The explicit simplified interface method for compressible multicomponent flows

SIAM Journal on Scientific Computing

Volumn 27, Issue 1, 2005, Pages 208-230

  Lombard, Bruno ^a   Donat, Rosa ^b  

^a LABORATOIRE DE MÉCANIQUE ET D ACOUSTIQUE   (France)

^b UNIVERSITY OF VALENCIA   (Spain)

Author keywords

ENO WENO; Euler equations; Ghost fluid method; Interface methods; Jump conditions; Level set; Multicomponent flows

Indexed keywords

APPROXIMATION THEORY; LINEAR SYSTEMS; OSCILLATIONS;

ENO-WENO; EULER EQUATIONS; GHOST FLUID METHOD; INTERFACE METHODS; JUMP CONDITIONS; LEVEL-SET; MULTICOMPONENT FLOWS;

INTERFACES (MATERIALS);

EID: 33144476647     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/030601041     Document Type: Article

References (34)

1. R. ABGRALL, How to prevent pressure oscillations in multicomponent flow calculations: A quasi conservative approach, J. Comput. Phys., 125 (1996), pp. 150-160.
2. R. ABGRALL AND S. KARNI, Computations of compressible multifluids, J. Comput. Phys., 169 (2001), pp. 594-623.
3. G. ALLAIRE, S. CLERC, AND S. KOKH, A five-equation model for the simulation of interfaces between compressible flows, J. Comput. Phys., 181 (2002), pp. 577-616.
4. M. ARIENTI, P. HUNG, E. MORANO, AND J. E. SHEPHERD, A level-set approach to Eulerian-Lagrangian coupling, J. Comput. Phys., 185 (2003), pp. 213-251.
5. T. D. ASLAM, A partial differential equation approach to multidimensional extrapolation, J. Comput. Phys., 193 (2003), pp. 349-355.
6. R. DONAT AND A. MARQUINA, Capturing shock reflections: An improved flux formula, J. Comput. Phys., 125 (1996), pp. 42-58.
7. R. P. FEDKIW, Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method, J. Comput. Phys., 175 (2002), pp. 200-224.
8. R. P. FEDKIW, T. ASLAM, B. MERRIMAN, AND S. OSHER, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys., 152 (1999), pp. 457-492.
9. R. P. FEDKIW, T. ASLAM, AND S. XU, The ghost fluid method for deflagration and detonation discontinuities, J. Comput. Phys., 154 (1999), pp. 393-427.
10. R. P. FEDKIW, B. MERRIMAN, R. DONAT, AND S. OSHER, The Penultimate Scheme for Systems of Conservation Laws: Finite-Difference ENO with Marquina's Flux Splitting, UCLA CAM Report 96-18, UCLA, Los Angeles, CA, 1996.
11. R. P. FEDKIW, B. MERRIMAN, AND S. OSHER, Simplified discretization of systems of hyperbolic conservation laws containing advection equations, J. Comput. Phys., 157 (2000), pp. 302-326.
12. T. Y. HOU, Z. LI, S. OSHER, AND H. ZHAO, A hybrid method for moving interface problems with application to Hele-Shaw flow, J. Comput. Phys., 134 (1997), pp. 236-252.
13. G.-S. JIANG AND C. W. SHU, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), pp. 202-228.
14. G.-S. JIANG AND D. PENG, Weighted ENO schemes for Hamilton-Jacobi equations, SIAM J. Sci. Comput., 21 (2000), pp. 2126-2143.
15. S. KARNI, Multicomponent flow calculations by a consistent primitive algorithm, J. Comput. Phys., 112 (1994), pp. 31-43.
16. S. KARNI, Hybrid multifluid algorithms, SIAM J. Sci. Comput., 17 (1996), pp. 1019-1039.
17. B. LARROUTUROU, How to preserve the mass fractions positivity when computing compressible multi-component flows, J. Comput. Phys., 95 (1991), pp. 59-84.
18. R. J. LEVEQUE AND Z. LI, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., 31 (1994), pp. 1019-1044.
19. R. J. LEVEQUE, Numerical Methods for Conservation Laws, Birkhäuser, Basel, 1990.
20. B. LOMBARD, Modélisation numérique de la propagation des ondes acoustiques et élastiques en présence d'interfaces, Ph.D. thesis, University of Aix-Marseille II, Marseille, France, 2002.
21. B. LOMBARD AND J. PIRAUX, How to incorporate the spring-mass conditions in finite-difference schemes, SIAM J. Sci. Comput., 24 (2003), pp. 1379-1407.
22. B. LOMBARD AND J. PIRAUX, Numerical treatment of two-dimensional interfaces for acoustic and elastic waves, J. Comput. Phys., 195 (2004), pp. 90-116.
23. A. MARQUINA AND P. MULET, A flux-split algorithm applied to conservative models for multicomponent compressible flows, J. Comput. Phys., 185 (2003), pp. 120-139.
24. W. MULDER, S. OSHER, AND J. A. SETHIAN, Computing interface motion in compressible gas dynamics, J. Comput. Phys., 100 (1992), pp. 209-228.
25. D. NGUYEN, F. GIBOU, AND R. P. FEDKIW, A fully conservative ghost fluid method and stiff detonation waves, in 12th International Detonation Symposium, San Diego, CA, 2002.
26. S. OSHER AND C.-W. SHU, High-order nonoscillatory schemes for Hamilton-Jacobi equations, SIAM J. Numer. Anal., 28 (1991), pp. 907-922.
27. J. PIRAUX AND B. LOMBARD, A new interface method for hyperbolic problems with discontinuous coefficients: One-dimensional acoustic example, J. Comput. Phys., 168 (2001), pp. 227-248.
28. G. RUSSO AND P. SMEREKA, A remark on computing distance functions, J. Comput. Phys., 163 (2000), pp. 51-67.
29. R. SAUREL AND R. ABGRALL, A simple method for compressible multifluid flows, SIAM J. Sci. Comput., 21 (1999), pp. 1115-1145.
30. C.-W. SHU AND S. OSHER, Efficient implementation of essentially nonoscillatory shock-capturing schemes. II, J. Comput. Phys., 83 (1989), pp. 32-78.
31. K. M. SHYUE, An efficient shock-capturing algorithm for compressible multicomponent problems, J. Comput. Phys., 142 (1998), pp. 208-242.
32. Y. STIRIBA, A. MARQUINA, AND R. DONAT, Equilibrium real gas computations using Marquina's scheme, Internat. J. Numer. Methods Fluids, 141 (2003), pp. 275-301.
33. M. SUSSMAN, P. SMEREKA, AND S. OSHER, A level-set approach for computing solutions to incompressible two-phase flows, J. Comput. Phys., 114 (1994), pp. 146-159.
34. C. ZHANG AND R. J. LEVEQUE, The immersed interface method for acoustic wave equations with discontinuous coefficients, Wave Motion, 25 (1997), pp. 237-263.