Journal of Scientific Computing

, Volume 81, Issue 3, pp 1906–1944 | Cite as

Modified Ghost Fluid Method with Acceleration Correction (MGFM/AC)

  • Tiegang LiuEmail author
  • Chengliang Feng
  • Liang Xu


In this work, we show that the modified ghost fluid method might suffer overheating and leads to inaccurate numerical results when directly applied to a moving rigid boundary with acceleration. We discover the insightful reasons and then develop a new technique to take into account the effect of boundary acceleration on the definition of ghost fluid states based on a generalized Piston–Riemann problem. Theoretical analysis and numerical results show that the modified ghost fluid method with acceleration correction can overcome such difficulty effectively.


General piston problem Moving boundary Ghost fluid method Modified ghost fluid method Generalized Piston–Riemann problem 



The research was supported in part by the Science Challenge Project (No. JCKY2016212A502) and National Natural Science Foundation of China (Nos. 11601013 and 91530325).


  1. 1.
    Larrouturou, B.: How to preserve the mass fractions positivity when computing compressible multicomponent flows. J. Comput. Phys. 95, 59–84 (1991)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Karni, S.: Multicomponent flow calculations by a consistent primitive algorithm. J. Comput. Phys. 112, 31–43 (1994)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Karni, S.: Hybrid multifluid algorithms. SIAM J. Sci. Comput. 17, 1019–1039 (1996)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Abgrall, R.: How to prevent oscillations in multicomponent flow calculations: a quasi conservative approach. J. Comput. Phys. 125, 150–160 (1996)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Jenny, P., Muller, B., Thomann, H.: Correction of conservative Euler solvers for gas mixtures. J. Comput. Phys. 132, 91–107 (1997)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Abgrall, R., Karni, S.: Computations of compressible multifluids. J. Comput. Phys. 169, 594–623 (2001)MathSciNetCrossRefGoogle Scholar
  7. 7.
    van Brummelen, E.H., Koren, B.: A pressure-invariant conservative Godunov-type method for barotropic two-fluid flows. J. Comput. Phys. 185, 289–308 (2003)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Nourgaliev, R.R., Dinh, T.N., Theofanous, T.G.: Adaptive characteristics-based matching for compressible multifluid dynamics. J. Comput. Phys. 213, 500–529 (2006)CrossRefGoogle Scholar
  9. 9.
    Johnsen, E., Colonius, T.: Implementation of WENO schemes in compressible multicomponent flow problems. J. Comput. Phys. 219, 715–732 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hirt, C., Nichols, B.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225 (1981)CrossRefGoogle Scholar
  11. 11.
    Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 146–159 (1994)CrossRefGoogle Scholar
  12. 12.
    Unverdi, S.O., Tryggvason, G.: A front-tracking method for viscous incompressible multi-fluid flows. J. Comput. Phys. 100, 25–37 (1992)CrossRefGoogle Scholar
  13. 13.
    Glimm, J., Marchesin, D., McBryan, O.: Subgrid resolution of fluid discontinuities, II. J. Comput. Phys. 37, 336–354 (1980)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Glimm, J., Marchesin, D., McBryan, O.: A numerical method for two phase flow with an unstable interface. J. Comput. Phys. 39, 179–200 (1981)MathSciNetCrossRefGoogle Scholar
  15. 15.
    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, 457–492 (1999)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Fedkiw, R.P.: Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method. J. Comput. Phys. 175, 200–224 (2002)CrossRefGoogle Scholar
  17. 17.
    Liu, T.G., Khoo, B.C., Yeo, K.S.: Ghost fluid method for strong shock impacting on material interface. J. Comput. Phys. 190, 651–681 (2003)CrossRefGoogle Scholar
  18. 18.
    Hu, X.Y., Khoo, B.C.: An interface interaction method for compressible multifluids. J. Comput. Phys. 198, 35–64 (2004)CrossRefGoogle Scholar
  19. 19.
    Wang, C.W., Liu, T.G., Khoo, B.C.: A real-ghost fluid method for the simulation of multimedium compressible flow. SIAM J. Sci. Comput. 28, 278–302 (2006)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Liu, T.G., Khoo, B.C., Wang, C.W.: The ghost fluid method for compressible gas–water simulation. J. Comput. Phys. 204, 193–221 (2005)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Hao, Y., Prosperetti, A.: A numerical method for three-dimensional gas–liquid flow computations. J. Comput. Phys. 196, 126–144 (2004)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Farhat, C., Rallu, A., 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, 7674–7700 (2008)CrossRefGoogle Scholar
  23. 23.
    Terashima, H., Tryggvason, G.: A front-tracking/ghost-fluid method for fluid interfaces in compressible flows. J. Comput. Phys. 228, 4012–4037 (2009)CrossRefGoogle Scholar
  24. 24.
    Xu, L., Feng, C.L., Liu, T.G.: Practical techniques in ghost fluid method for compressible multi-medium flows. Commun. Comput. Phys. 20, 619–659 (2016)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Qiu, J.X., Liu, T.G., Khoo, B.C.: Simulations of compressible two-medium flow by Runge–Kutta discontinuous Galerkin methods with the ghost fluid method. Commun. Comput. Phys. 3, 479–504 (2008)MathSciNetzbMATHGoogle Scholar
  26. 26.
    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. SIAM J. Sci. Comput. 30, 1105–1130 (2008)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Liu, T.G., Khoo, B.C., Xie, W.F.: The modified ghost fluid method as applied to extreme fluid–structure interaction in the presence of cavitation. Commun. Comput. Phys. 1, 898–919 (2006)zbMATHGoogle Scholar
  28. 28.
    Sambasivan, S., UdayKumar, H.S.: Ghost fluid method for strong shock interactions. Part 1: fluid–fluid interfaces. AIAA J. 47, 2907–2922 (2009)CrossRefGoogle Scholar
  29. 29.
    Barton, P.T., Drikakis, D.: An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces. J. Comput. Phys. 229, 5518–5540 (2010)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Xu, L., Liu, T.G.: Modified ghost fluid method as applied to fluid–plate interaction. Adv. Appl. Math. Mech. 6(1), 24–48 (2014)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Gao, S., Liu, T.G.: 1D Exact elastic-perfectly plastic solid Riemann solver and its multi-material application. Adv. Appl. Math. Mech. 9(3), 621–650 (2017)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Gao, S., Liu, T.G., Yao, C.B.: A complete list of exact solution for one-dimensional elastic-perfectly plastic solid Riemann problem without vacuum. Commun. Nonlinear Sci. Numer. Simul. 63, 205–227 (2018)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Xu, L., Liu, T.G.: Optimal error estimation of the modified ghost fluid method. Commun. Comput. Phys. 8, 403–426 (2010)MathSciNetzbMATHGoogle Scholar
  34. 34.
    Xu, L., Liu, T.G.: Accuracies and conservation errors of various ghost fluid methods for multimedium Riemann problem. J. Comput. Phys. 230, 4975–4990 (2011)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Ben-Artzi, M., Li, J.Q., Warnecke, G.: A direct Eulerian GRP scheme for compressible fluid flows. J. Comput. Phys. 218(1), 19–43 (2006)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Liu, T.G., Khoo, B.C., 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, 291–314 (2001)CrossRefGoogle Scholar
  37. 37.
    Leer, B.V.: Towards the ultimate conservative difference scheme. V—a second-order sequel to Godunov’s method. J. Comput. Phys. 32(1), 101–136 (1979)CrossRefGoogle Scholar
  38. 38.
    Courant, R., Friedrichs, K.O.: Supersonic Flows and Shock Waves, p. 424. Interscience Publishers, New York (1948)zbMATHGoogle Scholar
  39. 39.
    Toro, E.F.: Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer, Berlin (1999)CrossRefGoogle Scholar
  40. 40.
    Li, J.Q., Liu, T.G., Sun, Z.F.: Implementation of the GRP scheme for computing radially symmetric compressible fluid flows. J. Comput. Phys. 228(16), 5867–5887 (2009)MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.LMIB and School of Mathematics and Systems ScienceBeijing University of Aeronautics and AstronauticsBeijingPeople’s Republic of China
  2. 2.China Academy of Aerospace AerodynamicsBeijingPeople’s Republic of China

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