Recent zbMATH articles in MSC 86https://zbmath.org/atom/cc/862022-11-17T18:59:28.764376ZUnknown authorWerkzeugExistence and Ulam-Hyers stability of positive solutions for a nonlinear model for the antarctic circumpolar currenthttps://zbmath.org/1496.340482022-11-17T18:59:28.764376Z"Fečkan, Michal"https://zbmath.org/authors/?q=ai:feckan.michal"Li, Qixiang"https://zbmath.org/authors/?q=ai:li.qixiang"Wang, JinRong"https://zbmath.org/authors/?q=ai:wang.jinrongAuthors' abstract: In this paper, we study the existence of positive solutions for the nonlinear model of the antarctic circumpolar current and analyze their Ulam-Hyers stability. By introducing some conditions on the ocean nonlinear vorticity function depending on other functions and initial values, we establish sufficient conditions to guarantee the existence, multiplicity, location and construction of positive solutions via the approach of fixed point theorem in cones, upper and lower solutions, and monotone method, respectively. Finally, we show the existence and uniqueness and Ulam-Hyers stability of positive solutions when the ocean nonlinear vorticity function has uniformly Lipschitz continuity.
Reviewer: Hanying Feng (Shijiazhuang)Continuum covariance propagation for understanding variance loss in advective systemshttps://zbmath.org/1496.352502022-11-17T18:59:28.764376Z"Gilpin, Shay"https://zbmath.org/authors/?q=ai:gilpin.shay"Matsuo, Tomoko"https://zbmath.org/authors/?q=ai:matsuo.tomoko"Cohn, Stephen E."https://zbmath.org/authors/?q=ai:cohn.stephen-eConstant vorticity water flows in the modified equatorial \(\beta\)-plane approximationhttps://zbmath.org/1496.353022022-11-17T18:59:28.764376Z"Miao, Fahe"https://zbmath.org/authors/?q=ai:miao.fahe"Fečkan, Michal"https://zbmath.org/authors/?q=ai:feckan.michal"Wang, JinRong"https://zbmath.org/authors/?q=ai:wang.jinrongSummary: In this paper, we study three-dimensional equatorial flows with constant vorticity beneath a wave train and above a flat bed in the modified \(\beta\)-plane approximation. It is proved that the equatorial flow is necessarily irrotational and the free surface is necessarily flat if it exhibits a constant vorticity, due to the incorporation of a gravitational-correction term in the tangent plane approximation.Global solution of anisotropic quasi-geostrophic equations in Sobolev spacehttps://zbmath.org/1496.354162022-11-17T18:59:28.764376Z"Amara, Mustapha"https://zbmath.org/authors/?q=ai:amara.mustapha"Benameur, Jamel"https://zbmath.org/authors/?q=ai:benameur.jamelSummary: In [9], the author proved the global existence of the two-dimensional anisotropic quasi-geostrophic equations with condition on the parameters \(\alpha\), \(\beta\) in the Sobolev spaces \(H^s(\mathbb{R}^2)\); \(s \geq 2\). In this paper, we show that these equations have a global solution in the spaces \(H^s(\mathbb{R}^2)\), where \(\max \{2 - 2 \alpha, 2 - 2 \beta \} < s < 2\), with additional condition over \(\alpha\) and \(\beta \). The proof is based on the Gevrey-class regularity of the solution in neighborhood of zero.Fractional convection-dispersion equation with conformable derivative approachhttps://zbmath.org/1496.354212022-11-17T18:59:28.764376Z"Chaudhary, Manish"https://zbmath.org/authors/?q=ai:chaudhary.manish"Kumar, Rohit"https://zbmath.org/authors/?q=ai:kumar.rohit"Singh, Mritunjay Kumar"https://zbmath.org/authors/?q=ai:singh.mritunjay-kumarSummary: In this present work, a well-structured and limit-based derivative definition of fractional derivative term, known as conformable derivative, is employed to develop a local generalized form of time variable fractional convection-dispersion equation (FCDE). The fractional models of convection-dispersion equation have been widely established as more authentic mode to characterize the pollutant transport in geological structures. In this work, models are formulated corresponding to spatial dependency of velocity and dispersion coefficient and also for the temporally varying decay rate, that dealt with more realistic phenomenon of the pollutant transport in groundwater reservoir. Due to the non-linearity of the problem, homotopy analysis method (HAM) is adopted to investigate the complex solutions of FCDE. As the FCDE comprises the classical convection-dispersion equation (CDE) as a special case corresponding to the fractional order \(\alpha=1\), so the obtained solutions are validated by the corresponding numerical solution and exact analytical solution for \(\alpha=1\) and solutions are also verified for different fractional values of \(\alpha\). The effect of conformable derivative order \(\alpha\) is properly visible over concentration strength. Hence, this investigation helps to interpret the accurate description of time dependent behaviour of contaminant transport in porous structure.On weak martingale solutions to a stochastic Allen-Cahn-Navier-Stokes model with inertial effectshttps://zbmath.org/1496.354662022-11-17T18:59:28.764376Z"Medjo, T. Tachim"https://zbmath.org/authors/?q=ai:tachim-medjo.theodoreSummary: We consider a stochastic Allen-Cahn-Navier-Stokes equations with inertial effects in a bounded domain \(D\subset\mathbb{R}^d\), \(d = 2, 3\), driven by a multiplicative noise. The existence of a global weak martingale solution is proved under non-Lipschitz assumptions on the coefficients. The construction of the solution is based on the Faedo-Galerkin approximation, compactness method and the Skorokhod representation theorem.Conditional density estimation and simulation through optimal transporthttps://zbmath.org/1496.620682022-11-17T18:59:28.764376Z"Tabak, Esteban G."https://zbmath.org/authors/?q=ai:tabak.esteban-g"Trigila, Giulio"https://zbmath.org/authors/?q=ai:trigila.giulio"Zhao, Wenjun"https://zbmath.org/authors/?q=ai:zhao.wenyunSummary: A methodology to estimate from samples the probability density of a random variable \(x\) conditional to the values of a set of covariates \(\{z_l\}\) is proposed. The methodology relies on a data-driven formulation of the Wasserstein barycenter, posed as a minimax problem in terms of the conditional map carrying each sample point to the barycenter and a potential characterizing the inverse of this map. This minimax problem is solved through the alternation of a flow developing the map in time and the maximization of the potential through an alternate projection procedure. The dependence on the covariates \(\{z_l\}\) is formulated in terms of convex combinations, so that it can be applied to variables of nearly any type, including real, categorical and distributional. The methodology is illustrated through numerical examples on synthetic and real data. The real-world example chosen is meteorological, forecasting the temperature distribution at a given location as a function of time, and estimating the joint distribution at a location of the highest and lowest daily temperatures as a function of the date.Semiparametric Bayesian forecasting of spatiotemporal earthquake occurrenceshttps://zbmath.org/1496.621982022-11-17T18:59:28.764376Z"Ross, Gordon J."https://zbmath.org/authors/?q=ai:ross.gordon-j"Kolev, Aleksandar A."https://zbmath.org/authors/?q=ai:kolev.aleksandar-aSummary: The Epidemic Type Aftershock Sequence (ETAS) model is a self-exciting point process which is used to model and forecast the occurrence of earthquakes in a geographical region. The ETAS model assumes that the occurrence of mainshock earthquakes follows an inhomogeneous spatial point process, with their aftershock earthquakes modelled via a separate triggering kernel. Most previous studies of the ETAS model have relied on point estimates of the model parameters, due to the complexity of the likelihood function and the difficulty in estimating an appropriate spatial mainshock distribution. In order to take estimation uncertainty into account, we instead propose a fully Bayesian formulation of the ETAS model, which uses a nonparametric Dirichlet process mixture prior to capture the spatial mainshock process, and show how efficient parameter inference can be carried out using auxiliary latent variables. We demonstrate how our model can be used for medium-term earthquake forecasts in a number of geographical regions.Distributed quasi-Newton derivative-free optimization method for optimization problems with multiple local optimahttps://zbmath.org/1496.650692022-11-17T18:59:28.764376Z"Gao, Guohua"https://zbmath.org/authors/?q=ai:gao.guohua"Wang, Yixuan"https://zbmath.org/authors/?q=ai:wang.yixuan"Vink, Jeroen C."https://zbmath.org/authors/?q=ai:vink.jeroen-c"Wells, Terence J."https://zbmath.org/authors/?q=ai:wells.terence-j"Saaf, Fredrik J. F. E."https://zbmath.org/authors/?q=ai:saaf.fredrik-j-f-eSummary: The distributed Gauss-Newton (DGN) optimization method performs quite efficiently and robustly for history-matching problems with multiple best matches. However, this method is not applicable for generic optimization problems, e.g., life-cycle production optimization or well location optimization. This paper introduces a generalized form of the objective functions \(F(\boldsymbol{x}, \boldsymbol{y}(\boldsymbol{x})) = f(\boldsymbol{x})\) with both explicit variables \(\boldsymbol{x}\) and implicit variables (or simulated responses), \(\boldsymbol{y}(\boldsymbol{x})\). The split in explicit and implicit variables is such that partial derivatives of \(F(\boldsymbol{x}, \boldsymbol{y})\) with respect to both \(\boldsymbol{x}\) and \(\boldsymbol{y}\) can be computed analytically. An ensemble of quasi-Newton optimization threads is distributed among multiple high-performance-computing (HPC) cluster nodes. The simulation results generated from one optimization thread are shared with others by updating a common set of training data points, which records simulated responses of all simulation jobs. The sensitivity matrix at the current best solution of each optimization thread is approximated by the linear-interpolation method. The gradient of the objective function is then analytically computed using its partial derivatives with respect to \(\boldsymbol{x}\) and \(\boldsymbol{y}\) and the estimated sensitivities of \(\boldsymbol{y}\) with respect to \(\boldsymbol{x}\). The Hessian is updated using the quasi-Newton formulation. A new search point for each distributed optimization thread is generated by solving a quasi-Newton trust-region subproblem (TRS) for the next iteration. The proposed distributed quasi-Newton (DQN) method is first validated on a synthetic history matching problem and its performance is found to be comparable with the DGN optimizer. Then, the DQN method is tested on a variety of optimization problems. For all test problems, the DQN method can find multiple optima of the objective function with reasonably small numbers of iterations.Chaotic behavior in fractional Helmholtz and Kelvin-Helmholtz instability problems with Riesz operatorhttps://zbmath.org/1496.651252022-11-17T18:59:28.764376Z"Owolabi, Kolade M."https://zbmath.org/authors/?q=ai:owolabi.kolade-matthew"Gómez-Aguilar, J. F."https://zbmath.org/authors/?q=ai:gomez-aguilar.jose-francisco"Karaca, Yeliz"https://zbmath.org/authors/?q=ai:karaca.yeliz"Li, Yong-Min"https://zbmath.org/authors/?q=ai:li.yongmin"Saleh, Bahaa"https://zbmath.org/authors/?q=ai:saleh.bahaa-e-a"Aly, Ayman A."https://zbmath.org/authors/?q=ai:aly.ayman-aA fully-implicit parallel framework for complex reservoir simulation with mimetic finite difference discretization and operator-based linearizationhttps://zbmath.org/1496.651982022-11-17T18:59:28.764376Z"Li, Longlong"https://zbmath.org/authors/?q=ai:li.longlong"Abushaikha, Ahmad"https://zbmath.org/authors/?q=ai:abushaikha.ahmad-sSummary: As the main way to reproduce flow response in subsurface reservoirs, the reservoir simulation could drastically assist in reducing the uncertainties in the geological characterization and in optimizing the field development strategies. However, the challenges in providing efficient and accurate solutions for complex field cases constrain further utilization of this technology. In this work, we develop a new reservoir simulation framework based on advanced spatial discretization and linearization schemes, the mimetic finite difference (MFD) and operator-based linearization (OBL), for fully implicit temporal discretization. The MFD has gained some popularity lately since it was developed to solve for unstructured grids and full tensor properties while mimicking the fundamental properties of the system (i.e. conservation laws, solution symmetries, and the fundamental identities and theorems of vector and tensor calculus). On the other hand, in the OBL the mass-based formulations are written in an operator form where the parametric space of the unknowns is treated in a piece-wise manner for the linearization process. Moreover, the values of these operators are usually precomputed into a nodal tabulation and with the implementation of multi-linear interpolation, the values of these operators and their derivatives during a simulation run can be determined in an efficient way for the Jacobian assembly at any time-step. This saves computational time during complex phase behavior computations. By first coupling these two schemes within a parallel framework, we can solve large and complex reservoir simulation problems in an efficient manner. Finally, we present a benchmark case that compares the numerical solutions to a Buckley-Leverett analytical solution to assure their accuracy and convergence. Moreover, we test three challenging field cases to demonstrate the performance of the advanced parallel framework for complex reservoir simulation.Mathematical tools for the seismic analysis of reinforced concrete structures: a selected reviewhttps://zbmath.org/1496.740432022-11-17T18:59:28.764376Z"Demartino, Cristoforo"https://zbmath.org/authors/?q=ai:demartino.cristoforo"Zhou, Sicheng"https://zbmath.org/authors/?q=ai:zhou.sichengSummary: Response spectrum analysis represents the preferential strategy to analyze and design civil engineering structures subjected to seismic actions. Nevertheless, most structural codes were developed by following hand computation-oriented philosophies so that their prescriptions can be hard to be implemented in finite element frameworks and often prevent the use of innovative strategies. This contribution presents a review of innovative tools focused on reinforced concrete framed structures aiming to establish a possible organic workflow for design procedures. Some pivotal issues typical of such a structural typology are hereby addressed, and particularly, global torsion and capacity checks in the presence of axial force-biaxial bending responses. This has been done by correlating innovative solutions such as torsional spectra, seismic envelopes, and limit analysis and by presenting a numerical procedure capable of performing capacity checks of reinforced concrete cross sections. The presented strategy aims to be a computationally efficient and exhaustive procedure to be used within the framework of finite element analysis.
For the entire collection see [Zbl 1478.74002].The effect of contact conditions on the performance of flexural seismic metasurfaceshttps://zbmath.org/1496.741012022-11-17T18:59:28.764376Z"Alzaidi, Ahmed S. M."https://zbmath.org/authors/?q=ai:alzaidi.ahmed-s-m"Kaplunov, Julius"https://zbmath.org/authors/?q=ai:kaplunov.julius-d"Prikazchikova, Ludmila"https://zbmath.org/authors/?q=ai:prikazchikova.ludmila"Wootton, Peter"https://zbmath.org/authors/?q=ai:wootton.peter-t"Nikonov, Anatolij"https://zbmath.org/authors/?q=ai:nikonov.anatolijSummary: Plane-strain motion of a flexural seismic metasurface in the form of a regular array of thin Kirchhoff plates attached to the surface of an elastic half-space is analysed. Two types of contact conditions, including simply supported plates and plates moving along horizontal rails are studied. Dispersion of time harmonic waves is investigated both asymptotically and numerically. A major effect of the contact conditions on metasurface behaviour is discovered. In particular, it is shown that frequency band gaps are not the feature of the array composed of simply supported plates. It is also demonstrated that the scaling laws, expressed through geometric and material problem parameters, drastically differ from each other for two considered setups.A multi-domain IBEM for the wave scattering and diffraction of P- and SV-waves by complex local siteshttps://zbmath.org/1496.741212022-11-17T18:59:28.764376Z"Ba, Zhenning"https://zbmath.org/authors/?q=ai:ba.zhenning"Yu, Zhiying"https://zbmath.org/authors/?q=ai:yu.zhiying"Wang, Ying"https://zbmath.org/authors/?q=ai:wang.ying.6|wang.ying.3|wang.ying.2|wang.ying.5|wang.ying|wang.ying.8|wang.ying.1|wang.ying.4(no abstract)Mathematical introduction to geophysical fluid dynamics. Paper from the 31st Brazilian mathematics colloquium -- 31\(^{\text o}\) Colóquio Brasileiro de Matemática, IMPA, Rio de Janeiro, Brazil, July 30 -- August 5, 2017https://zbmath.org/1496.760022022-11-17T18:59:28.764376Z"Raphaldini, Breno"https://zbmath.org/authors/?q=ai:raphaldini.breno"Raupp, Carlos F. M."https://zbmath.org/authors/?q=ai:raupp.carlos-f-m"da Silva Dias, Pedro Leite"https://zbmath.org/authors/?q=ai:da-silva-dias.pedro-leite(no abstract)Three-dimensional surface gravity waves of a broad bandwidth on deep waterhttps://zbmath.org/1496.760312022-11-17T18:59:28.764376Z"Li, Yan"https://zbmath.org/authors/?q=ai:li.yan.16Summary: A new nonlinear Schrödinger equation (NLSE) is presented for ocean surface waves. Earlier derivations of NLSEs that describe the evolution of deep-water waves have been limited to a narrow bandwidth, for which the bound waves at second order in wave steepness are described in leading-order approximations. This work generalizes these earlier works to allow for deep-water waves of a broad bandwidth with large directional spreading. The new NLSE permits simple numerical implementations and can be extended in a straightforward manner in order to account for waves on water of finite depth. For the description of second-order waves, this paper proposes a semianalytical approach that can provide accurate and computationally efficient predictions. With a leading-order approximation to the new NLSE, the instability region and energy growth rate of Stokes waves are investigated. Compared with the exact results based on [\textit{J. W. McLean}, J. Fluid Mech. 114, 315--330 (1982; Zbl 0483.76027)], predictions by the new NLSE show better agreement than by \textit{K. Trulsen} et al. [Phys. Fluids 12, No. 10, Paper No. 2432, 6 p. (2000; Zbl 1184.76558)]. With numerical implementations of the new NLSE, the effects of wave directionality are investigated by examining the evolution of a directionally spread focused wave group. A downward shift of the spectral peak is observed, owing to the asymmetry in the change rate of energy in a more complex manner than that for uniform Stokes waves. Rapid oblique energy transfers near the group at linear focus are observed, likely arising from the instability of uniform Stokes waves appearing in a narrow spectrum subject to oblique sideband disturbances.Quantification of wave attenuation in mangroves in Manila Bay using nonlinear shallow water equationshttps://zbmath.org/1496.760322022-11-17T18:59:28.764376Z"Magdalena, Ikha"https://zbmath.org/authors/?q=ai:magdalena.ikha"La'lang, Raynaldi"https://zbmath.org/authors/?q=ai:lalang.raynaldi"Mendoza, Renier"https://zbmath.org/authors/?q=ai:mendoza.renier-gSummary: In this paper, we investigate the wave attenuation by mangroves using modified 2D Nonlinear Shallow Water Equations. Numerically, we solve the model using a staggered finite volume method that is free from damping error. Further, several benchmark tests are performed to show the robustness of our numerical model. Then, we implement our numerical model to investigate the effects of mangroves in the wave attenuation caused by tsunamis in Manila Bay. The bathymetry profile of Manila Bay used in this study is obtained from the General Bathymetric Chart of the Oceans (GEBCO). Numerical results show that the presence of mangroves can reduce ocean waves near the coast. Simulations on varying density and width of mangrove forest quantify how much the tsunami wave height can be reduced. The results of this work may guide the policymakers of the Philippines in deciding the best strategy in rehabilitating Manila Bay.Fractal-like actuator disc theory for optimal energy extractionhttps://zbmath.org/1496.760372022-11-17T18:59:28.764376Z"Dehtyriov, D."https://zbmath.org/authors/?q=ai:dehtyriov.daniel"Schnabl, A. M."https://zbmath.org/authors/?q=ai:schnabl.a-m"Vogel, C. R."https://zbmath.org/authors/?q=ai:vogel.christopher-r"Draper, S."https://zbmath.org/authors/?q=ai:draper.scott"Adcock, T. A. A."https://zbmath.org/authors/?q=ai:adcock.thomas-a-a"Willden, R. H. J."https://zbmath.org/authors/?q=ai:willden.richard-h-jSummary: The limit of power extraction by a device which makes use of constructive interference, i.e. local blockage, is investigated theoretically. The device is modelled using actuator disc theory in which we allow the device to be split into arrays and these then into sub-arrays an arbitrary number of times so as to construct an \(n\)-level multi-scale device in which the original device undergoes \(n-1\) sub-divisions. The alternative physical interpretation of the problem is a planar system of arrayed turbines in which groups of turbines are homogeneously arrayed at the smallest \(n\text{th}\) scale, and then these groups are homogeneously spaced relative to each other at the next smallest \(n-1\)th scale, with this pattern repeating at all subsequent larger scales. The scale-separation idea of \textit{T. Nishino} and \textit{R. H. J. Willden} [J. Fluid Mech. 708, 596--606 (2012; Zbl 1275.76045)] is employed, which assumes mixing within a sub-array occurs faster than mixing of the by-pass flow around that sub-array, so that in the \(n\)-scale device mixing occurs from the inner scale to the outermost scale in that order. We investigate the behaviour of an arbitrary level multi-scale device, and determine the arrangement of actuator discs (\(n\)th level devices) which maximises the power coefficient (ratio of power extracted to undisturbed kinetic energy flux through the net disc frontal area). We find that this optimal arrangement is close to fractal, and fractal arrangements give similar results. With the device placed in an infinitely wide channel, i.e. zero global blockage, we find that the optimum power coefficient tends to unity as the number of device scales tends to infinity, a 27/16 increase over the Lanchester-Betz limit of 0.593. For devices in finite width channels, i.e. non-zero global blockage, similar observations can be made with further uplift in the maximum power coefficient. We discuss the fluid mechanics of this energy extraction process and examine the scale distribution of thrust and wake velocity coefficients. Numerical demonstration of performance uplift due to multi-scale dynamics is also provided. We demonstrate that bypass flow remixing and ensuing energy losses increase the device power coefficient above the limits for single devices, so that although the power coefficient can be made to increase, this is at the expense of the overall efficiency of energy extraction which decreases as wake-scale remixing losses necessarily rise. For multi-scale devices in finite overall blockage two effects act to increase extractable power; an overall streamwise pressure gradient associated with finite blockage, and wake pressure recoveries associated with bypass-scale remixing.Boussinesq and non-Boussinesq gravity currents propagating on unbounded uniform slopes in the deceleration phasehttps://zbmath.org/1496.760482022-11-17T18:59:28.764376Z"Dai, Albert"https://zbmath.org/authors/?q=ai:dai.albert"Huang, Yu-Lin"https://zbmath.org/authors/?q=ai:huang.yulinSummary: Boussinesq and non-Boussinesq gravity currents produced from a finite volume of heavy fluid propagating into an environment of light ambient fluid on unbounded uniform slopes in the range \(0^\circ \leq \theta \leq 12^\circ\) are reported. The relative density difference \(\epsilon = (\rho_1-\rho_0)/\rho_0\) is varied in the range \(0.05 \leq \epsilon \le 0.15\) in this study, where \(\rho_1\) and \(\rho_0\) are the densities of the heavy and light ambient fluids, respectively. Our focus is on the influence of the relative density difference on the deceleration phase of the propagation. In the early deceleration phase, the front location history follows the power relationship \((x_f+x_0)^2 = (K_I B)^{1/2} (t+t_I)\), where \((x_f+x_0)\) is the front location measured from the virtual origin, \(K_I\) an experimental constant, \(B\) the total buoyancy, \(t\) the time and \(t_I\) the \(t\) intercept. The dimensionless constant \(K_I\) is influenced by the slope angle and the relative density difference. In the late deceleration phase for the gravity currents on the steeper slopes in this study \((12^\circ, 9^\circ\) and \(6^\circ)\), an `active' head separates from the body of the current and the front location history follows the power relationship \((x_f+x_0)^{8/3} = K_{VS} B^{2/3} V^{2/9}_0 \nu^{-1/3} (t+t_{VS})\), where \(K_{VS}\) is an experimental constant, \(V_0\) the total volume of heavy fluid, \(\nu\) the kinematic viscosity of fluid and \(t_{VS}\) the \(t\) intercept. The dimensionless constant \(K_{VS}\) is shown to be influenced by the slope angle but not significantly influenced by the relative density difference. In the late deceleration phase for the gravity currents on the milder slopes in this study \((3^\circ\) and \(0^\circ)\), the gravity currents maintain an integrated shape without violent mixing with the ambient fluid and the front location history follows the power relationship \((x_f+x_0)^4 = K_{VM} B^{2/3} V^{2/3}_0 \nu^{-1/3} (t+t_{VM})\), where \(K_{VM}\) is an experimental constant and \(t_{VM}\) the \(t\) intercept. The dimensionless constant \(K_{VM}\) is shown to be influenced by both the slope angle and the relative density difference. While the influence of the relative density difference on \(K_{VM}\) is carried along for the gravity currents on the milder slopes in the late deceleration phase, the relative density difference interestingly has no significant influence on \(K_{VS}\) for the gravity currents on the steeper slopes in the late deceleration phase. Our results suggest that the non-Boussinesq gravity currents on the milder slopes may remain non-Boussinesq ones in the late deceleration phase while the non-Boussinesq gravity currents on the steeper slopes may have become Boussinesq ones in the late deceleration phase.A linear stability analysis of two-layer moist convection with a saturation interfacehttps://zbmath.org/1496.760622022-11-17T18:59:28.764376Z"Fu, Hao"https://zbmath.org/authors/?q=ai:fu.haoSummary: The linear convective instability of a mixture of dry air, water vapour and liquid water, with a stable unsaturated layer residing on an unstable saturated layer, is studied. It may serve as a prototype model for understanding the instability that causes mixing at the top of stratocumulus cloud or fog. Such a cloud-clear air interface is modelled as an infinitely thin saturation interface where radiative and evaporative cooling take place. The interface position is determined by the Clausius-Clapeyron equation, and can undulate with the evolution of moisture and temperature. In the small-amplitude regime two physical mechanisms are revealed. First, the interface undulation leads to the undulation of the cooling source, which destabilizes the system by superposing a vertical dipole heating anomaly on the convective cell. Second, the evolution of the moisture field induces non-uniform evaporation at the interface, which stabilizes the system by introducing a stronger evaporative cooling in the ascending region and \textit{vice versa} in the descending region. These two mechanisms are competing, and their relative contribution to the instability is quantified by theoretically estimating their relative contribution to buoyancy flux tendency. When there is only evaporative cooling, the two mechanisms break even, and the marginal stability curve remains the same as the classic two-layer Rayleigh-Bénard convection with a fixed cooling source.Performance and wake characteristics of tidal turbines in an infinitely large arrayhttps://zbmath.org/1496.760702022-11-17T18:59:28.764376Z"Ouro, Pablo"https://zbmath.org/authors/?q=ai:ouro.pablo"Nishino, Takafumi"https://zbmath.org/authors/?q=ai:nishino.takafumiSummary: The efficiency of tidal stream turbines in a large array depends on the balance between negative effects of turbine-wake interactions and positive effects of bypass-flow acceleration due to local blockage, both of which are functions of the layout of turbines. In this study we investigate the hydrodynamics of turbines in an infinitely large array with aligned or staggered layouts for a range of streamwise and lateral turbine spacing. First, we present a theoretical analysis based on an extension of the linear momentum actuator disc theory for perfectly aligned and staggered layouts, employing a hybrid inviscid-viscous approach to account for the local blockage effect within each row of turbines and the viscous (turbulent) wake mixing behind each row in a coupled manner. We then perform large-eddy simulation (LES) of open-channel flow for 28 layouts of tidal turbines using an actuator line method with doubly periodic boundary conditions. Both theoretical and LES results show that the efficiency of turbines (or the power of turbines for a given bulk velocity) in an aligned array decreases as we reduce the streamwise turbine spacing, whereas that in a staggered array remains high and may even increase due to the positive local blockage effect (causing the local flow velocity upstream of each turbine to exceed the bulk velocity) if the lateral turbine spacing is sufficiently small. The LES results further reveal that the amplitude of wake meandering tends to decrease as we reduce the lateral turbine spacing, which leads to a lower wake recovery rate in the near-wake region. These results will help to understand and improve the efficiency of tidal turbines in future large arrays, even though the performance of real tidal arrays may depend not only on turbine-to-turbine interactions within the array but also on macro-scale interactions between the array and natural tidal currents, the latter of which are outside the scope of this study.Data assimilation of water elevation in shallow water flow based on the extended Kalman filter FEM using measurement data from image analysishttps://zbmath.org/1496.760852022-11-17T18:59:28.764376Z"Kurahashi, Takahiko"https://zbmath.org/authors/?q=ai:kurahashi.takahiko"Ikarashi, Kohei"https://zbmath.org/authors/?q=ai:ikarashi.kohei"Kenchi, Toshiaki"https://zbmath.org/authors/?q=ai:kenchi.toshiaki"Eto, Toshihiko"https://zbmath.org/authors/?q=ai:eto.toshihikoSummary: In this paper, we present a data assimilation analysis in a shallow water flow field considering shoreline movement, based on the extended Kalman filter finite element method (extended Kalman filter FEM). It is known that if the combined method of the Kalman filter and the finite element method (FEM) is employed, a solution can be obtained that is closer to the practical observed value than that based on normal FEM. A dam-break problem is targeted in numerical experiments. In this study, the observed values used in the extended Kalman filter FEM are obtained by image analysis, and we investigate the estimation accuracy by changing the governing equation for shallow water flow.A multi-timestep Dirichlet-Neumann domain decomposition method applied to the polymer injection in porous mediahttps://zbmath.org/1496.760882022-11-17T18:59:28.764376Z"Tavares, Rodrigo S."https://zbmath.org/authors/?q=ai:tavares.rodrigo-s"Santos, Renatha B."https://zbmath.org/authors/?q=ai:santos.renatha-b"Lima, Sidarta A."https://zbmath.org/authors/?q=ai:lima.sidarta-araujo"dos Santos, Adriano"https://zbmath.org/authors/?q=ai:dos-santos.adriano"Klein, Viviane"https://zbmath.org/authors/?q=ai:klein.vivianeSummary: The study of polymer flooding is of utmost relevance due to the diversity of applications. This paper proposes an innovative mathematical and computational model for polymer flooding that efficiently couples the process in the near-well region and the reservoir. For the mathematical model, in addition to the single-phase flow and transport equations, we postulate closure relationships for the adsorption isotherms, mechanical retention kinetics, and non-Newtonian pseudoplastic behavior. For the computational model, we propose a space-time domain decomposition method based on a predictor-corrector strategy. The resulting system of equations is discretized by the finite element method and linearized by the Newton-Raphson method. Moreover, we apply a consistent flux method to obtain the flow at the boundaries and quantify the injectivity ratio. Then, we validate the accuracy of the proposed method by comparing the discrete solutions with analytical and high-fidelity solutions. We also discuss the loss of injectivity due to the non-Newtonian behavior, mechanical retention, and formation damage at 2D and 3D domains that replicate a five-spot injection pattern. The numerical simulations show that the proposed computational model accurately captures the solutions with low computational costs in several scenarios for polymer injection in porous media.Convergence of single rate and multirate undrained split iterative schemes for a fractured Biot modelhttps://zbmath.org/1496.761312022-11-17T18:59:28.764376Z"Almani, T."https://zbmath.org/authors/?q=ai:almani.tameem"Kumar, K."https://zbmath.org/authors/?q=ai:kumar.kundanSummary: This paper considers a coupled flow and mechanics problem in a fractured poro-elastic medium. The fracture geometry is explicitly treated as a possibly non-planar interface. The model equations are of mixed dimensional type where the flow equation on a \(d - 1\) dimensional fracture surface is coupled to a \(d\) dimensional porous matrix. An extension of the widely used undrained split iterative coupling scheme to the fractured poro-elastic media is performed. The particularity is in the time-discretization where both the single rate scheme in which flow and mechanics share the exact same time step, and the multirate scheme in which flow takes multiple fine time steps within one coarse mechanics time step. In the coupled model considered here, the fracture flow model is a lubrication-type system [\textit{V. Girault} et al., Math. Models Methods Appl. Sci. 25, No. 4, 587--645 (2015; Zbl 1309.76194)] whereas in the porous matrix the linear quasi-static Biot equations are considered. Convergence analysis of the undrained split iterative scheme and Banach fixed-point contraction type results are obtained that establish the geometric convergence of the scheme and the uniqueness of the obtained solution.A numerical study of the additive Schwarz preconditioned exact Newton method (ASPEN) as a nonlinear preconditioner for immiscible and compositional porous media flowhttps://zbmath.org/1496.761332022-11-17T18:59:28.764376Z"Klemetsdal, Øystein"https://zbmath.org/authors/?q=ai:klemetsdal.oystein-strengehagen"Moncorgé, Arthur"https://zbmath.org/authors/?q=ai:moncorge.arthur"Møyner, Olav"https://zbmath.org/authors/?q=ai:moyner.olav"Lie, Knut-Andreas"https://zbmath.org/authors/?q=ai:lie.knut-andreasSummary: Domain decomposition methods are widely used as preconditioners for Krylov subspace linear solvers. In the simulation of porous media flow there has recently been a growing interest in nonlinear preconditioning methods for Newton's method. In this work, we perform a numerical study of a spatial additive Schwarz preconditioned exact Newton (ASPEN) method as a nonlinear preconditioner for Newton's method applied to both fully implicit or sequential implicit schemes for simulating immiscible and compositional multiphase flow. We first review the ASPEN method and discuss how the resulting linearized global equations can be recast so that one can use standard preconditioners developed for the underlying model equations. We observe that the local fully implicit or sequential implicit updates efficiently handle the local nonlinearities, whereas long-range interactions are resolved by the global ASPEN update. The combination of the two updates leads to a very competitive algorithm. We illustrate the behavior of the algorithm for conceptual one and two-dimensional cases, as well as realistic three dimensional models. A complexity analysis demonstrates that Newton's method with a fully implicit scheme preconditioned by ASPEN is a very robust and scalable alternative to the well-established Newton's method for fully implicit schemes.Application of diffuse source basis functions for improved near well upscalinghttps://zbmath.org/1496.761342022-11-17T18:59:28.764376Z"Liu, Ching-Hsien"https://zbmath.org/authors/?q=ai:liu.ching-hsien"Nunna, Krishna"https://zbmath.org/authors/?q=ai:nunna.krishna"King, Michael J."https://zbmath.org/authors/?q=ai:king.michael-jSummary: Near well flow can have a significant impact on the accuracy of the upscaling of geologic models. A recent benchmark study has shown that these errors may dominate over other aspects of upscaling in commercial reservoir simulators. This same study showed the advantage of ``Diffuse Source'' (DS) upscaling over previous approaches. We now demonstrate the application of the DS basis functions to the calculation of the upscaled well index and the well cell intercell transmissibilities. DS upscaling is an extension of pseudo-steady-state (PSS) flow based upscaling that utilizes the diffusive time of flight to distinguish well-connected and weakly-connected sub-volumes. DS upscaling retains the localization advantage of a PSS calculation: unlike steady state flow, the local upscaling problem does not couple to adjacent regions, and local-global iterations are not required. DS upscaling has been developed and utilized for the calculation of the intercell transmissibility, but we now apply it to the calculation of the upscaled well index. Consistent with other researchers, we adjust the intercell transmissibilities in the near well region. We also consider the upscaling of the well index for a reservoir model in which the well trajectory and the high resolution geologic model are not simultaneously available. For many practitioners, this remains the most common reservoir modeling workflow. The result is an algebraic well index upscaling calculation, which also improves upon commercial applications. The industry standard for the well index follows Peaceman. We show that PSS/DS upscaling reduces to Peaceman's well index on a coarse grid, and is consistent with Peaceman's numerical convergence analysis. (In contrast, steady state upscaling for the well index reduces to the Dietz well index.) The current approach is a generalization of Peaceman's well index, but now extended to represent near well reservoir heterogeneity and with the arbitrary placement of a well perforation within a simulation well cell. Consistent with steady state upscaling, we find an advantage in adjusting the intercell transmissibility in the near well region. However, we have found that it is only necessary to do so for the well cell itself, which may be a consequence of the improved localization of the current calculation. The new methodology performs very well. It is tested for two models, including the SPE10 reference model and the Amellago carbonate outcrop model. We compare the results to steady state flow based upscaling, the algebraic well index upscaling described above, and algorithms found in commercial applications.Effects of power-law entrainment on bubble fragmentation cascadeshttps://zbmath.org/1496.761372022-11-17T18:59:28.764376Z"Gaylo, Declan B."https://zbmath.org/authors/?q=ai:gaylo.declan-b"Hendrickson, Kelli"https://zbmath.org/authors/?q=ai:hendrickson.kelli"Yue, Dick K. P."https://zbmath.org/authors/?q=ai:yue.dick-k-pSummary: We consider the evolution of the bulk bubble-size distribution \(N(a,t)\) of large bubbles (Weber number \(We \gg 1)\) under free-surface entrainment described generally by an entrainment size distribution \(I(a)\) with power-law slope \(\gamma\) and large-radius cutoff \(a_{\max}\). Our main focus is the interaction between turbulence-driven fragmentation and free-surface entrainment, and, for simplicity, we ignore other mechanisms such as degassing, coalescence and dissolution. Of special interest are the equilibrium bulk distribution \(N_{eq}(a)\), with local power-law slope \(\tilde{\beta }_{eq}(a)\), and the time scale \(\tau_c\) to reach this equilibrium after initiation of entrainment. For bubble radii \(a\ll a_{\max}\), we find two regimes for the dependence of \(N_{eq}(a)\) on the entrainment distribution. There is a weak injection regime for \(\gamma \geq -4\), where \(\tilde{\beta}_{eq}(a)=-10/3\) independent of the entrainment distribution; and a strong injection regime for \(\gamma <-4\), where the power-law slope depends on \(\gamma\) and is given by \(\tilde{\beta}_{eq}(a)=\gamma +2/3\). The weak regime provides a general explanation for the commonly observed \(-10/3\) power law originally proposed by \textit{C. Garrett} et al. [``The connection between bubble size spectra and energy dissipation rates in the upper ocean'', J. Phys. Oceanogr. 30, No. 9, 2163--2171 (2000; \url{doi:10.1175/1520-0485(2000)030<2163:TCBBSS>2.0.CO;2})], and suggests that different weak entrainment mechanisms can all lead to this result. For \(a\sim a_{\max}\), we find that \(N_{eq}(a)\) exhibits a steepening deviation from a power law due to fragmentation and entrainment, similar to what has been observed, but here absent other mechanisms such as degassing. The evolution of \(N(a,t)\) to \(N_{eq}(a)\) is characterised by the critical time \(\tau_c \propto C_f \varepsilon^{-1/3} a_{\max}^{2/3}\), where \(\varepsilon\) is the turbulence dissipation rate and \(C_f\) is a new constant that quantifies the dependence on the daughter size distribution in a fragmentation event. For typical breaking waves, \( \tau_c\) can be quite small, limiting the time \(t\lesssim \tau_c\) when direct measurement of \(N(a,t)\) might provide information about the underlying entrainment size distribution.Computational fluid dynamics modelling of a transient solids concentration in a lagoonhttps://zbmath.org/1496.761442022-11-17T18:59:28.764376Z"Khan, Ashfaq A."https://zbmath.org/authors/?q=ai:khan.ashfaq-a"Ding, Yan"https://zbmath.org/authors/?q=ai:ding.yanSummary: Investigation of slurry flows is important for the mineral industry, biomass processing and waste processing. In the design of slurry handling systems such as channel flows, separators where solids concentrates are separated from clear liquid streams, knowledge of physics underlying slurry flows is required. In this study, slurry flows in tanks have been investigated. The transient profiles of the solids concentration along the length have been modelled using computational fluid dynamics (CFD). This investigation examines multiphase flows with settling solids in a non-Newtonian flow. The dynamical model gives guidance in determining formation accumulation of solids as a sludge blanket. In addition the clear liquid solids interface position has been determined this is needed for the recycle of the clear water for water conservation.
For the entire collection see [Zbl 1459.37002].A two-fluid model for immersed granular avalanches with dilatancy effectshttps://zbmath.org/1496.761522022-11-17T18:59:28.764376Z"Montellà, E. P."https://zbmath.org/authors/?q=ai:montella.eduard-puig"Chauchat, J."https://zbmath.org/authors/?q=ai:chauchat.julien"Chareyre, B."https://zbmath.org/authors/?q=ai:chareyre.bruno"Bonamy, C."https://zbmath.org/authors/?q=ai:bonamy.cyrille"Hsu, T. J."https://zbmath.org/authors/?q=ai:hsu.tian-jianSummary: When a deposited layer of granular material fully immersed in a liquid is suddenly inclined above a certain critical angle, it starts to flow down the slope. The initial dynamics of these underwater avalanches strongly depends on the initial volume fraction. If the granular bed is initially loose, i.e. looser than the critical state, the avalanche is triggered almost instantaneously and exhibits a strong acceleration, whereas for an initially dense granular bed, i.e. denser than the critical state, the avalanche's mobility remains low for some time before it starts flowing normally. This behaviour can be explained by a combination of geometrical granular dilatancy and pore pressure feedback on the granular media. In this contribution, a continuum formulation is presented and implemented in a three-dimensional continuum numerical model. The originality of the present model is to incorporate dilatancy as an elasto-plastic normal stress or pressure and not as a modification of the friction coefficient. This allows an explanation of the two different behaviours of initially loose and dense underwater avalanches. It also highlights the contribution from each depth-resolved variable in the strongly coupled transition to a flowing avalanche. The model compares favourably with existing experiments for the initiation of underwater granular avalanches. Results reveal the interplay between shear-induced changes of the granular stress and fluid pressure in the dynamics of avalanches. The characteristic time of the triggering phase is nearly independent of the local rheological parameters, whereas the initial drop in pore pressure and the surface velocity at steady state still strongly depend on them. Finally, the multidimensional capabilities of the model are illustrated for the two-dimensional Hele-Shaw configuration and some of the observed differences between one-dimensional simulations and experiments are clarified.Oceanic studies via a variable-coefficient nonlinear dispersive-wave system in the solar systemhttps://zbmath.org/1496.761602022-11-17T18:59:28.764376Z"Gao, Xin-Yi"https://zbmath.org/authors/?q=ai:gao.xinyi"Guo, Yong-Jiang"https://zbmath.org/authors/?q=ai:guo.yongjiang"Shan, Wen-Rui"https://zbmath.org/authors/?q=ai:shan.wenruiSummary: People pay attention to the oceans crossing the Solar System: the Earth, Enceladus and Titan. Hereby, on a variable-coefficient nonlinear dispersive-wave system for the shallow oceanic environment, (A) nonlinear-water-wave symbolic computation and Bell polynomials lead to two hetero-Bäcklund transformations and (B) nonlinear-water-wave symbolic computation gives rise to a similarity reduction, both depending on the variable coefficients representing the wave elevation and surface velocity of the water wave. This paper might be of some use for the future oceanic studies on the Solar System.Balanced ellipsoidal vortex equilibria in a background shear flow at finite Rossby numberhttps://zbmath.org/1496.761622022-11-17T18:59:28.764376Z"Mckiver, William J."https://zbmath.org/authors/?q=ai:mckiver.william-jSummary: We consider a uniform ellipsoid of potential vorticity (PV), where we exploit analytical solutions derived for a balanced model at the second order in the Rossby number, the next order to quasi-geostrophic (QG) theory, the so-called QG+1 model. We consider this vortex in the presence of an external background shear flow, acting as a proxy for the effect of external vortices. For the QG model the system depends on four parameters, the height-to-width aspect ratio of the vortex, \(h/r\), as well as three parameters characterising the background flow, the strain rate, \(\gamma\), the ratio of the background rotation rate to the strain, \(\beta\), and the angle from which the flow is applied, \(\theta\). However, the QG+1 model also depends on the PV, as well as the Prandtl ratio, \(f/N\) (\(f\) and \(N\) are the Coriolis and buoyancy frequencies, respectively). For QG and QG+1 we determine equilibria for different values of the background flow parameters for increasing values of the imposed strain rate up to the critical strain rate, \(\gamma_c\), beyond which equilibria do not exist. We also compute the linear stability of this vortex to second-order modes, determining the marginal strain \(\gamma_m\) at which ellipsoidal instability erupts. The results show that for QG+1 the most resilient cyclonic ellipsoids are slightly prolate, while anticyclonic ellipsoids tend to be more oblate. The highest values of \(\gamma_m\) occur as \(\beta \to 1\). For large values of \(f/N\), changes in the marginal strain rates occur, stabilising anticyclonic ellipsoids while destabilising cyclonic ellipsoids.Spectral analysis of small perturbations of geostrophic currents with a parabolic vertical profile of velocity as applied to the oceanhttps://zbmath.org/1496.761632022-11-17T18:59:28.764376Z"Skorokhodov, S. L."https://zbmath.org/authors/?q=ai:skorokhodov.sergey-l"Kuzmina, N. P."https://zbmath.org/authors/?q=ai:kuzmina.n-pSummary: The paper presents an analysis of stable and unstable perturbations of ocean currents of a finite transverse scale with a parabolic vertical profiles of velocity (Poiseuille-Couette-type flow), based on the potential vorticity equation in the quasi-geostrophic approximation and taking into account both linear and constant flow velocity shear. The model takes into account the effect of vertical diffusion of buoyancy and vertical friction and assumes that the maximum mean current velocity takes place at the boundary of the layer. The analysis is based on the small perturbation method. The problem depends on several physical parameters and reduces to solving a spectral non-self-adjoint problem for a fourth-order equation with a small parameter at the highest derivative. Asymptotic expansions of the eigenfunctions and eigenvalues are constructed for small values of the wavenumber \(k\). Using the method of continuation in the parameter \(k\), the trajectories of the eigenvalues are calculated for different values of the problem's physical parameters. A detailed analysis of how the features of the vertical flow structure influence the characteristics of stable and unstable perturbations is presented. It is shown that the phase velocities of unstable perturbations can vary significantly depending on the linear vertical shear of the flow velocity.The influence of environmental conditions on the biological availability and accumulation of \(^{137}Cs\) by wild-growing meadow grasses of the exclusion zonehttps://zbmath.org/1496.800102022-11-17T18:59:28.764376Z"Kalinichenko, S. A."https://zbmath.org/authors/?q=ai:kalinichenko.s-a"Nikitin, A. N."https://zbmath.org/authors/?q=ai:nikitin.a-n"Shurankova, O. A."https://zbmath.org/authors/?q=ai:shurankova.o-aSummary: The features of the influence of various environmental conditions on the biological availability and accumulation of \(^{137}Cs\) by meadow grasses of exclusion zone of the CNPP have been established. A decrease in the concentration of \(^{137}Cs\) in meadow grasses was found as the phytocenozes moved away from the epicenter of the accident, with a decrease in the quality indicators of the community (projective cover and physical condition of plants). The effect of soil agrochemical parameters, soil moisture content, and the ratio of radionuclide mobility forms in soil on the bioavailability of \(^{137}Cs\) was studied. The analysis of the soil-to-plant transfer factors \((C_f)\) and aggregated transfer factors \((T_{ag})\), the discrimination coefficient (DF) of \(^{137}Cs\) by a chemical analog element (potassium) was carried out. The species features of the plants associated with the transport of \(K^+-Cs^+\) cations make significant adjustments to the mechanisms of \(^{137}Cs\) accumulation.Slow migration of brine inclusions in first-year sea icehttps://zbmath.org/1496.800112022-11-17T18:59:28.764376Z"Kraitzman, Noa"https://zbmath.org/authors/?q=ai:kraitzman.noa"Promislow, Keith"https://zbmath.org/authors/?q=ai:promislow.keith"Wetton, Brian"https://zbmath.org/authors/?q=ai:wetton.brian-rThe authors propose a thermodynamically consistent system for a mixture of water, ice and salt in the 3D domain \(\Omega =[0,d_{0}]^{3}\) containing a brine inclusion. Introducing a gradient flow which conserves the internal energy, increases the entropy and conserves the total salt density, together with modifications of the entropy density, they end with the coupled system
\[
\begin{aligned}
\phi _{t}&=\frac{1}{H}\Delta \phi -HW_{0}^{\prime }(\phi )-W_{1}^{\prime }(\phi )(N+b(\widehat{\theta })/\widehat{\theta })+\frac{N}{\phi }, \\
u_{t}&=\sigma _{\theta }\Delta \widehat{\theta },\quad N_{t}=\sigma _{N}\nabla \cdot (N(W_{1}^{\prime }(\phi )-\frac{1}{\phi })\nabla \phi +\nabla N+\delta _{g}e_{3}N),
\end{aligned}
\]
where \(\phi \) is the liquid phase function, \(\theta \) the temperature, \(u\) the internal energy, \(N\) the salt weight fraction, \(W_{0}\) the double-well potential \(W_{0}(\phi )=18\phi ^{2}(1-\phi )^{2}\), \(W_{1}\) the function \(W_{1}(\phi )=2\phi ^{2}(\phi -3/2)\), and \(H\) the ratio between the brine inclusion length and\ the liquid-ice water interface width. Zero-flux boundary conditions are imposed. The authors then introduce \(\rho >0\) as a spatial constant defining the salt density relative to liquid water density, they remove the fast variation from the salt variable, they consider the temperature as a dependent variable, and the potential modified as \(V(\phi ;\theta ,\rho )=W_{0}(\phi )+\frac{1}{H}V_{1}(\phi ;\theta ,\rho ) \), where \(V_{1}\) is some perturbation which involves \(W_{1}\).\ Considering the case \(H\gg 1\), they derive a Stefan-type problem for the evolution of the ice-liquid interface \(\Gamma (t)\) through its normal velocity \( V_{n}(p,t)=-H^{-1}\overset{.}{z}\), where \(\overset{.}{z}\) gives the rate of approach of the front to a point \(x=x(z,p)\) and has an expansion of the form \(\overset{.}{z}=\overset{.}{z}_{0}+H^{-1}\overset{.}{z}_{1}+O(H^{-2})\). The authors introduce similar asymptotic expansions for the variables \(\theta \), \(\phi \) and \(N\), in the outer region and for the variables \(\theta \), \(\phi \) and \(\rho \), in the inner region. They draw computations on the first-order terms distinguishing between outer and inner systems. In the last part of their paper, the authors build a Stefan-type problem for a brine inclusion in sea ice. Considering the slow evolution of the evolving boundary \(\Gamma (t)\), which divides the domain \(\Omega \) into subdomains \(\Omega _{s}\) and \( \Omega _{l}\), they derive the nonlinear parabolic equation for the temperature \((1+b(\Theta _{0})\chi _{l})\partial _{t}\Theta _{0}=\sigma \theta \Delta \Theta _{0}\), in \(\Omega \), where \(\chi _{l}\) is the characteristic function of the inclusion, with the boundary conditions \( \Theta _{0}=\Theta _{b}(x,t)\) on \(\partial \overline{\Omega }\cup \partial \underline{\Omega }\), \(\partial _{n}\Theta _{0}\)\ on \(\partial \Omega _{l}\), with \(\partial \overline{\Omega }=[0,d_{0}]^{2}\times \{d_{0}\}\), \(\partial \underline{\Omega }=[0,d_{0}]^{2}\times \{0\}\), and the parabolic equation for the salt in the brine inclusion \(\partial _{t}N_{0}=\sigma _{N}\nabla \cdot (\nabla N_{0}+\delta _{g}e_{3}N_{0})\), in \(\Omega _{l}\), with the boundary condition \(\partial _{n}N_{0}\)\ on \(\partial \Omega \cap \Omega _{l} \). They consider a particular case leading to a quasi-equilibrium Stefan-type problem. They numerically solve this problem for axisymmetric surfaces. They finally analyze the impact of thermal gradients on the behavior of the system.
Reviewer: Alain Brillard (Riedisheim)Topological invariants for interface modeshttps://zbmath.org/1496.820222022-11-17T18:59:28.764376Z"Bal, Guillaume"https://zbmath.org/authors/?q=ai:bal.guillaumeSummary: This article concerns topologically non-trivial interface Hamiltonians that find many applications in materials science and geophysical fluid flows. The non-trivial topology manifests itself in the existence of topologically protected, asymmetric edge states at the interface between two two-dimensional half spaces. The asymmetric transport is characterized by a quantized interface conductivity. The objective of this article is to compute such a conductivity and show its stability under perturbations. We present two methods. The first one computes the conductivity using the winding number of branches of absolutely continuous spectrum of the interface Hamiltonian. This calculation is independent of any bulk properties but requires a sufficient understanding of the spectral decomposition of the Hamiltonian. In the fluid flow setting, it also applies in cases where the so-called bulk-interface correspondence fails. The second method establishes a bulk-interface correspondence between the interface conductivity and a so-called bulk-difference invariant. We introduce the bulk-difference invariants characterizing pairs of half spaces. We then relate the interface conductivity to the bulk-difference invariant by means of a Fedosov-Hörmander formula, which computes the index of a related Fredholm operator and is obtained using semiclassical calculus. The two methods are used to compute invariants for representative \(2 \times 2\) and \(3 \times 3\) systems of equations that appear in the applications.Stochastic physics and climate modelling. In part originating from a theme issue published in Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 366, No. 1875 (2008)https://zbmath.org/1496.860012022-11-17T18:59:28.764376ZPublisher's description: This is the first book to promote the use of stochastic, or random, processes to understand, model and predict our climate system. One of the most important applications of this technique is in the representation of comprehensive climate models of processes which, although crucial, are too small or fast to be explicitly modelled. The book shows how stochastic methods can lead to improvements in climate simulation and prediction, compared with more conventional bulk-formula parameterization procedures. Beginning with expositions of the relevant mathematical theory, the book moves on to describe numerous practical applications. It covers the complete range of time scales of climate variability, from seasonal to decadal, centennial, and millennial. With contributions from leading experts in climate physics, this book is invaluable to anyone working on climate models, including graduate students and researchers in the atmospheric and oceanic sciences, numerical weather forecasting, climate prediction, climate modelling, and climate change.Upscaling of two-phase discrete fracture simulations using a convolutional neural networkhttps://zbmath.org/1496.860022022-11-17T18:59:28.764376Z"Andrianov, Nikolai"https://zbmath.org/authors/?q=ai:andrianov.nikolaiSummary: Upscaling methods such as the dual porosity/dual permeability (DPDP) model provide a robust means for numerical simulation of fractured reservoirs. In order to close the DPDP model, one needs to provide the upscaled fracture permeabilities and the parameters of the matrix-fracture mass transfer for every fractured coarse block in the domain. Obtaining these model closures from fine-scale discrete fracture-matrix (DFM) simulations is a lengthy and computationally expensive process. We alleviate these difficulties by pixelating the fracture geometries and predicting the upscaled parameters using a convolutional neural network (CNN), trained on precomputed fine-scale results. We demonstrate that once a trained CNN is available, it can provide the DPDP model closures for a wide range of modeling parameters, not only those for which the training dataset has been obtained. The performance of the DPDP model with both reference and predicted closures is compared to the reference DFM simulations of two-phase flows using a synthetic and a realistic fracture geometries. While the both DPDP solutions underestimate the matrix-fracture transfer rate, they agree well with each other and demonstrate a significant speedup as compared to the reference fine-scale solution.Evaluating the impact of increasing temperatures on changes in soil organic carbon stocks: sensitivity analysis and non-standard discrete approximationhttps://zbmath.org/1496.860032022-11-17T18:59:28.764376Z"Diele, Fasma"https://zbmath.org/authors/?q=ai:diele.fasma"Luiso, Ilenia"https://zbmath.org/authors/?q=ai:luiso.ilenia"Marangi, Carmela"https://zbmath.org/authors/?q=ai:marangi.carmela"Martiradonna, Angela"https://zbmath.org/authors/?q=ai:martiradonna.angela"Woźniak, Edyta"https://zbmath.org/authors/?q=ai:wozniak.edytaSummary: The \textit{SOC change index}, defined as the normalized difference between the actual Soil Organic Carbon and the value assumed at an initial reference year, is here tailored to the RothC carbon model dynamics. It assumes as a baseline the value of the SOC equilibrium under constant environmental conditions. A sensitivity analysis is performed to evaluate the response of the model to changes in temperature, Net Primary Production (NPP), and land use soil class (forest, grassland, arable). A non-standard monthly time-stepping procedure has been proposed to approximate the SOC change index in the Alta Murgia National Park, a protected area in the Italian Apulia region, selected as a test site. The SOC change index exhibits negative trends for all the land use considered without fertilizers. The negative trend in the arable class can be inverted by a suitable organic fertilization program here proposed.Investigation of thermal-hydro-mechanical coupled fracture propagation considering rock damagehttps://zbmath.org/1496.860042022-11-17T18:59:28.764376Z"Jiao, Kaituo"https://zbmath.org/authors/?q=ai:jiao.kaituo"Han, Dongxu"https://zbmath.org/authors/?q=ai:han.dongxu"Wang, Daobing"https://zbmath.org/authors/?q=ai:wang.daobing"Chen, Yujie"https://zbmath.org/authors/?q=ai:chen.yujie"Li, Jingfa"https://zbmath.org/authors/?q=ai:li.jingfa"Gong, Liang"https://zbmath.org/authors/?q=ai:gong.liang"Bai, Bofeng"https://zbmath.org/authors/?q=ai:bai.bofeng"Yu, Bo"https://zbmath.org/authors/?q=ai:yu.bo|yu.bo.2|yu.bo.1Summary: Thermal-hydro-mechanical (THM) coupled fracture propagation is common in underground engineering. Rock damage, as an inherent property of rock, significantly affects fracture propagation, but how it influences the THM coupled fracturing remains stubbornly unclear. A pore-scale THM coupling model is developed to study this problem, which combines the lattice Boltzmann method (LBM), the discrete element method (DEM), and rock damage development theory together for the first time. This model can more accurately calculate the exchanged THM information at the fluid-solid boundary and fluid conductivity dependent on fracture and rock damage. Based on the developed model, the synergistic effect of injected temperature difference (fluid temperature below rock temperature) and rock damage (characterized by the parameter ``critical fracture energy'', abbreviated as ``CFE'') on fracture propagation of shale are investigated particularly. It is found that: (1) the generation of branched cracks is closely related to the temperature response frontier, and the fracture process zone of single bond failure increases in higher CFE. (2) through the analysis of micro failure events, hydraulic fracturing is more pronounced in the low CFE, while thermal fracturing displays the opposite trend. The fluid conductivity of fractured rock increases with a higher injected temperature difference due to the more penetrated cracks and wider fracture aperture. However, this enhancement weakens when rock damage is significant. (3) in the multiple-layered rock with various CFEs, branched cracks propagating to adjacent layers are more difficult to form when the injection hole stays in the layer with significant rock damage than without rock damage.Inclusion of variable characteristic length in microemulsion flash calculationshttps://zbmath.org/1496.860052022-11-17T18:59:28.764376Z"Magzymov, Daulet"https://zbmath.org/authors/?q=ai:magzymov.daulet"Johns, Russell T."https://zbmath.org/authors/?q=ai:johns.russell-tSummary: Recent developments in predicting microemulsion phase behavior for use in chemical flooding are based on the hydrophilic-lipophilic deviation (HLD) and net-average curvature (NAC) equation-of-state (EoS). The most advanced version of the HLD-NAC EoS assumes that the three-phase micelle characteristic length is constant as parameters like salinity and temperature vary. In this paper, we relax this assumption to improve the accuracy and thermodynamic consistency of these flash calculations. We introduce a variable characteristic length in the three-phase region based on experimental data that is monotonic with salinity or other formulation variables, such as temperature and pressure. The characteristic length at the boundary of the three-phase region is then used for flash calculations in the two-phase lobes for Winsor type I/II. The functional form of the characteristic length is made consistent with the Gibbs phase rule. The improved EoS can capture asymmetric phase behavior data around the optimum, whereas current HLD-NAC based models cannot. The variable characteristic length formulation also resolves the thermodynamic inconsistency of existing phase behavior models that give multiple solutions for the optimum. We show from experimental data and theory that the inverse of the characteristic length varies linearly with formulation variables. This important result means that it is easy to predict the characteristic length in the three-phase region, which also improves the estimation of surrounding two-phase lobes. The results show that the optimum solubilization ratio can change significantly by a factor of two when variable characteristic length is included as temperature and pressure change. This can in turn greatly impact the interfacial tension (IFT) at optimum. This improved physical understanding of microemulsion phase behavior should aid in the design of surfactant blends and improve recovery predictions in a chemical flooding simulator.Model-based characterization of permeability damage control through inhibitor injection under parametric uncertaintyhttps://zbmath.org/1496.860062022-11-17T18:59:28.764376Z"Mahmudova, Ayisha"https://zbmath.org/authors/?q=ai:mahmudova.ayisha"Borsi, Iacopo"https://zbmath.org/authors/?q=ai:borsi.iacopo"Porta, Giovanni Michele"https://zbmath.org/authors/?q=ai:porta.giovanni-micheleSummary: Damage in subsurface formations caused by mineral precipitation decreases the porosity and permeability, eventually reducing the production rate of wells in plants producing oil, gas or geothermal fluids. A possible solution to this problem consists in stopping the production followed by the injection of inhibiting species that slow down the precipitation process. In this work we model inhibitor injection and quantify the impact of a set of model parameters on the outputs of the system. The parameters investigated concern three key factors contributing to the success of the treatment: \textit{i)} the inhibitor affinity, described by an adsorption Langmuir isotherm, \textit{ii)} the concentration and time related to the injection and \textit{iii)} the efficiency of the inhibitor in preventing mineral precipitation. Our simulations are set in a stochastic framework where these inputs are characterized in probabilistic terms. Forward simulations rely on a purpose-built code based on finite differences approximation of the reactive transport setup in radial coordinates. We explore the sensitivity diverse outputs, encompassing the well bottom pressure and space-time scales characterizing the transport of the inhibitor. We find that practically relevant output variables, such as inhibitor lifetime and well bottom pressure, display a diverse response to input uncertainties and display poor mutual dependence. Our results quantify the probability of treatment failure for diverse scenarios of inhibitor-rock affinity. We find that treatment optimization based on single outputs may lead to high failure probability when evaluated in a multi-objective framework. For instance, employing an inhibitor displaying an appropriate lifetime may fail in satisfying criteria set in terms of well-bottom pressure history or injected inhibitor mass.A numerical model of the salinity of the Aral seahttps://zbmath.org/1496.860072022-11-17T18:59:28.764376Z"Tashmukhamedov, B. A."https://zbmath.org/authors/?q=ai:tashmukhamedov.b-a"Atabekov, I. U."https://zbmath.org/authors/?q=ai:atabekov.i-u(no abstract)Determination of two-phase relative permeability from a displacement with Safman-Rayleigh instability using a coarse-scale model history matching approachhttps://zbmath.org/1496.860082022-11-17T18:59:28.764376Z"Taura, Usman H."https://zbmath.org/authors/?q=ai:taura.usman-h"Mahzari, Pedram"https://zbmath.org/authors/?q=ai:mahzari.pedram"Sohrabi, Mehran"https://zbmath.org/authors/?q=ai:sohrabi.mehran"Al-Wahaibi, Yahya"https://zbmath.org/authors/?q=ai:al-wahaibi.yahya"Farzaneh, Sayyed Amir"https://zbmath.org/authors/?q=ai:farzaneh.sayyed-amirSummary: In heavy oil displacement by fluid injection, severe instability can occur due to the adverse mobility ratio, gravity segregation or compositional effects. However, when estimating relative permeability, most analytical methods assume a stable front in the displacement, which may be highly erroneous when used with unstable displacements. Quite often in such cases, history matching using a high-resolution model is preferred, however, it is computationally inefficient or impractical in some cases.
This work describes a relatively fast methodology for estimating relative permeability from displacement with instability and compositional effect. It involves defining a set of 2-dimensional (2D) coarse-grid models and the tuning of a three-parameter correlation. By this approach, an attempt is made to resolve the fine-scale information without direct solution of the global fine-scale problem.
The results of the coarse-grid history matching corrected by the proposed approach in this study showed that the improved methodology is three times faster, and required less than half the memory of a high-resolution 2D model.Physics-constrained deep learning forecasting: an application with capacitance resistive modelhttps://zbmath.org/1496.860092022-11-17T18:59:28.764376Z"Yewgat, Abderrahmane"https://zbmath.org/authors/?q=ai:yewgat.abderrahmane"Busby, Daniel"https://zbmath.org/authors/?q=ai:busby.daniel"Chevalier, Max"https://zbmath.org/authors/?q=ai:chevalier.max"Lapeyre, Corentin"https://zbmath.org/authors/?q=ai:lapeyre.corentin"Teste, Olivier"https://zbmath.org/authors/?q=ai:teste.olivierSummary: It is well known that the construction of traditional reservoir simulation models can be very time and resources consuming. Particularly in the case of mature fields with long history and large number of wells where such models can be extremely difficult and long to history match. In this case data driven models can represent a cost-effective alternative, or they can provide complementary analysis to classical reservoir modelling. Due to data scarcity full machine learning approaches are also usually doomed to fail. In this work we develop a new Physics-Constrained Deep Learning approach that combined neural networks with a reduced physics approach: Capacitance Resistive Model (CRM). CRM are data-driven methods that are based on a simple material balance approximation, that can provide very useful reservoir insight. CRM can be used to analyze the underlying connections between producer wells and injector wells that can then be used to better allocate water injection. Such analysis can usually require very long tracer tests or very expensive 4D seismic acquisition and interpretation. CRM can provide directly these wells connection information using only available production and pressure data. The problem with CRM approaches, based on classical optimizers, is that they often detect spurious correlations and can be not very robust and reliable. Our physics-constrained deep learning approach called Deep-CRM performs production data regularization via the neural network approximation that helps to provide a better CRM parameter identification also with the use of robust gradient descent optimization methods developed and widely used by the large deep learning community. We show first on a synthetic and then in real reservoir case that Deep-CRM was able to identify most of the injector-producer connections with higher accuracy with respect to traditional CRM. Deep-CRM produced also better liquid production forecasts on the performed blind tests.The use of flow diagnostics to rank model ensembleshttps://zbmath.org/1496.860102022-11-17T18:59:28.764376Z"Watson, Francesca"https://zbmath.org/authors/?q=ai:watson.francesca"Krogstad, Stein"https://zbmath.org/authors/?q=ai:krogstad.stein"Lie, Knut-Andreas"https://zbmath.org/authors/?q=ai:lie.knut-andreasSummary: Ensembles of geomodels provide an opportunity to investigate a range of parameters and possible operational outcomes for a reservoir. Full-featured dynamic modelling of all ensemble members is often computationally unfeasible, however some form of modelling, allowing us to discriminate between ensemble members based on their flow characteristics, is required. Flow diagnostics (based on a single-phase, steady-state simulation) can provide tools for analysing flow patterns in reservoir models but can be calculated in a much shorter time than a full-physics simulation. Heterogeneity measures derived from flow diagnostics can be used as proxies for oil recovery. More advanced flow diagnostic techniques can also be used to estimate recovery. With these tools we can rank ensemble members and choose a subset of models, representing a range of possible outcomes, which can then be simulated further. We demonstrate two types of flow diagnostics. The first are based on volume-averaged travel times, calculated on a cell by cell basis from a given flow field. The second use residence time distributions, which take longer to calculate but are more accurate and allow for direct estimation of recovery volumes. Additionally we have developed new metrics which work better for situations where we have a non-uniform initial saturation, e.g., a reservoir with an oil cap. Three different ensembles are analysed: Egg, Norne, and Brugge. Very good correlation, in terms of model ranking and recovery estimates, is found between flow diagnostics and full simulations for all three ensembles using both the cell-averaged and residence time based diagnostics.Asymptotic behavior of the perturbation of the primitive equations of the ocean with vertical viscosityhttps://zbmath.org/1496.860112022-11-17T18:59:28.764376Z"Belmiloudi, Aziz"https://zbmath.org/authors/?q=ai:belmiloudi.aziz(no abstract)Multiscale matrix-fracture transfer functions for naturally fractured reservoirs using an analytical, infinite conductivity, discrete fracture modelhttps://zbmath.org/1496.860122022-11-17T18:59:28.764376Z"Hazlett, R. D."https://zbmath.org/authors/?q=ai:hazlett.randy-d"Younis, R."https://zbmath.org/authors/?q=ai:younis.rahman-m|younis.rami-mSummary: Fracture matrix transfer functions have long been recognized as tools in modelling naturally fractured reservoirs. If a significant degree of fracturing is present, models involving single matrix blocks and matrix block distributions become relevant. However, this captures only the largest fracture sets and treats the matrix blocks as homogeneous, though possibly anisotropic. Herein, we produce the steady and transient baseline solutions for depletion for such models. Multiscale models pass below grid scale information to the larger scale system with some numerical cost. Instead, for below block scale information, we take the analytic solution to the Diffusivity Equation for transient inflow performance of wells of arbitrary trajectory, originally developed for Neumann boundary conditions, and recast it for Dirichlet boundaries with possible internal fractures of variable density, length, and orientation. As such, it represents the analytical solution for a heterogeneous matrix block surrounded by a constant pressure sink, we take to be the primary fracture system. Instead of using a constant rate internal boundary condition on a fracture surrounded by matrix, we segment the fracture and, through imposed material balance, force the internal complex fracture feature to be a constant pressure element with net zero flux. In doing so, we create a representative matrix block with infinite conductivity subscale fractures that impact the overall drainage into the surrounding fracture system. We vary the internal fracture structure and delineate sensitivity to fracture spacing and extent of fracturing. We generate the complete transient solution, enabling new well test interpretation for such systems in characterization of block size distributions or extent of below block-scale fracturing. The initial model for fully-penetrating fractures can be extended to 3D, generalized floating fractures of arbitrary inclination, and internal complex fracture networks.Efficient adjoint-based well-placement optimization using flow diagnostics proxieshttps://zbmath.org/1496.860132022-11-17T18:59:28.764376Z"Krogstad, Stein"https://zbmath.org/authors/?q=ai:krogstad.stein"Nilsen, Halvor Møll"https://zbmath.org/authors/?q=ai:nilsen.halvor-mollSummary: Model-based optimization of placement and trajectories of wells in petroleum reservoirs by the means of reservoir simulation forecasts is computationally demanding due to the high number of simulations typically required to achieve a local optimum. In this work, we develop an efficient flow-diagnostics proxy for net-present-value (NPV) with adjoint capabilities for efficient computation of well control gradients and approximate sensitivities with respect to placement/trajectory parameters. The suggested flow-diagnostic proxy consists of numerically solving a single pressure equation for the given scenario and the solution of a few inter-well time-of-flight and steady-state tracer equations, typically achieved in a few seconds for a reservoir model of medium size. Although the proxy may not be a particularly good approximation for the full reservoir simulation response, we find that for the cases considered, the correlation is very good and hence the proxy is suitable for use in an optimization loop. The adjoint simulation for the proxy model which provides control gradients and placement sensitivities is of similar computational complexity as the forward proxy model (a few seconds). We employ a version of the \textit{generalized reduced gradient} for handling individual well constraints (e.g., bottom-hole-pressures and rates). As a result, the individual well constraints are enforced within the flow-diagnostics computations, and hence every parameter update becomes feasible without sacrificing gradient information. We present two numerical experiments illustrating the efficiency and performance of the approach for well placement problems involving trajectories and simulation models of realistic complexity. The suggested placements are evaluated using full simulations. We conclude by discussing limitations and possible enhancements of the methodology.Calculation of the solar radiation field in the general circulation model of the Earth's lower and middle atmospherehttps://zbmath.org/1496.860142022-11-17T18:59:28.764376Z"Fedotova, E. A."https://zbmath.org/authors/?q=ai:fedotova.e-aSummary: The results of testing two radiation blocks used for economical calculation of radiation transfer in the general circulation model of the lower and middle atmosphere of the Earth are presented. The first block is designed to calculate the field of intrinsic radiation in the frequency range from 10 to \(3000 cm^{-1}\), and the second block is designed to calculate the field of solar radiation in the frequency range from 2000 to \(50,000 cm^{-1}\). Each of these blocks uses its own parameterization of the optical parameters of the air in the altitude range from the Earth's surface to 90 km. When constructing these parameterizations, the change in the gas composition of the atmosphere with altitude was taken into account. For the numerical solution of the radiation transfer equation, the method of discrete ordinates is used. The results of calculations performed using the radiation block of the model are compared with the results of line-by-line calculations of the solar radiation field in the lower and middle atmosphere of the Earth, performed with a very high frequency resolution. It is shown that the model block provides good accuracy of calculations both in the absence of clouds and in the presence of cloud layers with a large optical thickness.The strong solutions to the primitive equations coupled with multi-phase moisture atmospherehttps://zbmath.org/1496.860152022-11-17T18:59:28.764376Z"Tan, Shenyang"https://zbmath.org/authors/?q=ai:tan.shenyang"Liu, Wenjun"https://zbmath.org/authors/?q=ai:liu.wenjun-j|liu.wenjunSummary: The occurrence and development of cloud and precipitation are the products of the combination of atmospheric dynamic, thermal processes and cloud microphysical processes. In order to understand the interaction between these influencing factors in more detail, in this paper we study a moisture model with multi-phase for warm clouds, which consists of the primitive equations and a set of humidity equations where water is present in the form of water vapor, rain water and cloud condensates. This model has been considered by \textit{Y. Cao} et al. [Nonlinearity 31, No. 10, 4692--4723 (2018; Zbl 1395.35128)], where the velocity field is a given function in \(L^\infty((0, t_1) \times \mathcal{M})\). In this paper, the velocity field is governed by the atmosphere dynamic equation, which is more in line with the actual situation. In order to overcome the difficulty caused by the physical range requirement for the humidity, we introduce a new penalized function which is different from that introduced in [loc. cit.]. Then we obtain the global existence of both quasi-strong solutions and strong solutions.Efficient well placement optimization under uncertainty using a virtual drilling procedurehttps://zbmath.org/1496.860162022-11-17T18:59:28.764376Z"Kristoffersen, Brage S."https://zbmath.org/authors/?q=ai:kristoffersen.brage-s"Silva, Thiago L."https://zbmath.org/authors/?q=ai:silva.thiago-lima"Bellout, Mathias C."https://zbmath.org/authors/?q=ai:bellout.mathias-c"Berg, Carl Fredrik"https://zbmath.org/authors/?q=ai:berg.carl-fredrikSummary: An Automatic Well Planner (AWP) is used to efficiently adjust pre-determined well paths to honor near-well properties and increase overall production. AWP replicates modern geosteering decision-making where adjustments to pre-programmed well paths are driven by continuous integration of data obtained from logging-while-drilling and look-ahead technology. In this work, AWP is combined into a robust optimization scheme to develop trajectories that follow reservoir properties in a more realistic manner compared to common well representations for optimization purposes. Core AWP operation relies on an artificial neural network coupled with a geology-based feedback mechanism. Specifically, for each well path candidate obtained from an outer-loop optimization procedure, AWP customizes trajectories according to the particular geological near-well properties of each realization in an ensemble of models. While well placement searches typically rely on linear well path representations, AWP develops customized trajectories by moving sequentially from heel to the toe. Analog to realistic drilling operations, AWP determines subsequent trajectory points by efficiently processing neighboring geological information. Studies are performed using the Olympus ensemble. AWP and the two derivative-free algorithms used in this work, Asynchronous Parallel Pattern Search (APPS) and Particle Swarm Optimization (PSO), are implemented using NTNU's open-source optimization framework FieldOpt. Results show that, with both APPS and PSO, the AWP solutions outperform the solutions obtained with a straight-line parameterization in all the three tested well placement optimization scenarios, which varied from the simplest scenario with a sole producer in a single-realization environment to a scenario with the full ensemble and multiple producers.A robust, multi-solution framework for well placement and control optimizationhttps://zbmath.org/1496.860172022-11-17T18:59:28.764376Z"Salehian, Mohammad"https://zbmath.org/authors/?q=ai:salehian.mohammad"Sefat, Morteza Haghighat"https://zbmath.org/authors/?q=ai:sefat.morteza-haghighat"Muradov, Khafiz"https://zbmath.org/authors/?q=ai:muradov.khafiz-mSummary: Field development and control optimization aim to maximize the economic profit of oil and gas production while considering several sources of uncertainty. This results in a high-dimensional optimization problem with a computationally demanding and uncertain objective function based on the simulated reservoir model. The limitations of many current robust optimization methods are: 1) it is single-level optimization (e.g. optimization of well locations/placement only; or of well production/injection control variables only) that ignores interference between the control variables from different levels; and 2) they provide a single optimal solution, whereas operational problems often add unexpected constraints likely to reduce that optimal, inflexible solution to a sub-optimal scenario. This paper presents a robust, multi-solution framework based on sequential iterative optimization of control variables at multiple levels using the Simultaneous Perturbation Stochastic Approximation (SPSA) optimization algorithm. A systematic realization selection process, tailored to the objective of the subsequent optimization stage, is used to select a small representative ensemble of reservoir model realizations to be used for calculating the expected objective value. The estimated gradients are calculated using a 1:1 ratio mapping ensemble of control variables perturbations at each iteration onto the ensemble of selected reservoir model realizations to reduce the computational cost. An ensemble of close-to-optimum solutions is then chosen from each level (e.g. from the well placement optimization level) and transferred to the next level of optimization (e.g. where the control settings are optimized), and this loop continues until no significant improvement is observed in the expected objective value. Fit-for-purpose clustering techniques are developed to systematically select an ensemble of solutions, with maximum differences in control variables but close-to-optimum objective values, at each optimization level. The proposed framework has been tested on a benchmark case study (Brugge field). Multiple solutions are obtained with different well locations and control settings but close-to-optimum objective values. We show that suboptimal solutions from an early optimization level can approach and even outdo the optimal one at the next level(s). Results demonstrate the advantage of the developed framework in more efficient exploration of the search space and providing the much-needed operational flexibility to field operators.Sequential design strategy for kriging and cokriging-based machine learning in the context of reservoir history-matchinghttps://zbmath.org/1496.860182022-11-17T18:59:28.764376Z"Thenon, A."https://zbmath.org/authors/?q=ai:thenon.arthur"Gervais, V."https://zbmath.org/authors/?q=ai:gervais.veronique"Le Ravalec, M."https://zbmath.org/authors/?q=ai:le-ravalec.mickaeleSummary: Numerical models representing geological reservoirs can be used to forecast production and help engineers to design optimal development plans. These models should be as representative as possible of the true dynamic behavior and reproduce available static and dynamic data. However, identifying models constrained to production data can be very challenging and time consuming. Machine learning techniques can be considered to mimic and replace the fluid flow simulator in the process. However, the benefit of these approaches strongly depends on the simulation time required to train reliable predictors. Previous studies highlighted the potential of the multi-fidelity approach rooted in cokriging to efficiently provide accurate estimations of fluid flow simulator outputs. This technique consists in combining simulation results obtained on several levels of resolution for the reservoir model to predict the output properties on the finest level (the most accurate one). The degraded levels can correspond for instance to a coarser discretization in space or time, or to less complex physics. The idea behind is to take advantage of the coarse level low-cost information to limit the total simulation time required to train the meta-models. In this paper, we propose a new sequential design strategy for iteratively and automatically training (kriging and) cokriging based meta-models. As highlighted on two synthetic cases, this approach makes it possible to identify training sets leading to accurate estimations for the error between measured and simulated production data (objective function) while requiring limited simulation times.Conditioning geological surfaces to horizontal wellshttps://zbmath.org/1496.860192022-11-17T18:59:28.764376Z"Almendral Vázquez, Ariel"https://zbmath.org/authors/?q=ai:almendral-vazquez.ariel"Dahle, Pål"https://zbmath.org/authors/?q=ai:dahle.pal"Abrahamsen, Petter"https://zbmath.org/authors/?q=ai:abrahamsen.petter"Sektnan, Audun"https://zbmath.org/authors/?q=ai:sektnan.audunSummary: Kriging is a standard method for conditioning surfaces to observations. Kriging works for vertical wells, but may produce surfaces that cross horizontal wells between surface observations. We establish an approach that also works for horizontal wells, where surfaces are modeled as a set of correlated Gaussian random fields. The constraints imposed by the horizontal wells makes the conditional surfaces non-Gaussian. We present a method for exact conditional simulation and an approximation for prediction and prediction uncertainty. Thousands of constraints can be handled efficiently without numerical instabilities. The approach is illustrated with synthetic and real examples that show how the constraints influence the surfaces and reduce uncertainty.Huff-n-Puff (HNP) design for shale reservoirs using local dual-porosity, dual-permeability compositional simulationhttps://zbmath.org/1496.860202022-11-17T18:59:28.764376Z"Hamdi, Hamidreza"https://zbmath.org/authors/?q=ai:hamdi.hamidreza"Clarkson, Christopher R."https://zbmath.org/authors/?q=ai:clarkson.christopher-r"Esmail, Ali"https://zbmath.org/authors/?q=ai:esmail.ali"Costa Sousa, Mario"https://zbmath.org/authors/?q=ai:sousa.mario-costaSummary: Before implementing an HNP pilot in the field, reservoir studies are usually conducted, and compositional numerical simulations performed to assess the impact of uncertainty on HNP design parameters. In a previous study by the authors, the effect of \textit{parametric} uncertainty on designing a single-well HNP was demonstrated using effective single-porosity models. However, recent studies have shown that a limited region of complex fracturing is likely to be created during the hydraulic fracturing process. In this study, we expand on the earlier work and address the impact of \textit{model} uncertainty on designing an optimal HNP for a Duvernay shale example. In particular, the complex fracture regions are represented by local dual-porosity dual-permeability (DP-DK) models near the primary hydraulic fractures. Further, a multi-well HNP design is utilized to assess the impact of fracture communication during the cyclic gas injection scenarios. A unified framework is required to conduct Bayesian history matching and perform HNP simulations using the Markov chain Monte Carlo process. This task is achieved by implementing new adaptive sampling designs and employing some surrogate modeling techniques (Gaussian processes) to obtain the distributions for probabilistic HNP forecasts. The simulation results demonstrate that, for an equivalent calibrated DP-DK model, the efficiency of HNP, for both lean and rich gas injection scenarios, can be substantially higher than that predicted with the calibrated single-porosity model. In particular, lean gas injection, projected to have a low efficiency using single porosity models, is predicted to result in substantial incremental recovery in DP-DK models. The history matching and HNP simulation results demonstrate that DP-DK models provide the highest efficiency during early cycles with a reduced performance for later cycles. For single porosity models, the efficiency is much lower than the DP-DK models and is relatively constant across most of the cycles. The high efficiency of the DP-DK models is related to an enhanced mixing and extraction process due to pervasive communication (contact area) between the fracture network and the matrix. Additionally, the compositional simulations demonstrate that hydraulic communication between nearby wells through primary hydraulic fractures can substantially reduce the HNP performance. This study provides a novel workflow to accurately assess the impact of model uncertainty on HNP design for unconventional shale and low-permeability light oil reservoirs.Use of low-fidelity models with machine-learning error correction for well placement optimizationhttps://zbmath.org/1496.860212022-11-17T18:59:28.764376Z"Tang, Haoyu"https://zbmath.org/authors/?q=ai:tang.haoyu"Durlofsky, Louis J."https://zbmath.org/authors/?q=ai:durlofsky.louis-jSummary: Well placement optimization is commonly performed using population-based global stochastic search algorithms. These optimizations are computationally expensive due to the large number of multiphase flow simulations that must be conducted. In this work, we present an optimization framework in which these simulations are performed with low-fidelity (LF) models. These LF models are constructed from the underlying high-fidelity (HF) geomodel using a global transmissibility upscaling procedure. Tree-based machine-learning methods, specifically random forest and light gradient boosting machine, are applied to estimate the error in objective function value (in this case net present value, NPV) associated with the LF models. In the offline (preprocessing) step, preliminary optimizations are performed using LF models, and a clustering procedure is applied to select a representative set of 100--150 well configurations to use for training. HF simulation is then performed for these configurations, and the tree-based models are trained using an appropriate set of features. In the online (runtime) step, optimization with LF models, with the machine-learning correction, is conducted. Differential evolution is used for all optimizations. Results are presented for two example cases involving the placement of vertical wells in 3D bimodal channelized geomodels. We compare the performance of our procedure to optimization using HF models. In the first case, 25 optimization runs are performed with both approaches. Our method provides an overall speedup factor of 46 relative to optimization using HF models, with the best-case NPV within 1\% of the HF result. In the second case fewer HF optimization runs are conducted (consistent with actual practice), and the overall speedup factor with our approach is about 8. In this case, the best-case NPV from our procedure exceeds the HF result by 3.8\%.An intelligent multi-fidelity surrogate-assisted multi-objective reservoir production optimization method based on transfer stackinghttps://zbmath.org/1496.860222022-11-17T18:59:28.764376Z"Wang, Lian"https://zbmath.org/authors/?q=ai:wang.lian"Yao, Yuedong"https://zbmath.org/authors/?q=ai:yao.yuedong"Zhang, Liang"https://zbmath.org/authors/?q=ai:zhang.liang.2|zhang.liang.3|zhang.liang.1|zhang.liang"Adenutsi, Caspar Daniel"https://zbmath.org/authors/?q=ai:adenutsi.caspar-daniel"Zhao, Guoxiang"https://zbmath.org/authors/?q=ai:zhao.guoxiang"Lai, Fengpeng"https://zbmath.org/authors/?q=ai:lai.fengpengSummary: Recently, many researchers have focused on reservoir production optimization because it is one of the most essential processes in closed-loop reservoir management. Surrogate-assisted production optimization in particular has received a lot of research attention. This technique applies a simple yet vigorous approximation model to substitute expensive numerical simulation runs. However, almost all the existing methods independently use a single approximation model and neglect the potential synergies between these models. In order to make full use of the potential synergies of these existing approximation models, a novel multi-fidelity (MF) surrogate-assisted multi-objective production optimization (MOPO) method based on transfer stacking (MFTS-MOPO) is proposed. In the MFTS-MOPO method, the radial basis function network and support vector regression surrogate models are applied to approximate the high-fidelity (HF) model as the two additional low-fidelity (LF) models. Then a multi-fidelity surrogate model is adopted to evaluate objectives during the optimization process by transferring the two additional and streamline low-fidelity models to the computationally expensive high-fidelity model. Furthermore, two sampling infill strategies are applied to efficiently improve the quality of the multi-fidelity surrogate model. The uniqueness of the proposed MFTS-MOPO method is that the transfer stacking technique is employed to efficiently use the information from different fidelity models to establish the MF surrogate model and the infill sampling strategy used to improve its performance. In addition, three benchmark problems and two reservoirs with different scales were applied to illustrate the effectiveness and accuracy of the MFTS-MOPO method. It was found that the MFTS-MOPO method had superior performance in convergence and diversity than other conventional methods.3D reconstruction of porous media using a batch normalized variational auto-encoderhttps://zbmath.org/1496.860232022-11-17T18:59:28.764376Z"Zhang, Ting"https://zbmath.org/authors/?q=ai:zhang.ting.1|zhang.ting.3|zhang.ting|zhang.ting.2"Yang, Yi"https://zbmath.org/authors/?q=ai:yang.yi"Zhang, Anqin"https://zbmath.org/authors/?q=ai:zhang.anqinSummary: The 3D reconstruction of porous media plays a key role in many engineering applications. There are two main methods for the reconstruction of porous media: physical experimental methods and numerical reconstruction methods. The former are usually expensive and restricted by the limited size of experimental samples, while the latter are relatively cost-effective but still suffer from a lengthy processing time and unsatisfactory performance. With the vigorous development of deep learning in recent years, applying deep learning methods to 3D reconstruction of porous media has become an important direction. Variational auto-encoder (VAE) is one of the typical deep learning methods with a strong ability of extracting features from training images (TIs), but it has the problem of posterior collapse, meaning the generated data from the decoder are not related to its input data, i.e. the latent space \(Z\). This paper proposes a VAE model (called SE-FBN-VAE) based on squeeze-and-excitation network (SENet) and fixed batch normalization (FBN) for the reconstruction of porous media. SENet is a simple and efficient channel attention mechanism, which improves the sensitivity of the model to channel characteristics. The application of SENet to VAE can further improve its ability of extracting features from TIs. Batch normalization (BN) is a common method for data normalization in neural networks, which reduces the convergence time of the network. In this paper, BN is slightly modified to solve the problem of posterior collapse of VAE. Compared with some other numerical methods, the effectiveness and practicability of the proposed method are demonstrated.Implementation of a volume-of-fluid method in a finite element code with applications to thermochemical convection in a density stratified fluid in the Earth's mantlehttps://zbmath.org/1496.860242022-11-17T18:59:28.764376Z"Robey, Jonathan M."https://zbmath.org/authors/?q=ai:robey.jonathan-m"Puckett, Elbridge Gerry"https://zbmath.org/authors/?q=ai:puckett.elbridge-gerrySummary: We describe the implementation of a second-order accurate Volume-of-Fluid interface tracking algorithm in the open source finite element code ASPECT that is designed to model convection and other processes in the Earth's mantle. This involves the solution of the incompressible Stokes equations coupled to an advection diffusion equation for the temperature, a Boussinesq approximation that governs the dependence of the density on the temperature, and an advection equation for a marker indicating two initial (constant) density states, that are passively advected in the underlying flow field. The Volume-of-Fluid method in ASPECT is fully parallelized and fully integrated with ASPECT's adaptive mesh refinement algorithm. We present the results of several interface tracking benchmarks in order to demonstrate the accuracy of the method, as well as the results of several benchmarks commonly used in the computational mantle convection community. Finally, we present the results of computations with and without adaptive mesh refinement of a model problem involving thermochemical convection in a computationally stratified fluid designed to provide insight into how thermal plumes, that eventually reach the Earth's surface as ocean island basalts, originate at structures near the core-mantle boundary known as Large Low Shear wave Velocity Provinces or ``LLSVPs''. LLSVPs are structures in parts of the lowermost portion of the Earth's mantle, characterized by slow shear wave velocities and higher density than the surrounding mantle, which were discovered by seismic tomography of the deep Earth.