An all Mach number finite volume method for isentropic two-phase flow

References

[1] A. Ambroso, C. Chalons, and P.-A. Raviart, A Godunov-type method for the seven-equation model of compressible two-phase flow, Comput. & Fluids 54 (2012), 67–9110.1016/j.compfluid.2011.10.004Suche in Google Scholar

[2] N. Andrianov, R. Saurel, and G.Warnecke, A simple method for compressible multiphase mixtures and interfaces, Int. J. Numer. Methods Fluids 41 (2003), No. 2, 109–13110.1002/fld.424Suche in Google Scholar

[3] N. Andrianov and G.Warnecke, The Riemann problem for the Baer–Nunziato two-phase flow model, J. Comput. Phys 195 (2004), No. 2, 434–46410.1016/j.jcp.2003.10.006Suche in Google Scholar

[4] M. R. Baer and J. W. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials, Int. J. Multiph. Flow 12 (1986), No. 6, 861–88910.1016/0301-9322(86)90033-9Suche in Google Scholar

[5] G. Bispen, M. Lukáčová-Medvid’ová, and L. Yelash, Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation, J. Comput. Phys 335 (2017), 222–24810.1016/j.jcp.2017.01.020Suche in Google Scholar

[6] S. Busto, L. Río-Martín, M. E. Vázquez-Cendón, and M. Dumbser, A semi-implicit hybrid finite volume/finite element scheme for all Mach number flows on staggered unstructured meshes, Appl. Math. Comput 402 (2021), 12611710.1016/j.amc.2021.126117Suche in Google Scholar

[7] S. Chiocchetti and C. Müller, A solver for stiff finite-rate relaxation in Baer–Nunziato two-phase flow models, Fluid Mech. Appl 121 (2020), 31–4410.1007/978-3-030-33338-6_3Suche in Google Scholar

[8] F. Cordier, P. Degond, and A. Kumbaro, An asymptotic-preserving all-speed scheme for the Euler and Navier–Stokes equations, J. Comput. Phys 231 (2012), No. 17, 5685–570410.1016/j.jcp.2012.04.025Suche in Google Scholar

[9] V. Daru, P. Le Quéré, M.-C. Duluc, and O. Le Maitre, A numerical method for the simulation of low Mach number liquid–gas flows, J. Comput. Phys 229 (2010), No. 23, 8844–886710.1016/j.jcp.2010.08.013Suche in Google Scholar

[10] P. Degond and M. Tang, All speed scheme for the low Mach number limit of the isentropic Euler equations, Commun. Comput. Phys 10 (2011), No. 1, 1–3110.4208/cicp.210709.210610aSuche in Google Scholar

[11] S. Dellacherie, Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number, J. Comput. Phys 229 (2010), No. 4, 978–101610.1016/j.jcp.2009.09.044Suche in Google Scholar

[12] A. D. Demou, N. Scapin, M. Pelanti, and L. Brandt, A pressure-based diffuse interface method for low-Mach multiphase flows with mass transfer, J. Comput. Phys 448 (2022), 11073010.1016/j.jcp.2021.110730Suche in Google Scholar

[13] G. Dimarco, R. Loubère, V. Michel-Dansac, and M.-H. Vignal, Second-order implicit–explicit total variation diminishing schemes for the Euler system in the low Mach regime, J. Comput. Phys 372 (2018), 178–20110.1016/j.jcp.2018.06.022Suche in Google Scholar

[14] M. Dumbser, I. Peshkov, E. Romenski, and O. Zanotti, High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids, J. Comput. Phys 314 (2016), 824–86210.1016/j.jcp.2016.02.015Suche in Google Scholar

[15] M. Feistauer, V. Dolejší, and V. Kučera, On the discontinuous Galerkin method for the simulation of compressible flow with wide range of Mach numbers, Comput. Vis. Sci 10 (2007), No. 1, 17–2710.1007/s00791-006-0051-8Suche in Google Scholar

[16] M. Feistauer and V. Kučcera, A new technique for the numerical solution of the compressible Euler equations with arbitrary Mach numbers. In: Hyperbolic Problems: Theory, Numerics, Applications Springer, 2008, pp. 523–53110.1007/978-3-540-75712-2_50Suche in Google Scholar

[17] S. K. Godunov, An interesting class of quasilinear systems, Dokl. Akad. Nauk SSSR 139 (1961), No. 3, 521–523Suche in Google Scholar

[18] S. K. Godunov and E. I. Romenskii, Elements of Continuum Mechanics and Conservation Laws Kluwer Academic/Plenum Publishers, 200310.1007/978-1-4757-5117-8Suche in Google Scholar

[19] S. K. Godunov and E. I. Romensky, Thermodynamics, conservation laws and symmetric forms of differential equations in mechanics of continuous media, Computational Fluid Dynamics Review 95 (1995), 19–31Suche in Google Scholar

[20] H. Gouin and S. Gavrilyuk, Hamilton’s principle and Rankine–Hugoniot conditions for general motions of mixtures, Meccanica 34 (1999), No. 1, 39–4710.1023/A:1004370127958Suche in Google Scholar

[21] H. Guillard and C. Viozat, On the behaviour of upwind schemes in the low Mach number limit, Comput. & Fluids 28 (1999), No. 1, 63–8610.1016/S0045-7930(98)00017-6Suche in Google Scholar

[22] S. Jin, Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations, SIAM J. Sci. Comput 21 (1999), No. 2, 441–45410.1137/S1064827598334599Suche in Google Scholar

[23] K. Kaiser, J. Schütz, R. Schöbel, and S. Noelle, A new stable splitting for the isentropic Euler equations, J. Sci. Comput 70 (2017), No. 3, 1390–140710.1007/s10915-016-0286-6Suche in Google Scholar

[24] A. K. Kapila, R. Menikoff, J. B. Bdzil, S. F. Son, and D. S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations, Phys. Fluids 13 (2001), No. 10, 3002–302410.1063/1.1398042Suche in Google Scholar

[25] S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Commun. Pur. Appl. Math 34 (1981), No. 4, 481–52410.1002/cpa.3160340405Suche in Google Scholar

[26] R. Klein, Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics I: One-dimensional flow, J. Comput. Phys 121 (1995), No. 2, 213 – 23710.1016/S0021-9991(95)90034-9Suche in Google Scholar

[27] J. J. Kreeft and B. Koren, A new formulation of Kapila’s five-equation model for compressible two-fluid flow, and its numerical treatment, J. Comput. Phys 229 (2010), No. 18, 6220–624210.1016/j.jcp.2010.04.025Suche in Google Scholar

[28] V. Kučera, M. Lukáčová-Medvid’ová, S. Noelle, and J. Schütz, Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations, Numer. Math 150 (2022), No. 1, 79–10310.1007/s00211-021-01240-5Suche in Google Scholar

[29] S. Müller, M. Hantke, and P. Richter, Closure conditions for non-equilibrium multi-component models, Contin. Mech. Thermodyn 28 (2016), No. 4, 1157–118910.1007/s00161-015-0468-8Suche in Google Scholar

[30] J. H. Park and C.-D. Munz, Multiple pressure variables methods for fluid flow at all Mach numbers, Int. J. Numer. Methods Fluids 49 (2005), No. 8, 905–93110.1002/fld.1032Suche in Google Scholar

[31] M. Pelanti, Low Mach number preconditioning techniques for Roe-type and HLLC-type methods for a two-phase compressible flow model, Appl. Math. Comput 310 (2017), 112–13310.1016/j.amc.2017.04.014Suche in Google Scholar

[32] I. Peshkov, M. Dumbser, W. Boscheri, E. Romenski, S. Chiocchetti, and M. Ioriatti, Simulation of non-Newtonian viscoplastic flows with a unified first order hyperbolic model and a structure-preserving semi-implicit scheme, Comput. & Fluids 224 (2021), 10496310.1016/j.compfluid.2021.104963Suche in Google Scholar

[33] I. Peshkov, M. Pavelka, E. Romenski, and M. Grmela, Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations, Contin. Mech. Thermodyn 30 (2018), No. 6, 1343–137810.1007/s00161-018-0621-2Suche in Google Scholar

[34] B. Re and R. Abgrall, A pressure-based method for weakly compressible two-phase flows under a Baer–Nunziato type model with generic equations of state and pressure and velocity disequilibrium, Int. J. Numer. Methods Fluids 94 (2022), No. 8, 1183–123210.1002/fld.5087Suche in Google Scholar

[35] E. Romenski, A. A. Belozerov, and I. M. Peshkov, Conservative formulation for compressible multiphase flows, Quart. Appl. Math 74 (2016), No. 1, 113–13610.1090/qam/1409Suche in Google Scholar

[36] E. Romenski, D. Drikakis, and E. Toro, Conservative models and numerical methods for compressible two-phase flow, J. Sci. Comput 42 (2010), No. 1, 6810.1007/s10915-009-9316-ySuche in Google Scholar

[37] E. Romenski, G. Reshetova, I. Peshkov, and M. Dumbser, Two-phase computational model for small-amplitude wave propagation in a saturated porous medium. In: Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov’s Legacy Springer International Publishing, Cham, 2020, pp. 313–32010.1007/978-3-030-38870-6_41Suche in Google Scholar

[38] E. Romenski and E. F. Toro, Compressible two-phase flows: Two-pressure models and numerical methods, Comput. Fluid Dyn. J 13 (2004), 403–41610.1007/s00193-004-0229-2Suche in Google Scholar

[39] E. I. Romensky, Hyperbolic systems of thermodynamically compatible conservation laws in continuum mechanics, Mathematical and Computer Modelling 28 (1998), No. 10, 115–13010.1016/S0895-7177(98)00159-9Suche in Google Scholar

[40] R. Saurel and R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows, J. Comput. Phys 150 (1999), No. 2, 425–46710.1006/jcph.1999.6187Suche in Google Scholar

[41] F. Thein, E. Romenski, and M. Dumbser, Exact and numerical solutions of the Riemann problem for a conservative model of compressible two-phase flows, J. Sci. Comput 93 (2022), No. 3, 8310.1007/s10915-022-02028-xSuche in Google Scholar

[42] J. Zeifang, J. Schütz, K. Kaiser, A. Beck, M. Lukáčová-Medvid’ová, and S. Noelle, A novel full-Euler low Mach number IMEX splitting, Commun. Comput. Phys 27 (2020), 292–32010.4208/cicp.OA-2018-0270Suche in Google Scholar

[43] Z. Zou, E. Audit, N. Grenier, and C. Tenaud, An accurate sharp interface method for two-phase compressible flows at low-Mach regime, Flow, Turbulence and Combustion 105 (2020), No. 4, 1413–144410.1007/s10494-020-00125-1Suche in Google Scholar