Central-upwind schemes on triangular grids for hyperbolic systems of conservation laws

Numerical Methods for Partial Differential Equations

Volumn 21, Issue 3, 2005, Pages 536-552

  Kurganov, Alexander ^a   Petrova, Guergana ^b  

^a Tulane University   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Hyperbolic systems of conservation laws; Semi discrete central upwind schemes; Triangular grids

Indexed keywords

EID: 18744393724     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/num.20049     Document Type: Article

References (21)

1. 1 K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Comm Pure Appl Math 7 (1954), 345–392.
2. 2 P. D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm Pure Appl Math 7 (1954), 159–193.
3. 3 H. Nessyahu and E. Tadmor, Non‐oscillatory central differencing for hyperbolic conservation laws, J Comput Phys 87 (1990), 408–463.
4. 4 P. Arminjon and M.‐C. Viallon, Généralisation du schéma de Nessyahu‐Tadmor pour une équation hyperbolique à deux dimensions d'espace, CR Acad Sci Paris t. 320, série I (1995), 85–88.
5. 5 G.‐S. Jiang and E. Tadmor, Non‐oscillatory central schemes for multidimensional hyperbolic conservation laws, SIAM J Sci Comput 19 (1998), 1892–1917.
6. 6 D. Levy, G. Puppo, and G. Russo, A fourth‐order central WENO scheme for multidimensional hyperbolic systems of conservation laws, SIAM J Sci Comput 24 (2002), 480–506.
7. 7 A. Kurganov and D. Levy, A third‐order semi‐discrete central scheme for conservation laws and convection‐diffusion equations, SIAM J Sci Comput 22 (2000), 1461–1488.
8. 8 A. Kurganov and G. Petrova, A third‐order semi‐discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems, Numer Math 88 (2001), 683–729.
9. 9 A. Kurganov and E. Tadmor, New high‐resolution central schemes for nonlinear conservation laws and convection‐diffusion equations, J Comput Phys 160 (2000), 241–282.
10. 10 A. Kurganov, S. Noelle, and G. Petrova, Semi‐discrete central‐upwind scheme for hyperbolic conservation laws and Hamilton‐Jacobi equations, SIAM J Sci Comput 23 (2001), 707–740.
11. 11 D. Kröner, Numerical schemes for conservation laws, Wiley, Chichester, 1997.
12. 12 P. Arminjon and A. St‐Cyr, Nessyahu‐Tadmor‐type central finite volume methods without predictor for 3D Cartesian and unstructured tetrahedral grids, Appl Numer Math 46 (2003), 135–155.
13. 13 P. Arminjon, M.‐C. Viallon, and A. Madrane, A finite volume extension of the Lax‐Friedrichs and Nessyahu‐Tadmor schemes for conservation laws on unstructured grids, Int J Comput Fluid Dyn 9 (1997), 1–22.
14. 14 M. Ohlberger, private communications.
15. 15 M. Wierse, Solving the compressible Euler equations in timedependent geometries, Proc 5th International Conference on Hyperbolic Problems, Stony Brook, 1994.
16. 16 M. Wierse, Higher‐order upwind schemes on unstructured grids for the compressible Euler equations in timedependent geometries in 3‐D, PhD Thesis, University of Freiburg, 1994.
17. 17 S. Gottlieb, C.‐W. Shu, and E. Tadmor, Strong stability‐preserving high order time discretization methods, SIAM Rev 43 (2001), 89–112.
18. 18 A. Kurganov and E. Tadmor, Solution of two‐dimensional Riemann problems for gas dynamics without Riemann problem solvers, Numer Methods Partial Differential Eq 18 (2002), 584–608.
19. 19 G. Sod, A survey of several finite different methods for systems of nonlinear hyperbolic conservation laws, J Comput Phys 22 (1978), 1–31.
20. 20 C. W. Schulz‐Rinne, J. P. Collins, and H. M. Glaz, Numerical solution of the Riemann problem for two‐dimensional gas dynamics, SIAM J Sci Comput 14 (1993), 1394–1414.
21. 21 C. W. Schulz‐Rinne, Classification of the Riemann problem for two‐dimensional gas dynamics, SIAM J Math Anal 24 (1993), 76–88.