Remark on the generalized Riemann problem method for compressible fluid flows

Journal of Computational Physics

Volumn 222, Issue 2, 2007, Pages 796-808

  Li, Jiequan ^a   Sun, Zhongfeng ^a  

^a CAPITAL NORMAL UNIVERSITY   (China)

Author keywords

Resolution of rarefaction waves; Riemann invariants; The generalized Riemann problem (GRP) method

Indexed keywords

LAGRANGE MULTIPLIERS; PARTIAL DIFFERENTIAL EQUATIONS;

COMPRESSIBLE FLUID FLOW; EULERIAN; FLOW BASED; LAGRANGIAN FORMULATIONS; RAREFACTION WAVES; RESOLUTION OF RAREFACTION WAVE; RIEMANN INVARIANTS; RIEMANN PROBLEM; SECOND ORDERS; THE GENERALIZED RIEMANN PROBLEM METHOD;

COMPRESSIBLE FLOW;

EID: 33847026042     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.08.017     Document Type: Article

References (12)

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. Statist. 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
5. M. Ben-Artzi, J. Li, Hyperbolic balance laws: Riemann invariants and the generalized Riemann problem, Preprint, 2006.
6. Ben-Artzi M., Li J., and Warnecke G. A direct Eulerian GRP scheme for compressible fluid flows. J. Comput. Phys. 28 (2006) 19-43
7. Dafermos C.M. Hyperbolic Conservation Laws in Continuum Physics (2000), Springer
8. van Leer B. Towards the ultimate conservative difference scheme, V. A second-order sequel to Godunov's method. J. Comput. Phys. 32 1 (1979) 101-136
9. Li J., and Chen G. The generalized Riemann problem method for the shallow water equations with bottom topography. Int. J. Numer. Methods Eng. 65 6 (2006) 834-862
10. Bourgeade A., LeFloch Ph., 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
11. LeFloch Ph., and Raviart P.-A. An asymptotic expansion for the solution of the generalized Riemann problem. I. General theory. Ann. Inst. H. Poincar Anal. Non Linaire 5 2 (1988) 179-207
12. Toro E. Riemann Solvers and Numerical Methods for Fluid Dynamics. A Practical Introduction (1997), Springer-Verlag, Berlin