axisymmetric fluid flows.https://zbmath.org/1449.760042021-01-08T12:24:00+00:00"Prosviryakov, Evgeniĭ Yur'evich"https://zbmath.org/authors/?q=ai:prosviryakov.evgenii-yurevichSummary: Swirling axisymmetric stationary flows of an ideal incompressible fluid are considered within the framework of the Euler equations. A number of new exact solutions to the Euler equations are presented, where, as distinct from the known Gromeka-Beltrami solutions, vorticity is noncollinear with velocity. One of the obtained solutions corresponds to the flow inside a closed volume, with the nonpermeability condition fulfilled at its boundary, the vector lines of vorticity being coiled on revolution surfaces homeomorphic to a torus.On the electrostatic field in expansion dynamics of gas bubbles.https://zbmath.org/1449.760632021-01-08T12:24:00+00:00"Museibli, Parviz T."https://zbmath.org/authors/?q=ai:museibli.parviz-tSummary: The work is devoted to the study of the dynamics of the formation of bubbles in a gas-liquid system taking into account the potential difference. The electrical conductivity of the fluid is determined depending on the concentration of the electrolyte and, accordingly, the electrostatic field that occurs when the fluid flows. The effect of the electrostatic field on the bubble formation dynamics has shown that the radius of the gas bubbles and the dynamics of its expansion, formed by the pressure difference, can be regulated by the potential difference parameter. Depending on the electrolytic concentration, the electric conductivity of the liquid and, accordingly, the electrostatic field arising from friction in fluid are determined. The effect of the electrostatic field on the dynamics of the bubble formation has shown that the radius of gas bubbles and expansion dynamics formed by the pressure drop can be regulated by the potential difference parameter. It is presented that one of the main factors affecting the flow of two-phase fluids is the nature of the liquid phase and the concentration of electrolyte added. The results of regulation of the bubble formation dynamics in the gas-liquid system via the electrostatic field and a number of physical parameters can be applied in the oil and gas industry, chemical processes, biomechanics.BKM's blow-up criterion in homogeneous Triebel-Lizorkin spaces for the 3D dissipative system in electro-hydrodynamics.https://zbmath.org/1449.351212021-01-08T12:24:00+00:00"Li, Xiurong"https://zbmath.org/authors/?q=ai:li.xiurong"Liang, Hong"https://zbmath.org/authors/?q=ai:liang.hongSummary: In this paper, we study the breakdown of local smooth solutions for a class of nonlinear dissipative electro-hydrodynamics system. This system is a strongly coupled system by the well-known incompressible Navier-Stokes equations in hydromechanics and Poisson-Nernst-Planck equations in electrodynamics, modeling the drift, diffusion and convection phenomena of charged particle in an isothermal, incompressible and viscous fluids. Based on the Littlewood-Paley decomposition theory, the BKM's blow-up criterion in terms of horizontal component of velocity field in homogeneous Triebel-Lizorkin spaces is established for local smooth solutions, and generalizes the previous results. In particular, this blow-up criterion reveals that the horizontal component of velocity field is more important than the density functions of charged particles in the blow-up theory of the system.A new mixed method for the Stokes equations based on stress-velocity-vorticity formulation.https://zbmath.org/1449.760332021-01-08T12:24:00+00:00"Penati, Mattia"https://zbmath.org/authors/?q=ai:penati.mattia"Miglio, Edie"https://zbmath.org/authors/?q=ai:miglio.edieSummary: In this paper, we develop and analyze a mixed finite element method for the Stokes flow. This method is based on a stress-velocity-vorticity formulation. A new discretization is proposed: the stress is approximated using the Raviart-Thomas elements, the velocity and the vorticity by piecewise discontinuous polynomials. It is shown that if the orders of these spaces are properly chosen then the advocated method is stable. We derive error estimates for the Stokes problem, showing optimal accuracy for both the velocity and vorticity.A semi-Langrangian vortex penalization method for 3D incompressible flows.https://zbmath.org/1449.760362021-01-08T12:24:00+00:00"Mimeau, Chlo"https://zbmath.org/authors/?q=ai:mimeau.chlo"Mortazavi, Iraj"https://zbmath.org/authors/?q=ai:mortazavi.iraj"Cottet, Georgeshenri"https://zbmath.org/authors/?q=ai:cottet.georgeshenriSummary: A remeshed vortex method is proposed in this work to simulate three-dimensional incompressible flows. The convection equation is solved on particles, using a vortex method, which are then remeshed on a Cartesian underlying grid. The other differential operators involved in the governing incompressible Navier-Stokes equations are discretized on the grid, through finite differences method or in spectral space. In the present work, the redistribution of the particles on the Cartesian mesh is performed using a directional splitting, allowing to save significant computational efforts especially in the case of 3D flows. A coupling of this semi-Lagrangian method with an immersed boundary method, namely the Brinkman penalization technique, is proposed in this paper in order to efficiently take into account the presence of solid and porous obstacles in the fluid flow and then to perform passive flow control using porous medium. This method, which combines the robustness of particle methods and the flexibility of penalization method, is validated and exploited in the context of different flow physics.Mathematical modeling of particle aggregation and sedimentation in the inclined tubes.https://zbmath.org/1449.760652021-01-08T12:24:00+00:00"Baranets, V."https://zbmath.org/authors/?q=ai:baranets.v-o"Kizilova, N."https://zbmath.org/authors/?q=ai:kizilova.n-mSummary: Sedimentation of the aggregating particles of different technical suspensions, blood and nanofluids in the gravity is investigated. The dependence of the sedimentation rate on the angle of inclination is considered. The two phase model of the aggregating particles is generalized to the inclined tubes. In the suggestion of small angles of inclination the equations are averaged over the transverse coordinate and the obtained hyperbolic system of equations is solved by the method of characteristics.The linear instability of the gravity driven viscous Navier-Stokes flow in three-dimension.https://zbmath.org/1449.350612021-01-08T12:24:00+00:00"Yang, Jing"https://zbmath.org/authors/?q=ai:yang.jing"Ge, Qing"https://zbmath.org/authors/?q=ai:ge.qing"Li, Ji'na"https://zbmath.org/authors/?q=ai:li.jinaSummary: We investigate the instability of some steady-states of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity. When the steady density is heavier with increasing height (i.e., the Rayleigh-Taylor steady-state), we show that the steady-state is linear unstable by constructing a (standard) energy functional and exploiting the modified variational method.Convective flow of blood in square and circular cavities.https://zbmath.org/1449.760702021-01-08T12:24:00+00:00"Senel, P."https://zbmath.org/authors/?q=ai:senel.pelin"Tezer-Sezgin, M."https://zbmath.org/authors/?q=ai:tezer-sezgin.munevverSummary: In this study, the fully developed, steady, laminar flow of blood is studied in a long pipe with square and circular cross-sections subjected to a magnetic field generated by an electric wire. Temperature difference between the walls causes heat transfer within the fluid by the displacement of the magnetizable fluid particles in the cavity. The governing equations are the coupled Navier-Stokes and energy equations including magnetization terms. The axial velocity is also computed with the obtained plane velocity. The dual reciprocity boundary element method (DRBEM) is used by taking all the terms other than Laplacian as inhomogeneity which transforms the partial differential equations into the boundary integral equations. Numerical results are given for increasing values of magnetic $(Mn)$ and Rayleigh $(Ra)$ numbers. The numerical results reveal that an increase in $Mn$ accelerates the plane velocity in the cavity but decelerates the axial velocity around the magnetic source. Pressure increases through the channel starting from the magnetic source. Isotherms show the cooling of the channel with high $Mn$ and $Ra$ only leaving a thin hot layer near the top heated wall. As $Ra$ increases viscous effect is reduced leaving its place to convection in the channel. The use of DRBEM has considerably small computational expense compared to domain type methods.The modified weak Galerkin finite element method for solving Brinkman equations.https://zbmath.org/1449.653242021-01-08T12:24:00+00:00"Sun, Li'na"https://zbmath.org/authors/?q=ai:sun.lina"Feng, Yue"https://zbmath.org/authors/?q=ai:feng.yue"Liu, Yuanyuan"https://zbmath.org/authors/?q=ai:liu.yuanyuan.3|liu.yuanyuan|liu.yuanyuan.2|liu.yuanyuan.1"Zhang, Ran"https://zbmath.org/authors/?q=ai:zhang.ran.1|zhang.ran.2|zhang.ranSummary: A modified weak Galerkin (MWG) finite element method is introduced for the Brinkman equations in this paper. We approximate the model by the variational formulation based on two discrete weak gradient operators. In the MWG finite element method, discontinuous piecewise polynomials of degree \(k\) and \(k-1\) are used to approximate the velocity \(u\) and the pressure \(p\), respectively. The main idea of the MWG finite element method is to replace the boundary functions by the average of the interior functions. Therefore, the MWG finite element method has fewer degrees of freedom than the WG finite element method without loss of accuracy. The MWG finite element method satisfies the stability conditions for any polynomial with degree no more than \(k-1\). The MWG finite element method is highly flexible by allowing the use of discontinuous functions on arbitrary polygons or polyhedra with certain shape regularity. Optimal order error estimates are established for the velocity and pressure approximations in \(H^1\) and \(L^2\) norms. Some numerical examples are presented to demonstrate the accuracy, convergence and stability of the method.Mathematical modeling of coalescence and breakage of droplets and bubbles in an isotropic turbulent flow: a review.https://zbmath.org/1449.760282021-01-08T12:24:00+00:00"Kelbaliev, Gudret Isfandiyar"https://zbmath.org/authors/?q=ai:kelbaliev.gudret-isfandiyar"Rasulov, Sakit Rauf"https://zbmath.org/authors/?q=ai:rasulov.sakit-raufSummary: This review devoted to the theoretical analysis, calculation, and modeling of the processes of merging and breakage of droplets and bubbles in an isotropic turbulent flow. We have analyzed a number of studies on these issues. The problems of determining the minimum and maximum sizes of droplets and bubbles, as well as breakage and merging frequencies, which are associated with the solution of the diffusion equation of mass transfer, are considered. The merging of droplets is considered as a result of the thinning of the interfacial film formed by two drops as a result of their collision. A mathematical description of the refinement of the interfacial film, taking into account the Marangoni effect, is proposed. Analysis of many studies, including our own, showed that, depending on the scale of turbulent pulsations, the extreme size, as well as the frequencies of coalescence and breakage of droplets and bubbles, depend on the specific dissipation energy in the turbulent flow, on their sizes and on the physical properties of the particles and the medium. Important parameters that provide aggregative stability of a liquid-liquid or liquid-gas type dispersion medium to breakage, deformation and fusion are the surface tension coefficient and energy dissipation, the physical properties of the medium and particles, and in an isotropic turbulent flow the ratio of the surface coefficient tension to specific energy dissipation. Problems related to the evolution of the particle distribution function in time and size under isotropic turbulence using solutions of the Fokker-Planck stochastic equation for continuous variation of the sizes of droplets and bubbles and the integro-differential kinetic equation of coalescence and fragmentation for jump-like changes in particle sizes are also considered. A set of analytical solutions of these equations for particular cases is proposed. A more in-depth analysis based on the mathematical laws of the transport phenomena makes it possible in the standard way to calculate such systems in an approximation, such as continuous, with an infinitely small jump. It is shown that the deterministic description of these phenomena without taking into account their stochastic nature is incomplete and can lead to significant deviations from the true nature of the above processes. The results obtained are compared with the existing experimental data on coalescence and breakage of droplets and bubbles, which showed satisfactory agreement with the calculated values.Generalized public transportation scheduling using max-plus algebra.https://zbmath.org/1449.150662021-01-08T12:24:00+00:00"Subiono"https://zbmath.org/authors/?q=ai:subiono.s"Fahim, Kistosil"https://zbmath.org/authors/?q=ai:fahim.kistosil"Adzkiya, Dieky"https://zbmath.org/authors/?q=ai:adzkiya.diekySummary: In this paper, we discuss the scheduling of a wide class of transportation systems. In particular, we derive an algorithm to generate a regular schedule by using max-plus algebra. Inputs of this algorithm are a graph representing the road network of public transportation systems and the number of public vehicles in each route. The graph has to be strongly connected, which means there is a path from any vertex to every vertex. Let us remark that the algorithm is general in the sense that we can allocate any number of vehicles in each route. The algorithm itself consists of two main steps. In the first step, we use a novel procedure to construct the model. Then in the second step, we compute a regular schedule by using the power algorithm. We describe our proposed framework for an example.Closed vortex lines in fluid and gas.https://zbmath.org/1449.760132021-01-08T12:24:00+00:00"Sizykh, Grigoriĭ Borisovich"https://zbmath.org/authors/?q=ai:sizykh.grigorii-bSummary: Continuous fluid and gas flows with closed vortex tubes are investigated. The circulation along the vortex line of the ratio of the density of the resultant of all forces (applied to the fluid or gas) to the density of the fluid or gas is considered. It coincides with the circulation (along the same vortex line) of the partial derivative of the velocity vector with respect to time and, therefore, for stationary flows, it is equal to zero on any closed vortex line. For non-stationary flows, vortex tubes are considered, which remain closed for at least a certain time interval. A previously unknown regularity has been discovered, consisting in the fact that at, each fixed moment of time, such circulation is the same for all closed vortex lines that make up the vortex tube. This regularity is true for compressible and incompressible, viscous (various rheologies) and non-viscous fluids in a field of potential and non-potential external mass forces. Since this regularity is not embedded in modern numerical algorithms, it can be used to verify the numerical calculations of unsteady flows with closed vortex tubes by checking the equality of circulations on different closed vortex lines (in a tube).
The expression for the distribution density of the resultant of all forces applied to fluid or gas may contain higher-order derivatives. At the same time, the expression for the partial derivative of the velocity vector with respect to time and the expression for the vector of vorticity (which is necessary for constructing the vortex line) contain only the first derivatives; which makes it possible to use new regularity for verifying the calculations made by methods of high and low orders simaltaniously.Using the enriched radial basis function in solving the singular sudden expansion incompressible fluid flow.https://zbmath.org/1449.760192021-01-08T12:24:00+00:00"Li, T. S."https://zbmath.org/authors/?q=ai:li.tak-sing"Wong, S. M."https://zbmath.org/authors/?q=ai:wong.simanSummary: In this paper, we will use radial basis functions (RBFs) to solve the sudden-expansion problem when incompressible fluid flows around a sharp corner. Stress singularities would occur at the sharp corner. Normal ways to deal with the singularities are to add more node points near the sharp corner. This paper adopts a series solution method for enhancing the approximation of the flow around the sharp corner. The original RBF formulation of the problem is modified so that some extra terms of the series solution are added. Our results show that the accuracy has been improved significantly.Self-adjointness, conservation laws and invariant solutions of the Buckmaster equation.https://zbmath.org/1449.580032021-01-08T12:24:00+00:00"Rashidi, Saeede"https://zbmath.org/authors/?q=ai:rashidi.saeede"Hejazi, Seyed Reza"https://zbmath.org/authors/?q=ai:hejazi.seyed-rezaSummary: The present paper considers the group analysis of extended (1 + 1)-dimensional Buckmaster equation and its conservation laws. Symmetry operators of Buckmaster equation are found via Lie algorithm of differential equations. The method of non-linear self-adjointness is applied to the considered equation. The infinite set of conservation laws associated with the finite algebra of Lie point symmetries of the Buckmaster equation is computed. The corresponding conserved quantities are obtained from their respective densities. Furthermore, the similarity reductions corresponding to the symmetries of the equation are constructed.Analytical model of vertical oil-water displacement with the account of viscous, capillary and gravity forces.https://zbmath.org/1449.760242021-01-08T12:24:00+00:00"Bulgakova, Guzel' Talgatovna"https://zbmath.org/authors/?q=ai:bulgakova.guzel-talgatovna"Kondrat'eva, N. R."https://zbmath.org/authors/?q=ai:kondrateva.n-rSummary: A mathematical model of water displacement in vertical porous media is presented. The mathematical formulation takes the form of a nonlinear convection-diffusion equation. Its contribution comes from consideration of the three chief forces: viscous, capillary and gravity in oil recovery processes. A numerical model was based on the simulator Schlumberger ECLIPSE ver. 2004a\_1. Finally, analytical and numerical results are compared.Mathematical modeling of suspension clarification in a dynamic layer.https://zbmath.org/1449.760582021-01-08T12:24:00+00:00"Polyakov, V. L."https://zbmath.org/authors/?q=ai:polyakov.v-lSummary: A non-linear non-steady task of undetachable cake filtration at a constant pressure difference at moving and stationary cake layer boundaries is formulated and solved exactly. Sorption and conductivity possibilities are described by arbitrary functions. The solution obtained in the parametric form enables one to predict reliably changes in time of the filtrate quantity and productivity of a cake filtration installation. The effects of layer sorption properties, autocatalysis, and rate of cake formation on the main filtration characteristics are analyzed for a number of test examples. It is established that a considerable decrease in the suspended substance content in a filtrate, and filtration rate occurs during a short time, and the deposition is distributed along the dynamic layer height essentially unevenly with the maximum at its exit.Optimal control over inserted point source intensity for humidification of a two-dimensional porous medium.https://zbmath.org/1449.760572021-01-08T12:24:00+00:00"Lyashko, S. I."https://zbmath.org/authors/?q=ai:lyashko.sergei-ivanovich"Klyushin, D. A."https://zbmath.org/authors/?q=ai:klyushin.dmitry-a|klyushin.dmytro-a"Tymoshenko, A. A."https://zbmath.org/authors/?q=ai:tymoshenko.a-aSummary: The humidity transfer process through an unsaturated porous medium with inserted point sources modeled by the Richards-Klute equation has calculation complexity and is unstable. The reason for that is a large number of diverse parameters for the equation used to describe the physical process. To reduce the difficulty, an approach is offered based on the Kirchhoff transformation, which allows one to bring down the quasilinear parabolic initial-boundary problem to a linear dimensionless one. A two-dimensional quasilinear problem of optimal control using point sources for a rectangular unsaturated porous medium with zero initial conditions, zero humidity at the bounds, and the achievable given target humidity is considered, studied, and solved for the first time.
The initial problem is transformed into the linear dimensionless optimal control problem of non-stationary moisture transport in an unsaturated porous medium using the Kirchhoff transformation. A variation algorithm identifying the optimal source power is used, which allows modeling the process with realistic assumptions. For this algorithm, the finite difference method is used for both direct and conjugate problems, followed by the numerical method application to solve the SLAE. The correctness of the linearized dimensionless problem of moisture transport is shown. In particular, the theorems of existence and uniqueness of the generalized solution are mentioned, as well as the existence and uniqueness of the optimal control over the source power.
The current paper is devoted to the modeling of the moisture transport from an inserted source in a dry ground area. Results of numerical experiments demonstrating a high accuracy of the method are given. The proposed method allows one to solve actual problems of optimal parameter choice for a drop irrigation system, and to improve its effectiveness.Continuous dependence on boundary parameters for three-dimensional viscous primitive equation of large-scale ocean atmospheric dynamics.https://zbmath.org/1449.350362021-01-08T12:24:00+00:00"Li, Yuanfei"https://zbmath.org/authors/?q=ai:li.yuanfeiSummary: By using a priori bounds of the solutions of the equations and the technique of differential inequality, the author proved that the solution of the three-dimensional viscous primitive equation of large-scale ocean atmospheric dynamics was continuously dependent on the boundary parameters.Global existence of self-similar Leray weak solution for three dimensional incompressible magnetohydrodynamics equations.https://zbmath.org/1449.351612021-01-08T12:24:00+00:00"Guo, Hua"https://zbmath.org/authors/?q=ai:guo.hua"Yuan, Rong"https://zbmath.org/authors/?q=ai:yuan.rongSummary: This paper deals with the Cauchy problem of the three dimensional incompressible magnetohydrodynamics equations. Using the regularity estimation of the local space near the initial time and the Leray-Schauder fixed point theorem, the global existence of a smooth self-similar Leray weak solution to the Cauchy problem with the smooth and scale-invariant initial data is achieved.On fluid-shell coupling using an arbitrary Lagrangian-eulerian fluid solver coupled to a positional Lagrangian shell solver.https://zbmath.org/1449.760182021-01-08T12:24:00+00:00"Sanches, Rodolfo André Kuche"https://zbmath.org/authors/?q=ai:sanches.rodolfo-andre-kuche"Coda, Humberto Breves"https://zbmath.org/authors/?q=ai:coda.humberto-brevesSummary: In this work, we develop a partitioned algorithm for three-dimensional geometric non-linear fluid-structure interaction analysis using the finite element method. The fluid solver is explicit and its time integration based on characteristics, which automatically introduces stabilising terms on stream direction. The Navier-Stokes equations are written using the arbitrary Lagrangian-Eulerian (ALE) description, in order to accept moving boundaries and coupling with Lagrangian shell elements. The structure is modelled using a novel finite element method formulation for geometric non-linear shell dynamics. Such shell formulation, so-called positional formulation, is based on the minimum potential energy theorem, written regarding nodal positions and generalised unconstrained vectors, not displacements and rotations. These characteristics avoid the use of large rotation approximations. The coupling between the two different meshes is done by mapping the fluid boundary nodes local positions over the shell elements and \textit{vice versa}, avoiding the need for matching fluid and shell nodes. The fluid mesh is adapted using a simple approach based on shell positions and velocities. The efficiency and robustness of the proposed approach is demonstrated by examples.Asymptotic behavior of compressible Navier-Stokes fluid in porous medium.https://zbmath.org/1449.350852021-01-08T12:24:00+00:00"Yuan, Guozhi"https://zbmath.org/authors/?q=ai:yuan.guozhi"Zhao, Hongxing"https://zbmath.org/authors/?q=ai:zhao.hongxingSummary: We study the asymptotic behavior of the solution to the full compressible Navier-Stokes fluid in porous medium. By using standard energy and two-scale convergence, we prove the strong convergence of the density and the temperature with characteristic size of the pores \(\varepsilon\) in \({R^n}\) for \(n = 2\) or 3 and obtain the homogenized result for this model, when \(\varepsilon \to 0\), which gives another explanation to the results in references.Analysis of a fully implicit SUPG scheme for a filtration and separation model.https://zbmath.org/1449.652632021-01-08T12:24:00+00:00"Wilson, A. B."https://zbmath.org/authors/?q=ai:wilson.a-b"Jenkins, E. W."https://zbmath.org/authors/?q=ai:jenkins.eleanor-wSummary: We describe and analyze a streamline-upwinded, Petrov-Galerkin (SUPG) method for numerical simulation of transport models with adsorption kinetics. Specifically, we rewrite the adsorption term to pose the problem using a single mass accumulation term for the liquid phase concentration. The rate of adsorption is used in the nonlinear coefficient for the mass accumulation. We use streamline upwinding to stabilize the advection-dominated applications we consider. We provide a priori error analysis verified by numerical results, and we provide additional numerical results demonstrating the usefulness of our scheme. We consider a variety of adsorption model parameters and describe the performance of our algorithm in these cases.Simulations of population balance systems with the characteristic line method.https://zbmath.org/1449.652262021-01-08T12:24:00+00:00"Li, Yu"https://zbmath.org/authors/?q=ai:li.yu"Xie, Hehu"https://zbmath.org/authors/?q=ai:xie.hehuSummary: Precipitation processes are modeled by population balance systems consisting of equations describing the flow field, equations for the chemical reaction and an equation for the particle size distribution. The main difficulties for simulating the precipitation processes include the coupling of these equations, the solving of time dependent convection-dominated convection-diffusion-reaction equations and the high dimensional property of the particle size distribution equation. In this paper, using the characteristic line method to solve the particle size distribution equation is replaced by solving a series of low dimensional problems which can be carried out in the parallel way. The calcium carbonate deposition process is simulated in the square cavity. And the relationship between the size of sediment particles and the positions of inflow and outflow is investigated qualitatively.The boundary layer for MHD equations in a plane-parallel channel.https://zbmath.org/1449.353562021-01-08T12:24:00+00:00"Wang, Na"https://zbmath.org/authors/?q=ai:wang.na"Wang, Shu"https://zbmath.org/authors/?q=ai:wang.shuSummary: In this paper, we study the boundary layer problem for the incompressible MHD equations in a plane-parallel channel. Using the multiscale analysis and the careful energy method, we prove the convergence of the solution of viscous and diffuse MHD equations to that of the ideal MHD equations as the viscosity and magnetic diffusion coefficients tend to zero.Elementary energy estimates of three-dimensional axially symmetric nonhomogeneous incompressible MHD equations under the rectangular coordinate system.https://zbmath.org/1449.353542021-01-08T12:24:00+00:00"Liu, Fangjun"https://zbmath.org/authors/?q=ai:liu.fangjun"Ma, Qian"https://zbmath.org/authors/?q=ai:ma.qianSummary: It is known that elementary energy estimates of three-dimensional axially symmetric nonhomogeneous incompressible MHD equations is crucial for the global existence of the subsequent solution to MHD equations. In order to make it applied widely, by relying on elementary energy estimates of three-dimensional axially symmetric MHD equations under the cylindrical coordinate system and removing the constraint condition of the cylindrical coordinate, the problem-solving process of each of the items in elementary energy estimates of MHD equations is explicitly given under the rectangular coordinate system. Finally, by making full use of mass conservation formula and the incompressible constraint condition of MHD equations under the rectangular coordinate system, the elementary energy estimates of MHD equations under the rectangular coordinate system are successfully deduced.Application of a heterogenous multiscale method to multi-batch driven pipeline.https://zbmath.org/1449.760482021-01-08T12:24:00+00:00"Blažič, Sašo"https://zbmath.org/authors/?q=ai:blazic.saso"Geiger, Gerhard"https://zbmath.org/authors/?q=ai:geiger.gerhard"Matko, Drago"https://zbmath.org/authors/?q=ai:matko.dragoSummary: The problem of simulating pipelines that are used for transporting different fluids is addressed in the paper. The model of the multi-batch pipeline is obtained by extending the classical ``water hammer equations'' (dealing with pressure and velocity of the medium) with fluid density. In such way a system of nonlinear partial differential equations is derived and solved by the method of characteristics. However, the ordinary differential equations resulting from the method of characteristics are defined on domains with very different slopes in the \((x,t)\) space. A heterogenous multiscale method using two grids is capable of coping with associated numerical problems as shown by comparison of simulated and measured data on a real pipeline.Global strong solution for incompressible MHD system with variable magnetic diffusion and magnetic dissipation coefficients.https://zbmath.org/1449.351692021-01-08T12:24:00+00:00"Chen, Hong"https://zbmath.org/authors/?q=ai:chen.hong|chen.hong.1"Yuan, Rong"https://zbmath.org/authors/?q=ai:yuan.rongSummary: In this paper, we study the initial boundary value problem of three dimensional incompressible MHD system with variable magnetic diffusion and magnetic dissipation coefficients in a bounded region \(\Omega \subset {R^3}\) with smooth boundary. The existence of the unique local strong solution to the MHD system is proved, and the local strong solution can be extended to the global strong solution of the MHD system.An implicit scheme for solving unsteady Boltzmann model equation.https://zbmath.org/1449.651932021-01-08T12:24:00+00:00"Li, Xiaowei"https://zbmath.org/authors/?q=ai:li.xiaowei"Li, Chunxin"https://zbmath.org/authors/?q=ai:li.chunxin"Zhang, Dan"https://zbmath.org/authors/?q=ai:zhang.dan"Li, Zhihui"https://zbmath.org/authors/?q=ai:li.zhihuiSummary: When solving hyperbolic Boltzmann model equation with discrete velocity models (DVM), the strong discontinuity of the velocity distribution function can be captured well by utilizing the non-oscillatory and non-free parameter dissipation (NND) finite difference scheme. However, most NND scheme solvers march in time explicitly, which compromise the computation efficiency due to the limitation of stability condition, especially when solving unsteady problems. In order to improve the efficiency, an implicit scheme based on NND is presented in this paper. Linearization factors are introduced to construct the implicit scheme and to reduce the stencil size. With the help of dual time-stepping method, the convergence rate of unsteady rarefied flow simulation can be massively improved. Numerical tests of steady and unsteady supersonic flow around cylinders are computed in different flow regimes. Results are shown to prove the validity and efficiency of the implicit scheme.Existence, uniqueness and blow-up of solutions for the 3D Navier-Stokes equations in homogeneous Sobolev-Gevrey spaces.https://zbmath.org/1449.351132021-01-08T12:24:00+00:00"Braz e Silva, P."https://zbmath.org/authors/?q=ai:braz-e-silva.pablo"Melo, W. G."https://zbmath.org/authors/?q=ai:melo.wilberclay-g"Rocha, N. F."https://zbmath.org/authors/?q=ai:rocha.nata-firminoSummary: We show existence and uniqueness of solutions for the classical Navier-Stokes equations in Sobolev-Gevrey spaces \(\dot{H}_{a,\sigma}^s(\mathbb{R}^3)\), where \(s\in (1/2,3/2)\), \(a>0\) and \(\sigma \geq 1\); furthermore, we present some blow-up criteria considering these same spaces with \(\sigma >1\).An exponentially convergent method for simulation of pollution spread from moving sources.https://zbmath.org/1449.760522021-01-08T12:24:00+00:00"Vasylyk, V. B."https://zbmath.org/authors/?q=ai:vasylyk.v-b"Sytnyk, D. O."https://zbmath.org/authors/?q=ai:sytnyk.d-o"Komashchenko, N. O."https://zbmath.org/authors/?q=ai:komashchenko.n-oSummary: An exponentially convergent method is constructed for approximate solution of the boundary value problem for the convection-diffusion equation which describes the process of propagation of pollution from moving sources of emission. The method is based on the representation of the solution by means of fundamental solutions and Sinc-quadrature formulas. The test calculations were conducted to simulate the spread of air pollution during the take-off of an airplane.Study on weak solution and strong solution of incompressible MHD equations with damping in three-dimensional systems.https://zbmath.org/1449.351652021-01-08T12:24:00+00:00"Li, Kai"https://zbmath.org/authors/?q=ai:li.kai"Yang, Han"https://zbmath.org/authors/?q=ai:yang.han"Wang, Fan"https://zbmath.org/authors/?q=ai:wang.fanSummary: In this paper, the Cauchy problem of the MHD equations with damping is studied. When \(\beta \ge 1\) and initial data satisfy \({u_0}, {b_0} \in {L^2}\left(\mathbb{R}^3\right)\), the Galerkin method is used to prove the global weak solution of the equations. When the initial data satisfy \({u_0} \in H_0^1 \cap {L^{\beta + 1}}\left(\mathbb{R}^3\right), {b_0} \in H_0^1\left(\mathbb{R}^3\right)\), it is possible to obtain a unique local strong solution for the equation group.On gas flow beyond strong shock wave front, form of which approaches a certain curve.https://zbmath.org/1449.760312021-01-08T12:24:00+00:00"Bogatko, V. I."https://zbmath.org/authors/?q=ai:bogatko.v-i"Kolton, G. A."https://zbmath.org/authors/?q=ai:kolton.g-a"Potekhina, E. A."https://zbmath.org/authors/?q=ai:potekhina.e-a|potekhina.elena-aSummary: The plane auto model problem of the in viscid gas motion beyond intensive shock wave is studied. It is supposed, that shock wave front approaches some curve, the form of which is known. Solution is constructed in the form of series on the small parameter degrees. This parameter characterizes the relation of gas densities at shock wave front. Certain cases are studied as examples: when intensive shock wave front form is closely approximated to the straight line or to the circle. Solution of the problem is reduced to the Euler-Darboux equation integration.Parameter estimation in the stochastic superparameterization of two-layer quasigeostrophic flows. Estimation of subgrid-scale modeling parameters in the stochastic superparameterization of two-layer quasigeostrophic turbulence.https://zbmath.org/1449.760292021-01-08T12:24:00+00:00"Lee, Yoonsang"https://zbmath.org/authors/?q=ai:lee.yoonsangSummary: Geophysical turbulence has a wide range of spatiotemporal scales that requires a multiscale prediction model for efficient and fast simulations. Stochastic parameterization is a class of multiscale methods that approximates the large-scale behaviors of the turbulent system without relying on scale separation. In the stochastic parameterization of unresolved subgrid-scale dynamics, there are several modeling parameters to be determined by tuning or fitting to data. We propose a strategy to estimate the modeling parameters in the stochastic parameterization of geostrophic turbulent systems. The main idea of the proposed approach is to generate data in a spatiotemporally local domain and use physical/statistical information to estimate the modeling parameters. In particular, we focus on the estimation of modeling parameters in the stochastic superparameterization, a variant of the stochastic parameterization framework, for an idealized model of synoptic scale turbulence in the atmosphere and oceans. The test regimes considered in this study include strong and moderate turbulence with complicated patterns of waves, jets, and vortices.