Central schemes and contact discontinuities

Mathematical Modelling and Numerical Analysis

Volumn 34, Issue 6, 2000, Pages 1259-1275

  Kurganov, Alexander ^a   Petrova, Guergana ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Euler equations of gas dynamics; Fully discrete and semi discrete central schemes; Partial characteristic decomposition

Indexed keywords

EID: 0034551267     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2000126     Document Type: Article

References (26)

1. P. Arminjon and M.-C. Viallon, Généralisation du schéma de Nessyahu-Tadmor pour une équation hyperbolique à deux dimensions d'espace. C.R. Acad. Sci. Paris Sér. 1 320 (1995) 85-88.
2. 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.
3. F. Bianco, G. Puppo and G. Russo, High order central schemes for hyperbolic systems of conservation laws. SIAM J. Sci. Comput. 21 (1999) 294-322.
4. B. Einfeldt, On Godunov-type methods for gas dynamics. SIAM J. Numer. Anal. 25 (1988) 294-318.
5. K.O. Friedrichs, Symmetric hyperbolic linear differential equations. Comm. Pure Appl. Math. 7 (1954) 345-392.
6. A. Harten, The artificial compression method for computation of shocks and contact discontinuities. III. Self-adjusting hybrid schemes. Math. Comp. 32 (1978) 363-389.
7. A. Harten, High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49 (1983) 357-393.
8. A. Harten, B. Engquist, S. Osher and S.R. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes III. J. Comput. Phys. 71 (1987) 231-303.
9. G.-S. Jiang and E. Tadmor, Non-oscillatory central schemes for multidimensional hyperbolic conservation laws. SIAM J. Sci. Comput. 19 (1998) 1892-1917.
10. A. Kurganov, Conservation laws: stability of numerical approximations and nonlinear regularization. Ph.D. thesis, Tel-Aviv University, Israel (1997).
11. A. Kurganov and D. Levy, A third-order semi-discrete central scheme for conservation laws and convection-diffusion equations. SIAM J. Sci. Comput. (to appear).
12. A. Kurganov and G. Petrova, A third-order semi-discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems. Numer. Math. (to appear).
13. A. Kurganov, S. Noelle and G. Petrova, Semi-Discrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations. SIAM J. Sci. Comput. (submitted).
14. 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.
15. P.D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation. Comm. Pure Appl. Math. 7 (1954) 159-193.
16. B. van Leer, Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's method. J. Comput. Phys. 32 (1979) 101-136.
17. D. Levy, G. Puppo and G. Russo, Central WENO schemes for hyperbolic systems of conservation laws. ESAIM: M2AN 33 (1999) 547-571.
18. D. Levy, G. Puppo and G. Russo, A third order central WENO scheme for 2D conservation laws. Appl. Numer. Math. 33 (2000) 407-414.
19. D. Levy, G. Puppo and G. Russo, Compact central WENO schemes for multidimensional conservation laws. SIAM J. Sci. Comput. 22 (2000) 656-672.
20. K.-A. Lie and S. Noelle, Remarks on high-resolution non-oscillatory central schemes fcr multi-dimensional systems of conservation laws. Part I: An improved quadrature rule for the flux-computation. SIAM J. Sci. Comput. (submitted).
21. X.-D. Liu and E. Tadmor, Third order nonoscillatory central scheme for hyperbolic conservation laws. Numer. Math. 79 (1998) 397-425.
22. H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408-463.
23. S. Osher and E. Tadmor, On the convergence of difference approximations to scalar conservation laws. Math. Comp. 50 (1988) 19-51.
24. R. Sanders and A. Weiser, A high order staggered grid method for hyperbolic systems of conservation laws in one space dimension. Comput. Methods Appl. Mech. Engrg. 75 (1989) 91-107.
25. R. Sanders and A. Weiser, High resolution staggered mesh approach for nonlinear hyperbolic systems of conservation laws. J. Comput. Phys. 101 (1992) 314-329.
26. P. Woodward and P. Colella, The numerical solution of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54 (1988) 115-173.