Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-24T14:36:09.478Z Has data issue: false hasContentIssue false
  • English
  • Français

A Conservative Modification to the Ghost Fluid Method for Compressible Multiphase Flows

Published online by Cambridge University Press:  20 August 2015

Wei Liu ,
Li Yuan  and
Chi-Wang Shu
Wei Liu*
Affiliation:
Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Li Yuan*
Affiliation:
Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Chi-Wang Shu*
Affiliation:
Division of Applied Mathematics, Brown University, Providence RI 02912, USA
*
Email:liuwei@lsec.cc.ac.cn
Email:lyuan@lsec.cc.ac.cn
Corresponding author.Email:shu@dam.brown.edu
Get access

Abstract

A conservative modification to the ghost fluid method (GFM) is developed for compressible multiphase flows. The motivation is to eliminate or reduce the conservation error of the GFM without affecting its performance. We track the conservative variables near the material interface and use this information to modify the numerical solution for an interfacing cell when the interface has passed the cell. The modification procedure can be used on the GFM with any base schemes. In this paper we use the fifth order finite difference WENO scheme for the spatial discretization and the third order TVD Runge-Kutta method for the time discretization. The level set method is used to capture the interface. Numerical experiments show that the method is at least mass and momentum conservative and is in general comparable in numerical resolution with the original GFM.

Keywords

76M2076T99WENO schemeghost fluid method (GFM)mass conservationmultiphase flow
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 4 , October 2011 , pp. 785 - 806
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Abgrall, R., How to prevent pressure oscillations in multicomponent flow calculations: a quasi-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.CrossRefGoogle Scholar
[3]Adalsteinsson, D. and Sethian, J.A., A fast level set method for propagating interfaces, J. Comput. Phys., 118 (1995), 269–277.Google Scholar
[4]Bailey, D.A., Sweby, P.K. and Glaister, P., A ghost fluid, moving finite volume plus continuous remap method for compressible Euler flow, Int. J. Numer. Methods Fluids, 47 (2005), 833–840.Google Scholar
[5]Fedkiw, R.P., Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method, J. Comput. Phys., 175 (2002), 200–224.CrossRefGoogle Scholar
[6]Fedkiw, R.P., Aslam, T., Merriman, B. and 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]Fedkiw, R.P., Marquina, A. and Merriman, B., An isobaric fix for the overheating problem in multimaterial compressible flows, J. Comput. Phys., 148 (1999), 545–578.Google Scholar
[8]Glimm, J., Grove, J.M., Li, X.L. and Zhao, N., Simple front tracking, in: Chen, G.Q., Di Bebe-detto, E. (Eds.), Contemporary Mathematics, vol. 238, AMS, Providence, RI, 1999.Google Scholar
[9]Glimm, J., Marchesin, D. and McBryan, O., A numerical method for two phase flow with an unstable interface, J. Comput. Phys., 39 (1981), 179–200.Google Scholar
[10]Haas, J.-F. and Sturtevant, B., Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities, J. Fluid Mech., 181 (1987), 41–76.Google Scholar
[11]Jiang, G. and Peng, D.-P., Weighted ENO schemes for Hamilton-Jacobi equations, SIAM J. Sci. Comput., 21 (2000), 2126–2143.Google Scholar
[12]Jiang, G. and Shu, C.-W., Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), 202–228.Google Scholar
[13]Johnsen, E. and Colonius, T., Implementation of WENO schemes in compressible multi-component flow problems, J. Comput. Phys., 219 (2006), 715–732.CrossRefGoogle Scholar
[14]Liu, T.G., Khoo, B.C. and Wang, C.W., The ghost fluid method for compressible gas-water simulation, J. Comput. Phys., 204 (2005), 193–221.CrossRefGoogle Scholar
[15]Liu, T.G., Khoo, B.C. and Yeo, K.S., The simulation of compressible multi-medium flow. Part I: a new methodology with applications to 1D gas-gas and gas-water cases, Computers & Fluids, 30 (2001), 291–314.Google Scholar
[16]Liu, T.G., Khoo, B.C. and Yeo, K.S., The simulation of compressible multi-medium flow. Part II: applications to 2D underwater shock refraction, Computers & Fluids, 30 (2001), 315–337.Google Scholar
[17]Liu, T.G., Khoo, B.C. and Yeo, K.S., Ghost fluid method for strong shock impacting on material interface, J. Comput. Phys., 190 (2003), 651–681.CrossRefGoogle Scholar
[18]Marquina, A. and Mulet, P., A flux-split algorithm applied to conservative models for multi-component compressible flows, J. Comput. Phys., 185 (2003), 120–138.Google Scholar
[19]Mulder, W., Osher, S. and Sethian, J.A., Computing interface motion in compressible gas dynamics, J. Comput. Phys., 100 (1992), 209–228.Google Scholar
[20]Osher, S., Fedkiw, R.P., Level Set Methods and Dynamic Implicit Surfaces, Springer, 2003.Google Scholar
[21]Osher, S., Sethian, J.A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton Jacobi formulations, J. Comput. Phys., 79 (1988), 12–49.Google Scholar
[22]Qiu, J., Liu, T. and Khoo, B.C., Simulations of compressible two-medium flow by Runge-Kutta discontinuous Galerkin methods with the Ghost Fluid Method, Commun. Comput. Phys., 3 (2008), 479–504.Google Scholar
[23]Quirk, J. and Karni, S., On the dynamics of a shock-bubble interaction, J. Fluid Mech., 318 (1996), 129–163.Google Scholar
[24]Sethian, J.A., Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999.Google Scholar
[25]Shu, C.-W., Total-variation-diminishing time discretizations, SIAM J. Sci. Stat. Comput., 9 (1988), 1073–1084.Google Scholar
[26]Shu, C.-W. and Osher, S., Efficient implementation of essentially non-oscillatory shock-capturing schemes, J. Comput. Phys., 77 (1988), 439–471.Google Scholar
[27]Sussman, M., Smereka, P. and Osher, S., A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys., 114 (1994), 146–159.Google Scholar
[28]Wang, C.W., Liu, T.G. and Khoo, B.C., A real-ghost fluid method for the simulation of multimedium compressible flow, SIAM J. Sci. Comput., 28 (2006), 278–302.Google Scholar