Central schemes and contact discontinuities
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 34 (2000) no. 6, pp. 1259-1275.
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author = {Kurganov, Alexander and Petrova, Guergana},
title = {Central schemes and contact discontinuities},
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Kurganov, Alexander; Petrova, Guergana. Central schemes and contact discontinuities. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 34 (2000) no. 6, pp. 1259-1275. http://www.numdam.org/item/M2AN_2000__34_6_1259_0/

[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. 1320 (1995) 85-88. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[4] B. Einfeldt, On Godunov-type methods for gas dynamics. SIAM J. Numer, Anal. 25 (1988) 294-318. | MR | Zbl

[5] K.O. Friedrichs, Symmetric hyperbolic linear differential equations. Comm. Pure Appl. Math. 7 (1954) 345-392. | MR | Zbl

[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. | MR | Zbl

[7] A. Harten, High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49 (1983) 357-393. | MR | Zbl

[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. | MR | Zbl

[9] G.-S. Jiang and E. Tadmor, Non-oscillatory central schemes for multidimensional hyperbolic conservation laws. SIAM J. Sci. Comput. 19 (1998) 1892-1917. | MR | Zbl

[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). | MR | Zbl

[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). | MR | Zbl

[13] A. Kurganov, S. Nolle and G. Petrova, Semi-Discrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations. SIAM J. Sci. Comput. (submitted). | Zbl

[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. | MR | Zbl

[15] P.D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation. Comm. Pure Appl. Math. 7 (1954) 159-193. | MR | Zbl

[16] B. Van Leer, Towards the ultimate conservative diffrence scheme. V. A second order sequel to Godunov's method. J. Comput. Phys. 32 (1979) 101-136. | MR | Zbl

[17] D. Levy, G. Puppo and G. Russo, Central WENO schemes for hyperbolic Systems of conservation laws. ESAIM: M2AN 33 (1999) 547-571. | Numdam | MR | Zbl

[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. | MR | Zbl

[19] D. Levy, G. Puppo and G. Russo, Compact central WENO schemes for multidimensional conservation laws. SIAM J. Sci. Comput. 22 (2000) 656-672. | MR | Zbl

[20] K.-A. Lie and S. Nolle, Remarks on high-resolution non-oscillatory central schemes for 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. | MR | Zbl

[22] H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408-463. | MR | Zbl

[23] S. Osher and E. Tadmor, On the convergence of difference approximations to scalar conservation laws. Math. Comp. 50 (1988) 19-51. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[26] P. Woodward and P. Colella, The numerical solution of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54 (1988) 115-173. | MR | Zbl