Design Principles of Ghost Fluid Method

Abstract

Abstract: By analyzing ghost fluid method for compressible multi-medium flows, fundamentals for defining ghost fluid state with a general equation of state are described. All possible definitions of ghost fluid states are derived according to wave patterns and free variables in ghost fluid region. Following these treatments, it reveals that solution of multi-medium Riemann problem can be obtained exactly in theory. Several simple but effective definitions independent with wave patterns in ghost fluid region, are further summarized. One of these ways is similar to reflective boundary condition. An essential prerequisite is that interfacial velocity must be predicted exactly. Numerical results show that this methodology indeed works reasonably for multi-medium flows.

Key words: compressible multi-medium flows, ghost fluid method, multi-medium Riemann problem, ghost fluid state, general equation of state

CLC Number:

O359

XU Liang, FENG Chengliang, LIU Tiegang. Design Principles of Ghost Fluid Method[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(6): 671-680.

References

[1] LARROUTUROU B. How to preserve the mass fractions positivity when computing compressible multi-component flows[J]. J Comput Phys, 1991, 95(1):59-84.
[2] KARNI S. Hybrid multifluid algorithms[J]. SIAM J Sci Comput, 1996, 17(5):1019-1039.
[3] JENNY P, MULLER B, THOMANN H. Correction of conservative Euler solvers for gas mixtures[J]. J Comput Phys, 1997, 132(1):91-107.
[4] TANG W J,JIANG L, CHENG J B. Algorithm preserving mass fraction maximum principle for multi-component flow[J]. Chinese J Comput Phys, 2014, 31(3):292-306.
[5] COCCHI J P, SAUREL R. A Riemann problem based method for the resolution of compressible multimaterial flows[J]. J Comput Phys, 1997, 137(2):265-298.
[6] LIU T G, KHOO B C, YEO K S. Ghost fluid method for strong shock impacting on material interface[J]. J Comput Phys, 2003, 190(2):651-681.
[7] WANG C W, LIU T G, KHOO B C. A real ghost fluid method for the simulation of multimedium compressible flow[J]. SIAM J Sci Comput, 2006, 28(1):278-302.
[8] FEDKIW R P, ASLAM T, MERRIMAN B, Osher S. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)[J]. J Comput Phys, 1999, 152(2):457-492.
[9] DING Y, YUAN L, YANG L. An explicit-implicit algorithm for ghost fluid method[J]. Chinese J Comput Phys, 2013, 30(1):27-34.
[10] LIU T G, KHOO B C, WANG C W. The ghost fluid method for compressible gas-water simulation[J]. J Comput Phys, 2005, 204(1):193-221.
[11] SONG P C, WANG C W. Interface treating method for multi-medium flow on triangular meshes[J]. Chinese J Comput Phys, 2012, 29(1):36-42.
[12] LIU T G, XIE W F, KHOO B C. The modified ghost fluid method for coupling of fluid and structure constituted with hydro-elasto-plastic equation of state[J]. SIAM J Sci Comput, 2008, 30(3):1105-1130.
[13] HAAS J F, STURTEVANT B. Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities[J]. J Fluid Mech, 1987, 181(1):41-76.
[14] LIU T G, KHOO B C, YEO K S. The simulation of compressible multi-medium flow Ⅱ:Applications to 2D underwater shock refraction[J]. Comput Fluids, 2001, 30(3):315-337.