Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-29T11:06:39.910Z Has data issue: false hasContentIssue false

Practical Techniques in Ghost Fluid Method for Compressible Multi-Medium Flows

Published online by Cambridge University Press:  31 August 2016

Liang Xu*
Affiliation:
China Academy of Aerospace Aerodynamics, Beijing 100074, P.R. China
Chengliang Feng*
Affiliation:
LMIB and School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, P.R. China
Tiegang Liu*
Affiliation:
LMIB and School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, P.R. China
*
*Corresponding author. Email addresses:[email protected] (L. Xu), [email protected] (C. Feng), [email protected] (T. Liu)
*Corresponding author. Email addresses:[email protected] (L. Xu), [email protected] (C. Feng), [email protected] (T. Liu)
*Corresponding author. Email addresses:[email protected] (L. Xu), [email protected] (C. Feng), [email protected] (T. Liu)
Get access

Abstract

The modified ghost fluid method (MGFM), due to its reasonable treatment for ghost fluid state, has been shown to be robust and efficient when applied to compressible multi-medium flows. Other feasible definitions of the ghost fluid state, however, have yet to be systematically presented. By analyzing all possible wave structures and relations for a multi-medium Riemann problem, we derive all the conditions to define the ghost fluid state. Under these conditions, the solution in the real fluid region can be obtained exactly, regardless of the wave pattern in the ghost fluid region. According to the analysis herein, a practical ghost fluid method (PGFM) is proposed to simulate compressible multi-medium flows. In contrast with the MGFM where three degrees of freedomat the interface are required to define the ghost fluid state, only one degree of freedomis required in this treatment. However, when these methods proved correct in theory are used in computations for the multi-medium Riemann problem, numerical errors at the material interface may be inevitable. We show that these errors are mainly induced by the single-medium numerical scheme in essence, rather than the ghost fluid method itself. Equipped with some density-correction techniques, the PGFM is found to be able to suppress these unphysical solutions dramatically.

Type
Research Article
Copyright
Copyright © Global-Science Press 2016 

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] Larrouturou, B., How to preserve the mass fractions positivity when computing compressible multi-component flows, J. Comput. Phys., 95 (1991), 5984.CrossRefGoogle Scholar
[2] Karni, S., Multicomponent flow calculations by a consistent primitive algorithm, J. Comput. Phys., 112 (1994), 3143.CrossRefGoogle Scholar
[3] Karni, S., Hybrid multifluid algorithms, SIAM J. Sci. Comput., 17 (1996), 10191039.CrossRefGoogle Scholar
[4] Abgrall, R., How to prevent oscillations in multicomponent flow calculations: a quasi conservative approach, J. Comput. Phys., 125 (1996), 150160.CrossRefGoogle Scholar
[5] Jenny, P., Muller, B. and Thomann, H., Correction of conservative Euler solvers for gas mixtures, J. Comput. Phys., 132 (1997), 91107.CrossRefGoogle Scholar
[6] Abgrall, R. and Karni, S., Computations of compressible multifluids, J. Comput. Phys., 169 (2001), 594623.CrossRefGoogle Scholar
[7] van Brummelen, E. H. and Koren, B., A pressure-invariant conservative Godunov-type method for barotropic two-fluid flows, J. Comput. Phys., 185 (2003), 289308.CrossRefGoogle Scholar
[8] Nourgaliev, R. R., Dinh, T. N. and Theofanous, T. G., Adaptive characteristics-based matching for compressible multifluid dynamics, J. Comput. Phys., 213 (2006), 500529.CrossRefGoogle Scholar
[9] Johnsen, E. and Colonius, T., Implementation of WENO schemes in compressible multicomponent flow problems, J. Comput. Phys., 219 (2006), 715732.CrossRefGoogle Scholar
[10] Hirt, C. and Nichols, B., Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys., 39 (1981), 201225.CrossRefGoogle Scholar
[11] Sussman, M., Smereka, P. and Osher, S., A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys., 114 (1994), 146159.CrossRefGoogle Scholar
[12] Unverdi, S.O. and Tryggvason, G., Afront-tracking method for viscous incompressible multifluid flows, J. Comput. Phys., 100 (1992), 2537.CrossRefGoogle Scholar
[13] Glimm, J., Marchesin, D. and McBryan, O., Subgrid resolution of fluid discontinuities, II, J. Comput. Phys., 37 (1980), 336354.CrossRefGoogle Scholar
[14] Glimm, J., Marchesin, D. and McBryan, O., A numerical method for two phase flow with an unstable interface, J. Comput. Phys., 39 (1981), 179200.CrossRefGoogle Scholar
[15] 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), 457492.CrossRefGoogle Scholar
[16] Fedkiw, R. P., Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method, J. Comput. Phys., 175 (2002), 200224.CrossRefGoogle 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), 651681.CrossRefGoogle Scholar
[18] Hu, X. Y. and Khoo, B. C., An interface interaction method for compressible multifluids, J. Comput. Phys., 198 (2004), 3564.CrossRefGoogle Scholar
[19] 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), 278302.CrossRefGoogle Scholar
[20] Liu, T. G., Khoo, B. C. and Wang, C. W., The ghost fluid method for compressible gas-water simulation, J. Comput. Phys., 204 (2005), 193221.CrossRefGoogle Scholar
[21] Hao, Y. and Prosperetti, A., A numerical method for three-dimensional gas-liquid flow computations, J. Comput. Phys., 196 (2004), 126144.CrossRefGoogle Scholar
[22] Farhat, C., Rallu, A. and Shankaran, S., A higher-order generalized ghost fluid method for the poor for the three-dimensional two-phase flow computation of underwater implosions, J. Comput. Phys., 227 (2008), 76747700.CrossRefGoogle Scholar
[23] Terashima, H. and Tryggvason, G., A front-tracking/ghost-fluid method for fluid interfaces in compressible flows, J. Comput. Phys., 228 (2009), 40124037.CrossRefGoogle Scholar
[24] Qiu, J. X., Liu, T. G. 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), 479504.Google Scholar
[25] Liu, T. G., Xie, W. F. and Khoo, B. C., The modified ghost fluid method for coupling of fluid and structure constituted with hydro-elasto-plastic equation of state, SIAM J. Sci. Comput., 30 (2008), 11051130.CrossRefGoogle Scholar
[26] Liu, T. G., Khoo, B. C. and Xie, W. F., The modified ghost fluid method as applied to extreme fluid-structure interaction in the presence of cavitation, Commun. Comput. Phys., 1 (2006), 898919.Google Scholar
[27] Sambasivan, S. and UdayKumar, H. S., Ghost fluid method for strong shock interactions. Part 1: Fluid-fluid interfaces, AIAA Journal, 47 (2009), 29072922.CrossRefGoogle Scholar
[28] Barton, P. T. and Drikakis, D., An Eulerian method for multi-component problems in nonlinear elasticity with sliding interfaces, J. Comput. Phys., 229 (2010), 55185540.CrossRefGoogle Scholar
[29] Xu, L. and Liu, T. G., Optimal error estimation of the modified ghost fluid method, Commun. Comput. Phys., 8 (2010), 403426.Google Scholar
[30] Xu, L. and Liu, T. G., Accuracies and conservation errors of various ghost fluid methods for multi-medium Riemann problem, J. Comput. Phys., 230 (2011), 49754990.CrossRefGoogle Scholar
[31] Fedkiw, R. P., Marquina, A. and Merriman, B., An isobaric fix for the overheating problem in multimaterial compressible flows, J. Comput. Phys., 148 (1999), 545578.CrossRefGoogle Scholar
[32] Toro, E. F., Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer-Verlag Berlin Heidelbert, 1999.CrossRefGoogle Scholar
[33] Liu, T. G., Khoo, B. C. and Yeo, K. S., The simulation of compressible multi-medium flow. Part I: A new methodology with test applications to 1D gas-gas and gas-water cases, Comput. Fluids, 30 (2001), 291314.CrossRefGoogle Scholar
[34] Harten, A., Lax, P. D. and van Leer, B., On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev., 25 (1983), 3561.CrossRefGoogle Scholar
[35] Haas, J. F. and Sturtevant, B., Interaction of weak shock waves with cylindrical and spherical inhomogeneities, J. Fluid Mech., 181 (1987), 4176.CrossRefGoogle Scholar
[36] Quirk, J. J. and Karni, S., On the dynamics of a shock-bubble interaction, J. Fluid Mech., 318 (1996), 129163.CrossRefGoogle Scholar
[37] Marquina, A. and Mulet, P., A flux-split algorithm applied to conservative models for multicomponent compressible flows, J. Comput. Phys., 185 (2003), 120138.CrossRefGoogle Scholar
[38] 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, Comput. Fluids, 30 (2001), 315337.CrossRefGoogle Scholar