×

A simplified approach for simulations of multidimensional compressible multicomponent flows: the grid-aligned ghost fluid method. (English) Zbl 1453.76212

Summary: In the present work the authors present a simplified formulation for the extension of a ghost fluid method in multidimensional space. In the proposed method, the Riemann problems at the interface are formulated along the grid rather than in a normal to the interface direction. The information that is required to construct these Riemann problems is acquire“on-the-fly” from the adjacent to the interface cells. With respect to existing multidimensional ghost fluid formulations, the method is computationally less expensive, as the procedures of determining ghost fluid regions, extending, interpolating and extrapolating variables and computing geometrical quantities are avoided. More importantly, it is markedly simple with respect to its implementation. By introducing the proposed formulation in a well-established front tracking framework we perform an extensive validation of the method and demonstrate that despite its simplicity it yields highly accurate results while remaining free of oscillations.

MSC:

76T10 Liquid-gas two-phase flows, bubbly flows
76M10 Finite element methods applied to problems in fluid mechanics

Software:

FronTier; FIVER
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Hirt, C. W.; Nichols, B. D., Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys., 39, 201-225 (1981) · Zbl 0462.76020
[2] Osher, S.; Sethian, J. A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79, 12-49 (1988) · Zbl 0659.65132
[3] Osher, S.; Fedkiw, R. P., Level set methods: an overview and some recent results, J. Comput. Phys., 169, 463-502 (2001) · Zbl 0988.65093
[4] Glimm, J.; Isaacson, E.; Marchesin, D.; McBryan, O., Front tracking for hyperbolic systems, Adv. Appl. Math., 2, 91-119 (1981) · Zbl 0459.76069
[5] Glimm, J.; McBryan, O. A., A computational model for interfaces, Adv. Appl. Math., 6, 422-435 (1985)
[6] Glimm, J.; Grove, J.; Lindquist, B.; McBryan, O. A.; Tryggvason, G., The bifurcation of tracked scalar waves, SIAM J. Sci. Stat. Comput., 9, 61-79 (1988) · Zbl 0636.65132
[7] Unverdi, S. O.; Tryggvason, G., A front-tracking method for viscous, incompressible, multi-fluid flows, J. Comput. Phys., 100, 25-37 (1992) · Zbl 0758.76047
[8] Abgrall, R.; Karni, S., Computations of compressible multifluids, J. Comput. Phys., 169, 594-623 (2001) · Zbl 1033.76029
[9] Grove, J. W.; Menikoff, R., The anomalous reflection of a shock wave at a fluid interface, J. Fluid Mech., 219, 313-336 (1990)
[10] Haller, K.; Ventikos, Y.; Poulikakos, D.; Monkewitz, P., Computational study of high-speed liquid droplet impact, J. Appl. Phys., 92, 2821-2828 (2002)
[11] Liu, X.; George, E.; Bo, W.; Glimm, J., Turbulent mixing with physical mass diffusion, Phys. Rev. E, 73, Article 056301 pp. (2006)
[12] Liu, X.; Li, Y.; Glimm, J.; Li, X., A front tracking algorithm for limited mass diffusion, J. Comput. Phys., 222, 644-653 (2007) · Zbl 1116.76063
[13] Lim, H.; Iwerks, J.; Yu, Y.; Glimm, J.; Sharp, D., Verification and validation of a method for the simulation of turbulent mixing, Phys. Scr., 2010, Article 014014 pp. (2010)
[14] Hawker, N. A.; Ventikos, Y., Interaction of a strong shockwave with a gas bubble in a liquid medium: a numerical study, J. Fluid Mech., 701, 59-97 (2012) · Zbl 1248.76105
[15] Betney, M. R.; Hawker, N. A.; Tully, B.; Ventikos, Y., Computational modelling of the interaction of shock waves with multiple gas bubbles in a liquid, Phys. Fluids, 27, Article 036101 pp. (2015)
[16] Hao, Y.; Prosperetti, A., A numerical method for three-dimensional gas-liquid flow computations, J. Comput. Phys., 196, 126-144 (2004) · Zbl 1109.76383
[17] Terashima, H.; Tryggvason, G., A front-tracking/ghost-fluid method for fluid interfaces in compressible flows, J. Comput. Phys., 228, 4012-4037 (2009) · Zbl 1171.76046
[18] Terashima, H.; Tryggvason, G., A front-tracking method with projected interface conditions for compressible multi-fluid flows, Comput. Fluids, 39, 1804-1814 (2010) · Zbl 1245.76113
[19] Bo, W.; Liu, X.; Glimm, J.; Li, X., A robust front tracking method: verification and application to simulation of the primary breakup of a liquid jet, SIAM J. Sci. Comput., 33, 1505-1524 (2011) · Zbl 1465.76084
[20] Wang, D.; Zhao, N.; Hu, O.; Liu, J., A ghost fluid based front tracking method for multimedium compressible flows, Acta Math. Sci., 29, 1629-1646 (2009) · Zbl 1212.65383
[21] Lu, H.; Zhao, N.; Wang, D., A front tracking method for the simulation of compressible multimedium flows, Commun. Comput. Phys., 19, 124-142 (2016) · Zbl 1373.76180
[22] Fedkiw, R. P.; Aslam, T.; Merriman, B.; Osher, S., A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys., 152, 457-492 (1999) · Zbl 0957.76052
[23] Fedkiw, R. P.; Aslam, T.; Xu, S., The ghost fluid method for deflagration and detonation discontinuities, J. Comput. Phys., 154, 393-427 (1999) · Zbl 0955.76071
[24] Fedkiw, R. P., Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method, J. Comput. Phys., 175, 200-224 (2002) · Zbl 1039.76050
[25] Liu, T.; Khoo, B.; Yeo, K., The simulation of compressible multi-medium flow. I. A new methodology with test applications to 1D gas-gas and gas-water cases, Comput. Fluids, 30, 291-314 (2001) · Zbl 1052.76046
[26] Liu, T.; Khoo, B.; Yeo, K., Ghost fluid method for strong shock impacting on material interface, J. Comput. Phys., 190, 651-681 (2003) · Zbl 1076.76592
[27] Liu, T.; Khoo, B.; Wang, C., The ghost fluid method for compressible gas-water simulation, J. Comput. Phys., 204, 193-221 (2005) · Zbl 1190.76160
[28] Hu, X. Y.; Khoo, B. C., An interface interaction method for compressible multifluids, J. Comput. Phys., 198, 35-64 (2004) · Zbl 1107.76378
[29] Wang, C.; Liu, T.; Khoo, B., A real ghost fluid method for the simulation of multimedium compressible flow, SIAM J. Sci. Comput., 28, 278-302 (2006) · Zbl 1114.35119
[30] Sambasivan, S. K.; Udaykumar, H., Ghost fluid method for strong shock interactions part 1: fluid-fluid interfaces, AIAA J., 47, 2907-2922 (2009)
[31] Xu, L.; Liu, T., Accuracies and conservation errors of various ghost fluid methods for multi-medium Riemann problem, J. Comput. Phys., 230, 4975-4990 (2011) · Zbl 1416.76233
[32] Glimm, J.; Grove, J. W.; Li, X. L.; Shyue, K.-M.; Zeng, Y.; Zhang, Q., Three-dimensional front tracking, SIAM J. Sci. Comput., 19, 703-727 (1998) · Zbl 0912.65075
[33] Glimm, J.; Grove, J. W.; Li, X.; Zhao, N., Simple front tracking, Contemp. Math., 238, 133-149 (1999) · Zbl 0960.76058
[34] Glimm, J.; Grove, J. W.; Li, X.; Tan, D. C., Robust computational algorithms for dynamic interface tracking in three dimensions, SIAM J. Sci. Comput., 21, 2240-2256 (2000) · Zbl 0969.76062
[35] Glimm, J.; Grove, J. W.; Zhang, Y., Interface tracking for axisymmetric flows, SIAM J. Sci. Comput., 24, 208-236 (2002) · Zbl 1062.76034
[36] Du, J.; Fix, B.; Glimm, J.; Jia, X.; Li, X.; Li, Y.; Wu, L., A simple package for front tracking, J. Comput. Phys., 213, 613-628 (2006) · Zbl 1089.65128
[37] Menikoff, R.; Plohr, B. J., The Riemann problem for fluid flow of real materials, Rev. Mod. Phys., 61, 75-130 (1989) · Zbl 1129.35439
[38] Wagner, W.; Pruß, A., The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use, J. Phys. Chem. Ref. Data, 31, 387-535 (2002)
[39] Nagayama, K.; Mori, Y.; Shimada, K.; Nakahara, M., Shock Hugoniot compression curve for water up to 1 GPa by using a compressed gas gun, J. Appl. Phys., 91, 476-482 (2002)
[40] Ball, G. J.; Howell, B. P.; Leighton, T. G.; Schofield, M. J., Shock-induced collapse of a cylindrical air cavity in water: a free-Lagrange simulation, Shock Waves, 10, 265-276 (2000) · Zbl 0980.76090
[41] Lauer, E.; Hu, X. Y.; Hickel, S.; Adams, N. A., Numerical investigation of collapsing cavity arrays, Phys. Fluids, 24 (2012) · Zbl 1365.76231
[42] Johnsen, E.; Colonius, T., Numerical simulations of non-spherical bubble collapse, J. Fluid Mech., 629, 231 (2009) · Zbl 1181.76137
[43] Coralic, V.; Colonius, T., Finite-volume WENO scheme for viscous compressible multicomponent flows, J. Comput. Phys., 274, 95-121 (2014) · Zbl 1351.76100
[44] Tully, B.; Hawker, N.; Ventikos, Y., Modeling asymmetric cavity collapse with plasma equations of state, Phys. Rev. E, 93, Article 1 pp. (2016)
[45] Hu, X.; Adams, N. A.; Iaccarino, G., On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow, J. Comput. Phys., 228, 6572-6589 (2009) · Zbl 1261.76023
[46] Shu, C.-W., Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, (Advanced Numerical Approximation of Nonlinear Hyperbolic Equations (1998), Springer), 325-432 · Zbl 0927.65111
[47] Farhat, C.; Gerbeau, J.-F.; Rallu, A., FIVER: a finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps, J. Comput. Phys., 231, 6360-6379 (2012) · Zbl 1284.76264
[48] Zalesak, S. T., Fully multidimensional flux-corrected transport algorithms for fluids, J. Comput. Phys., 31, 335-362 (1979) · Zbl 0416.76002
[49] Zuzio, D., Direct Numerical Simulation of Two Phase Flows with Adaptive Mesh Refinement (2010), Ecole nationale superieure de l’aeronautique et de l’espace, Ph.D. thesis
[50] Haas, J.-F.; Sturtevant, B., Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities, J. Fluid Mech., 181, 41 (1987)
[51] Picone, J. M.; Boris, J. P., Vorticity generation by shock propagation through bubbles in a gas, J. Fluid Mech., 189, 23-51 (1988)
[52] Quirk, J. J.; Karni, S., On the dynamics of a shock-bubble interaction, J. Fluid Mech., 318, 129-163 (1996) · Zbl 0877.76046
[53] Nourgaliev, R. R.; Dinh, T.-N.; Theofanous, T. G., Adaptive characteristics-based matching for compressible multifluid dynamics, J. Comput. Phys., 213, 500-529 (2006) · Zbl 1136.76396
[54] Shankar, S. K.; Kawai, S.; Lele, S. K., Numerical Simulation of Multicomponent Shock Accelerated Flows and Mixing Using Localized Artificial Diffusivity Method (2010), AIAA Paper 2010-352 (2010)
[55] Keller, J. B.; Miksis, M., Bubble oscillations of large amplitude, J. Acoust. Soc. Am., 68, 628-633 (1980) · Zbl 0456.76087
[56] Plesset, M., On the stability of fluid flows with spherical symmetry, J. Appl. Phys., 25, 96-98 (1954) · Zbl 0055.18501
[57] Nagrath, S.; Jansen, K.; Lahey, R. T.; Akhatov, I., Hydrodynamic simulation of air bubble implosion using a level set approach, J. Comput. Phys., 215, 98-132 (2006) · Zbl 1140.76368
[58] Kamran, K.; Rossi, R.; Oñate, E.; Idelsohn, S., A compressible Lagrangian framework for the simulation of the underwater implosion of large air bubbles, Comput. Methods Appl. Mech. Eng., 255, 210-225 (2013) · Zbl 1297.76176
[59] Igra, D.; Takayama, K., Investigation of aerodynamic breakup of a cylindrical water droplet, At. Sprays, 11 (2001) · Zbl 1051.76045
[60] Chen, H., Two-dimensional simulation of stripping breakup of a water droplet, AIAA J., 46, 1135-1143 (2008)
[61] Meng, J.; Colonius, T., Numerical simulations of the early stages of high-speed droplet breakup, Shock Waves, 25, 399-414 (2015)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.