A direct Eulerian GRP scheme for compressible fluid flows

Journal of Computational Physics

Volumn 218, Issue 1, 2006, Pages 19-43

  Ben Artzi, Matania ^a   Li, Jiequan ^b   Warnecke, Gerald ^c  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b CAPITAL NORMAL UNIVERSITY   (China)

^c OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

Characteristic coordinates; Riemann invariants; The Eulerian version; The generalized Riemann problem scheme

Indexed keywords

PARTIAL DIFFERENTIAL EQUATIONS;

CHARACTERISTIC COORDINATE; COMPRESSIBLE FLUID FLOW; EULERIAN; EULERIAN FORMULATIONS; LAGRANGIAN SCHEME; MULTI-DIMENSIONAL CASE; RIEMANN INVARIANTS; RIEMANN PROBLEM; THE EULERIAN VERSION; THE GENERALIZED RIEMANN PROBLEM SCHEME;

COMPRESSIBLE FLOW;

EID: 33748558739     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.01.044     Document Type: Article

References (26)

1. Ben-Artzi M., and Falcovitz J. A second-order Godunov-type scheme for compressible fluid dynamics. J. Comput. Phys. 55 1 (1984) 1-32
2. Ben-Artzi M., and Falcovitz J. An upwind second-order scheme for compressible duct flows. SIAM J. Sci. Stat. Comput. 7 3 (1986) 744-768
3. Ben-Artzi M. The generalized Riemann problem for reactive flows. J. Comput. Phys. 81 1 (1989) 70-101
4. Ben-Artzi M., and Falcovitz J. Generalized Riemann Problems in Computational Gas Dynamics (2003), Cambridge University Press, Cambridge
5. Bourgeade A., LeFloch P., and Raviart P.-A. An asymptotic expansion for the solution of the generalized Riemann problem. II. Application to the equations of gas dynamics. Ann. Inst. H. Poincar Anal. Non Linaire 6 6 (1989) 437-480
6. Chang T., Chen G.-Q., and Yang S. On the 2-D Riemann problem for the compressible Euler equations I: Interaction of shocks and rarefaction waves. Discrete Contin. Dyn. Syst. 1 4 (1995) 555-584 II: Interaction of contact discontinuities. 6(2) (2000) 419-430
7. Courant R., and Friedrichs K.O. Supersonic Flow and Shock Waves (1948), Interscience, New York
8. Einfeldt B., Munz C.D., Roe P.L., and Sjogreen B.P.L. On Godunov-type methods near low densities. J. Comput. Phys. 92 2 (1991) 273-295
9. Godlewski E., and Raviart P.-A. Numerical approximation of hyperbolic systems of conservation laws. Applied Mathematical Sciences vol. 118 (1996), Springer, Germany
10. Godunov S.K. A finite difference method for the numerical computation and discontinuous solutions of the equations of fluid dynamics. Mat. Sb. 47 (1959) 271-295
11. Kurganov A., and Tadmor E. Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers. Numer. Meth. Partial Differ. Eq. 18 5 (2002) 584-608
12. LeFloch Ph., and Raviart P.-A. An asymptotic expansion for the solution of the generalized Riemann problem. I. General theory. Ann. Inst. H. Poincar é Anal. Non Liné aire 5 2 (1988) 179-207
13. Li J., and Chen G. The generalized Riemann problem method for the shallow water equations with bottom topography. Int. J. Numer. Meth. Eng. 65 6 (2006) 834-862
14. Li J., Zhang T., and Yang S. The two-dimensional Riemann problem in gas dynamics. Pitman Monographs and Surveys in Pure and Applied Mathematics vol. 98 (1998), Addison Wesley Longman, Harlow
15. Li T.T. Global classical solutions for quasilinear hyperbolic systems. Research in Applied Mathematics (1994), Wiley, Masson, Chichester, Paris
16. Liu X.-D., and Lax P.D. Solution of two-dimensional Riemann problems of gas dynamics by positive schemes. SIAM J. Sci. Comput. 19 2 (1998) 319-340
17. Schulz-Rinne C.W., Collins J.P., and Glaz H.M. Numerical solution of the Riemann problem for two-dimensional gas dynamics. SIAM J. Sci. Comput. 14 6 (1993) 1394-1414
18. Smoller J. Shock waves and reaction-diffusion equations. Grundlehren der Mathematischen Wissenschaften. second ed. vol. 258 (1994), Springer-Verlag, New York p. xxii
19. Sod G.A. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 27 (1978) 1-31
20. Strang G. Accurate partial difference methods. I: Linear Cauchy problems. Arch. Ration. Mech. Anal. 12 (1963) 392-402
21. II: Non-linear problems. Numer. Math. 6 (1964) 37-46
22. Toro E.F. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction (1997), Springer, Germany
23. van Leer B. Towards the ultimate conservative difference scheme. V.J. Comp. Phys. 32 (1979) 101-136
24. Woodward P., and Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54 (1984) 115-173
25. Zhang T., and Zheng Y. Conjecture on the structure of solutions of the Riemann problem for two-dimensional gas dynamics systems. SIAM J. Math. Anal. 21 3 (1990) 593-630
26. Zheng Y. Systems of conservation laws. Two-dimensional Riemann problems. Progress in Nonlinear Differential Equations and their Applications vol. 38 (2001), Birkhauser, Boston, MA