Central schemes and contact discontinuities

Alexander Kurganov; Guergana Petrova

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 6, page 1259-1275
  • ISSN: 0764-583X

How to cite

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Kurganov, Alexander, and Petrova, Guergana. "Central schemes and contact discontinuities." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.6 (2000): 1259-1275. <http://eudml.org/doc/194036>.

@article{Kurganov2000,
author = {Kurganov, Alexander, Petrova, Guergana},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {conservation laws; contact discontinuities; high-resolution methods; central schemes; numerical examples; Euler equations},
language = {eng},
number = {6},
pages = {1259-1275},
publisher = {Dunod},
title = {Central schemes and contact discontinuities},
url = {http://eudml.org/doc/194036},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Kurganov, Alexander
AU - Petrova, Guergana
TI - Central schemes and contact discontinuities
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 6
SP - 1259
EP - 1275
LA - eng
KW - conservation laws; contact discontinuities; high-resolution methods; central schemes; numerical examples; Euler equations
UR - http://eudml.org/doc/194036
ER -

References

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  1. [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. Zbl0831.65091MR1320837
  2. [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. Zbl0913.76063MR1609613
  3. [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. Zbl0940.65093MR1722134
  4. [4] B. Einfeldt, On Godunov-type methods for gas dynamics. SIAM J. Numer, Anal. 25 (1988) 294-318. Zbl0642.76088MR933726
  5. [5] K.O. Friedrichs, Symmetric hyperbolic linear differential equations. Comm. Pure Appl. Math. 7 (1954) 345-392. Zbl0059.08902MR62932
  6. [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. Zbl0409.76057MR489360
  7. [7] A. Harten, High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49 (1983) 357-393. Zbl0565.65050MR701178
  8. [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. Zbl0652.65067MR897244
  9. [9] G.-S. Jiang and E. Tadmor, Non-oscillatory central schemes for multidimensional hyperbolic conservation laws. SIAM J. Sci. Comput. 19 (1998) 1892-1917. Zbl0914.65095MR1638064
  10. [10] A. Kurganov, Conservation laws: stability of numerical approximations and nonlinear regularization. Ph.D. thesis, Tel-Aviv University, Israel (1997). 
  11. [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). Zbl0979.65077MR1797891
  12. [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). Zbl0987.65090MR1836876
  13. [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). Zbl0998.65091
  14. [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. Zbl0987.65085MR1756766
  15. [15] P.D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation. Comm. Pure Appl. Math. 7 (1954) 159-193. Zbl0055.19404MR66040
  16. [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. Zbl0939.76063MR1703646
  17. [17] D. Levy, G. Puppo and G. Russo, Central WENO schemes for hyperbolic Systems of conservation laws. ESAIM: M2AN 33 (1999) 547-571. Zbl0938.65110MR1713238
  18. [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. Zbl0964.65095MR1772918
  19. [19] D. Levy, G. Puppo and G. Russo, Compact central WENO schemes for multidimensional conservation laws. SIAM J. Sci. Comput. 22 (2000) 656-672. Zbl0967.65089MR1780619
  20. [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. [21] X.-D. Liu and E. Tadmor, Third order nonoscillatory central scheme for hyperbolic conservation laws. Numer. Math. 79 (1998) 397-425. Zbl0906.65093MR1626324
  22. [22] H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408-463. Zbl0697.65068MR1047564
  23. [23] S. Osher and E. Tadmor, On the convergence of difference approximations to scalar conservation laws. Math. Comp. 50 (1988) 19-51. Zbl0637.65091MR917817
  24. [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. Zbl0694.65042MR1035749
  25. [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. Zbl0756.65112MR1174626
  26. [26] P. Woodward and P. Colella, The numerical solution of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54 (1988) 115-173. Zbl0573.76057MR748569

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