Central WENO schemes for hyperbolic systems of conservation laws

Doron Levy; Gabriella Puppo; Giovanni Russo

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 3, page 547-571
  • ISSN: 0764-583X

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Levy, Doron, Puppo, Gabriella, and Russo, Giovanni. "Central WENO schemes for hyperbolic systems of conservation laws." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.3 (1999): 547-571. <http://eudml.org/doc/193935>.

@article{Levy1999,
author = {Levy, Doron, Puppo, Gabriella, Russo, Giovanni},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {systems of hyperbolic conservation laws; numerical examples; Runge-Kutta methods; central weighted essentially non-oscillatory difference schemes},
language = {eng},
number = {3},
pages = {547-571},
publisher = {Dunod},
title = {Central WENO schemes for hyperbolic systems of conservation laws},
url = {http://eudml.org/doc/193935},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Levy, Doron
AU - Puppo, Gabriella
AU - Russo, Giovanni
TI - Central WENO schemes for hyperbolic systems of conservation laws
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 3
SP - 547
EP - 571
LA - eng
KW - systems of hyperbolic conservation laws; numerical examples; Runge-Kutta methods; central weighted essentially non-oscillatory difference schemes
UR - http://eudml.org/doc/193935
ER -

References

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  1. [1] P. Arminjon, D. Stanescu and M.-C. Viallon, A Two-Dimensional Finite Volume Extension of the Lax-Friedrichs and Nessyahu-Tadmor Schemes for Compressible Flows, in Proc. 6th Int. Symp. on CFD, Lake Tahoe, Vol. IV. M. Hafez and K. Oshima Eds. (1995) 7-14. 
  2. [2] 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) Ser. I. Math. 320 (1995) 85-88. Zbl0831.65091MR1320837
  3. [3] 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. IJCFD 9 (1997) 1-22. Zbl0913.76063MR1609613
  4. [4] P. Arminjon, M.-C. Viallon, A. Madrane and L. Kaddouri, Discontinuous Finite Elements and Finite Volume Versions of the Lax-Friedrichs and Nessyahu-Tadmor Schemes for Compressible Flows on Unstructured Grids. Computational Fluid Dynamics Review M. Hafez and K. Oshima Eds., Wiley (1997). Zbl0913.76063
  5. [5] F. Bianco, G. Puppo and G. Russo, High Order Central Schemes for Hyperbolic Systems of Conservation Laws. SIAM J. Sci. Comp. (to appear.). Zbl0940.65093MR1722134
  6. [6] K.O. Friedrichs and P. D. Lax, Systems of Conservation Equations with a Convex Extension. Proc Nat. Acad. Sci. 68 (1971) 1686-1688. Zbl0229.35061MR285799
  7. [7] E. Godlewski and P.-A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer, New York (1996). Zbl0860.65075MR1410987
  8. [8] A. Harten, B. Engquist, S. Osher and S. Chakravarthy, Uniformly High Order Accurate Essentially Non-oscillatory Schemes III. JCP 71 (1987) 231-303. Zbl0652.65067MR897244
  9. [9] H.T. Huynh, A Piecewise-parabolic Dual-mesh Method for the Euler Equations. AIAA-95-1739-CP, The 12th AIAA CFD conference (1995). 
  10. [10] G.-S. Jiang, D. Levy, C.-T. Lin, S. Osher and E. Tadmor, High-Resolution Non-Oscillatory Central Schemes with Non-Staggered Grids for Hyperbolic Conservation Laws. SINUM 35 (1998) 2147-2168. Zbl0920.65053MR1655841
  11. [11] G.-S. Jiang and C.-W. Shu, Efficient Implementation of Weighted ENO Schemes. JCP 126 (1996) 202-228. Zbl0877.65065MR1391627
  12. [12] G.-S. Jiang and E. Tadmor, Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws. SIAM J. Sci. Comp. 19 (1998) 1892-1917. Zbl0914.65095MR1638064
  13. [13] S. Jin and Z.-P. Xin, The Relaxation Schemes for Systems of Conservation Laws in Arbitrary Space Dimensions.CPAM 48 (1995) 235-277. Zbl0826.65078MR1322811
  14. [14] P. D. Lax, Weak Solutions of Non-Linear Hyperbolic Equations and Their Numerical Computation. CPAM 7 (1954) 159-193. Zbl0055.19404MR66040
  15. [15] B. van Leer, Towards the Ultimate Conservative Difference Scheme, V. A. Second-Order Sequel to Godunov's Method. JCP 32 (1979) 101-136. Zbl0939.76063
  16. [16] R. J. Le Veque, Numerical Methods for Conservation Laws. Lectures in Mathematics, Birkhauser Verlag, Basel (1992). Zbl0723.65067
  17. [17] D. Levy, A Third-order 2D Central Schemes for Conservation Laws, Vol. I. INRIA School on Hyperbolic Systems (1998) 489-504. 
  18. [18] D. Levy, G. Puppo and G. Russo, Central WENO Schemes for Multi-Dimensional Hyperbolic Systems of Conservation Laws (in preparation). Zbl0938.65110
  19. [19] D. Levy and E. Tadmor, Non-oscillatory Central Schemes for the Incompressible 2-D Euler Equations. Math. Res. Lett. 4 (1997) 1-20. Zbl0883.76057MR1453063
  20. [20] X.-D. Lin and S. Osher, Nonoscillatory High Order Accurate Self-Similar Maximum Principle Satisfying Shock Capturing Schemes I. SINUM 33 (1996) 760-779. Zbl0859.65091MR1388497
  21. [21] X.-D. Liu, S. Osher and T. Chan, Weighted Essentially Non-oscillatory Schemes. JCP 115 (1994) 200-212. Zbl0811.65076MR1300340
  22. [22] X.-D. Liu and E. Tadmor, Third Order Nonoscillatory Central Scheme for Hyperbolic Conservation Laws.Numer Math. 79 (1998) 397-425. Zbl0906.65093MR1626324
  23. [23] H. Nessyahu and E. Tadmor, Non-oscillatory Central Differencing for Hyperbolic Conservation Laws. JCP 87 (1990) 408-463. Zbl0697.65068MR1047564
  24. [24] P.L. Roe, Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes. JCP 43 (1981) 357-372. Zbl0474.65066MR640362
  25. [25] R. Sanders and A. Weiser, A High Resolution Staggered Mesh Approach for Nonlinear Hyperbolic Systems of Conservation Laws. JCP 1010 (1992) 314-329. Zbl0756.65112MR1174626
  26. [26] C.-W. Shu, Numerical experiments on the accuracy of ENO and modified ENO schemes. J. Sci. Comp 5 (1990) 127-149. Zbl0732.65085
  27. [27] C.-W. Shu and S. Osher, Efficient Implementation of Essentially Non-Oscillatory Shoek-Capturing Schemes, II. JCP 83 (1989) 32-78. Zbl0674.65061MR1010162
  28. [28] G. Sod, A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws. JCP 22 (1978) 1-31. Zbl0387.76063MR495002
  29. [29] P.K. Sweby, High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws. SINUM 21 (1984) 995-1011. Zbl0565.65048MR760628
  30. [30] E. Tadmor, Approximate Solutions of Nonlinear Conservation Laws. CIME Lecture notes (1997), UCLA CAM Report 97-51. Zbl0927.65110MR1728853
  31. [31] P. Woodward and P. Colella, The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks. JCP 54 (1984) 115-173. Zbl0573.76057MR748569
  32. [32] H. Yang, An Artificial Compression Method for ENO schemes : the SLOpe Modification Method. JCP 89 (1990) 125-160. Zbl0705.65062MR1063150
  33. [33] M. Zennaro, Natural Continuous Extensions of Runge-Kutta Methods. Math. Comp. 46 (1986) 119-133. Zbl0608.65043MR815835

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