A pressure-invariant conservative Godunov-type method for barotropic two-fluid flows

Journal of Computational Physics

Volumn 185, Issue 1, 2003, Pages 289-308

  van Brummelen, E H ^a   Koren, B ^a,b  

^a CWI   (Netherlands)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Godunov type methods; Hyperbolic systems; Interface capturing; Osher's scheme; Two fluid flows

Indexed keywords

BAROTROPIC; DISCRETIZATIONS; FLUID FLOW PROBLEMS; GODUNOV-TYPE METHOD; HYPERBOLIC SYSTEM; INTERFACE-CAPTURING; OSHER SCHEME; PRESSURE OSCILLATION; TWO-FLUID FLOW; TYPE METHODS;

EID: 0037429529     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(02)00058-X     Document Type: Article

References (32)

1. R. Abgrall, How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach, J. Comput. Phys. 125 (1996) 150-160.
2. R. Abgrall, S. Karni, Computations of compressible multifluids, J. Comput. Phys. 169 (2001) 594-623.
3. G. Allaire, S. Clerc, S. Kokh, A five-equation model for the numerical simulation of interfaces in two-phase flows, C.R. Acad. Sci. Paris, Série I 331 (2000) 1017-1022.
4. E.H. van Brummelen, Numerical Methods for Steady Viscous Free-Surface Flows, Ph.D. Thesis, University of Amsterdam, Netherlands, 2002.
5. Y.C. Chang, T.Y. Hou, B. Merriman, S. Osher, A level set formulation of Eulerian interface capturing methods for incompressible fluid flows, J. Comput. Phys. 124 (1996) 449-464.
6. R.P. Fedkiw, T. Aslam, B. Merriman, S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost-fluid method), J. Comput. Phys. 152 (1999) 457-492.
7. J. Glimm, X.L. Li, Y. Liu, N. Zhao, Conservative front tracking and level set algorithms, PNAS 98 (25) (2001) 14198-14201.
8. S.K. Godunov, Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics, Mat. Sbornik. 47 (1959) 271-306 (In Russian).
9. R. Hartmann, P. Houston, Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic conservation laws. Technical Report IWR/SFB-Preprints 2001-20, Ruprecht-Karls-Universität Heidelberg, 2001. Available at http://www.iwr.uniheidelberg.de/sfb359/PP/Preprint2001-20.ps.gz.
10. P.W. Hemker, S.P. Spekreijse, Multiple grid and Osher's scheme for the efficient solution of the steady Euler equations, Appl. Numer. Math. 2 (1986) 475-493.
11. C. Hirsch, Numerical Computation of Internal and External Flows, Volume I: Fundamentals of Numerical Discretization, Numerical Methods in Engineering, Wiley, New York, 1995.
12. P. Houston, B. Senior, E. Süli, hp-discontinuous Galerkin finite element methods for hyperbolic problems: error analysis and adaptivity, Int. J. Numer. Meth. Fluids 40 (2002) 153-169.
13. E. Isaacson, H.B. Keller, Analysis of Numerical Methods, Wiley, New York, 1966.
14. P. Jenny, B. Müller, H. Thomann, Correction of conservative Euler solvers for gas mixtures, J. Comput. Phys. 132 (1997) 91-107.
15. S. Karni, Multicomponent flow calculations by a consistent primitive algorithm, J. Comput. Phys. 112 (1994) 31-43.
16. S. Karni, Hybrid multifluid algorithms, SIAM J. Sci. Comput. 17 (1996) 1019-1039.
17. F.J. Kelecy, R.H. Pletcher, The development of a free surface capturing approach for multidimensional free surface flows in closed containers, J. Comput. Phys. 138 (1997) 939-980.
18. B. Koren, MR. Lewis, E.H. van Brummelen, B. van Leer, Godunov and level-set approaches for homentropic two-fluid flow computations, J. Comput. Phys. 181 (2002) 654-674.
19. P.D. Lax, Hyperbolic systems of conservation laws II, Commun. Pure Appl. Math. 10 (1957) 537-566.
20. B. van Leer, On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe, SIAM J. Sci. Statist. Comput. 5 (1984) 1-20.
21. W. Mulder, S. Osher, J.A. Sethian, Computing interface motion in compressible gas dynamics, J. Comput. Phys. 100 (1992) 209-228.
22. D. Nguyen, F. Gibou, R. Fedkiw. A fully conservative ghost-fluid method and stiff detonation waves, Technical Papers of the 12th International Detonation Symposium. 12th International Detonation Symposium, San Diego, CA, 2002. Available at http://www.sainc.com/onr/detsymp/PaperSubmit/FinalManuscript/pdf/ Nguyen-37.pdf
23. S. Osher, F. Solomon, Upwind difference schemes for hyperbolic conservation laws, Math. Comput. 38 (1982) 339-374.
24. R. Saurel, R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows, J. Comput. Phys. 150 (1999) 425-467.
25. R. Saurel, R. Abgrall, A simple method for compressible multifluid flows, SIAM J. Sci. Comput. 21 (1999) 1115-1145.
26. K. Shyue, A fluid-mixture type algorithm for compressible multicomponent flow with van der Waals equation of state, J. Comput. Phys. 156 (1999) 43-88.
27. K. Shyue, A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of state, J. Comput. Phys. 171 (2001) 678-707.
28. J. Smoller, Shock Waves and Reaction-Diffusion Equations. Grundlehren der mathematischen Wissenschaften, Springer, New York, 1983.
29. S. Spekreijse, Multigrid solution of monotone second-order discretizations of hyperbolic conservation laws, Math. Comput. 49 (1987) 135-155.
30. P.K. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. Numer. Anal. 21 (1984) 995-1011.
31. P.A. Thompson, Compressible Fluid Dynamics, Advanced Engineering Series, McGraw-Hill, New York, 1972.
32. P. Wesseling, Principles of Computational Fluid Dynamics, volume 29 of Springer Series in Computational Mathematics, Springer, Berlin, 2001.