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A Gas Kinetic Scheme for the Simulation of Compressible Multicomponent Flows

Published online by Cambridge University Press:  03 June 2015

Liang Pan,
Guiping Zhao,
Baolin Tian and
Shuanghu Wang
Liang Pan*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, ChinaThe Graduate School of China Academy of Engineering Physics, Beijing 100088, China
Guiping Zhao*
Affiliation:
National Natural Science Foundation of China, Beijing 100085, China
Baolin Tian*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, ChinaKey Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
Shuanghu Wang*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, ChinaKey Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
*
Email:zhaogp@nsfc.gov.cn
Email:tianbaolin@iapcm.ac.cn
Corresponding author.Email:wangshuanghu@iapcm.ac.cn
Email:panliangjlu@sina.com
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Abstract

In this paper, a gas kinetic scheme for the compressible multicomponent flows is presented by making use of two-species GK model in [A. D. Kotelnikov and D. C. Montgomery, A Kinetic Method for Computing Inhomogeneous Fluid Behavior, J. Comput. Phys. 134 (1997) 364-388]. Different from the conventional BGK model, the collisions between different species are taken into consideration. Based on the Chapman-Enskog expansion, the corresponding macroscopic equations are derived from this two-species model. Because of the relaxation terms in the governing equations, the method of operator splitting is applied. In the hyperbolic part, the integral solutions of the BGK equations are used to construct the numerical fluxes at the cell interface in the framework of finite volume method. Numerical tests are presented in this paper to validate the current approach for the compressible multicomponent flows. The theoretical analysis on the spurious oscillations at the interface is also presented.

Keywords

76T1076P0576N15Multicomponent flowstwo-species BGK modelChapman-Enskog expansiongas kinetic scheme

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 5 , November 2013, pp. 1347 - 1371
Copyright
Copyright © Global Science Press Limited 2013

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References

[1]Abgrall, R., How to prevent pressure oscillations in multicomponent flow calculations, Aquasi conservative approach. J. Comput. Phys. 125 (1996) 150–160.Google Scholar
[2]Abgrall, R. and Karni, S., Computations of compressible multifluids, J. Comput. Phys. 169 (2001) 594–623.Google Scholar
[3]Bhatnagar, P.L., Gross, E.P., Krook, M., A Model for Collision Processes in Gases I: Small Amplitude Processes in Charged and Neutral One-Component Systems, Phys. Rev. 94 (1954) 511–525.Google Scholar
[4]Cercignani, C., The Boltzmann Equation and its Applications, Springer-Verlag, (1988).Google Scholar
[5]Chapman, S., Cowling, T.G., The Mathematical theory of Non-Uniform Gases, third edition, Cambridge University Press, (1990).Google Scholar
[6]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 (1999) 457–492.CrossRefGoogle Scholar
[7]Haas, J.F., Strurtevant, B., Interactions of a shock waves with cylindrical and spherical gas inhomogeneites. Journal of Fluids Mechnetics. 181 (1987) 41–76.Google Scholar
[8]Jiang, S., Ni, G.X., A γ-model BGK scheme for compressible multifluids, Int. J.Numer. Meth. Fluid 46 (2004) 163–182CrossRefGoogle Scholar
[9]Jiang, S., Ni, G.X., A second order γ-model BGK scheme for multifluids compressible flows. Applied numerical mathematics 57 (2007) 597–608.Google Scholar
[10]Kotelnikov, A.D., Montgomery, D.C., A Kinetic Method for Computing Inhomogeneous Fluid Behavior, J. Comput. Phys. 134 (1997) 364–388.Google Scholar
[11]Karni, S., Multicomponent flow calculations by a consistent premitive algorithm, J. Comput. Phys 128 (1994) 237–253.Google Scholar
[12]Karni, S., Hybrid multifluid algorithms, SIAM J. Sci. Comput. 17 (1996) 1019.Google Scholar
[13]Larrouturou, B., How to Preserve the Mass Fraction Positive When Computing Compressible Multi-component Flow, J. Comput. Phys. 95 (1991) 59–84.CrossRefGoogle Scholar
[14]Li, Q., Xu, K., Fu, S., A High-order Gas-Kinetic Navier-Stokes flow solver, J. Comput. Phys. 229 (2010) 6715–6731.Google Scholar
[15]Lian, Y.S., Xu, K., A Gas-Kinetic Scheme for Multimaterial Flows and Its Application in Chemical Reactions. J. Comput. Phys.163 (2000) 349–375.Google Scholar
[16]Osher, S., Fedkiw, R.P., Level set methods: An overview and some recent results, J. Comput. Phys. 169 (2001) 463–502.Google Scholar
[17]Quirk, J.J., Karni, S., On the dynamics of a shock bubble interaction, J. Fluid Mech. 318 (1996) 129–163.Google Scholar
[18]Roe, P.L., A new approach to computing discontinuous flow of several ideal gases, Technical Report, Cranfield Institute of Technology. 1984.Google Scholar
[19]Shyue, K.M., An efficient shock-capturing algorithm for compressible multicomponent problems, J. Comput. Phys. 142 (1998) 208–242.CrossRefGoogle Scholar
[20]Shyue, K.M., A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grueisen equation of state, J. Comput. Phys. 171 (2001) 678–707.Google Scholar
[21]Saurel, R., Abgrall, R., A simple method for compressible multifluid flows, SIAM J. Sci. Comput. 21 (1999) 1115–1145.Google Scholar
[22]Saurel, R., Abgrall, R., A multiphase Godunov method for compressible multifluid and multiphase flows, J. Comput. Phys. 150 (1999) 425–467.Google Scholar
[23]Tang, H.Z., Xu, K., A high-order gas-kinetic method for multidimentional ideal magnetohy-drodynamics. J. Comput. Phys. 165 (2000) 69–88Google Scholar
[24]Xu, K., Gas kinetic schemes for unsteady compressible flow simulations, Lecure Note Ser.,1998-03, Von Karman Institute for Fluid Dynamics Lecture. 1998.Google Scholar
[25]Xu, K., A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method, J. Comput. Phys. 171 (2001) 289–335.CrossRefGoogle Scholar
[26]Xu, K., BGK-based scheme for multicomponent flow calculations, J. Comput. Phys. 134 (1997) 122–133.Google Scholar
[27]Xu, K., Discontinuous Galerkin BGK method for viscous flow equations: one-dimensional systems, SIAM J. Sci. Comput. 23 (2004) 1941–1963.Google Scholar
[28]Xu, K., Gas-kinetic thoery based flux splitting method for ideal magnetohydrodynamics, J. Comput. Phys. 153 (1999) 344–375Google Scholar
[29]Xu, K., Huang, J.C., A unified gas-kinetic scheme for continuum and rarefiedflows J. Comput. Phys. 229 (2010), 7747–7764.Google Scholar
[30]Xu, K., A Well-Balanced Gas-Kinetic Scheme for the Shallow-Water Equations with Source Terms, J. Comput. Phys. 178 (2002) 533–562.Google Scholar
[31]Samtaney, R., Zabusky, N.J., Circulation deposition on shock-accelerated planar and curved density-stratified interfaces: models and scaling laws, J. Fluid Mechanics, 269, (1994), 45–78.CrossRefGoogle Scholar