Central WENO schemes for hyperbolic systems of conservation laws
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 33 (1999) no. 3, pp. 547-571.
@article{M2AN_1999__33_3_547_0,
     author = {Levy, Doron and Puppo, Gabriella and Russo, Giovanni},
     title = {Central {WENO} schemes for hyperbolic systems of conservation laws},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     pages = {547--571},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {3},
     year = {1999},
     zbl = {0938.65110},
     mrnumber = {1713238},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1999__33_3_547_0/}
}
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Levy, Doron; Puppo, Gabriella; Russo, Giovanni. Central WENO schemes for hyperbolic systems of conservation laws. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 33 (1999) no. 3, pp. 547-571. http://archive.numdam.org/item/M2AN_1999__33_3_547_0/

[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] 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. | MR | Zbl

[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. | MR | Zbl

[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).

[5] F. Bianco, G. Puppo and G. Russo, High Order Central Schemes for Hyperbolic Systems of Conservation Laws. SIAM J. Sci. Comp. (to appear.). | MR | Zbl

[6] K.O. Friedrichs and P. D. Lax, Systems of Conservation Equations with a Convex Extension. Proc Nat. Acad. Sci. 68 (1971) 1686-1688. | MR | Zbl

[7] E. Godlewski and P.-A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer, New York (1996). | MR | Zbl

[8] A. Harten, B. Engquist, S. Osher and S. Chakravarthy, Uniformly High Order Accurate Essentially Non-oscillatory Schemes III. JCP 71 (1987) 231-303. | MR | Zbl

[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] 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. | MR | Zbl

[11] G.-S. Jiang and C.-W. Shu, Efficient Implementation of Weighted ENO Schemes. JCP 126 (1996) 202-228. | MR | Zbl

[12] G.-S. Jiang and E. Tadmor, Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws. SIAM J. Sci. Comp. 19 (1998) 1892-1917. | MR | Zbl

[13] S. Jin and Z.-P. Xin, The Relaxation Schemes for Systems of Conservation Laws in Arbitrary Space Dimensions.CPAM 48 (1995) 235-277. | MR | Zbl

[14] P. D. Lax, Weak Solutions of Non-Linear Hyperbolic Equations and Their Numerical Computation. CPAM 7 (1954) 159-193. | MR | Zbl

[15] B. Van Leer, Towards the Ultimate Conservative Difference Scheme, V. A. Second-Order Sequel to Godunov's Method. JCP 32 (1979) 101-136. | Zbl

[16] R. J. Le Veque, Numerical Methods for Conservation Laws. Lectures in Mathematics, Birkhauser Verlag, Basel (1992). | Zbl

[17] D. Levy, A Third-order 2D Central Schemes for Conservation Laws, Vol. I. INRIA School on Hyperbolic Systems (1998) 489-504.

[18] D. Levy, G. Puppo and G. Russo, Central WENO Schemes for Multi-Dimensional Hyperbolic Systems of Conservation Laws (in preparation).

[19] D. Levy and E. Tadmor, Non-oscillatory Central Schemes for the Incompressible 2-D Euler Equations. Math. Res. Lett. 4 (1997) 1-20. | MR | Zbl

[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. | MR | Zbl

[21] X.-D. Liu, S. Osher and T. Chan, Weighted Essentially Non-oscillatory Schemes. JCP 115 (1994) 200-212. | MR | Zbl

[22] X.-D. Liu and E. Tadmor, Third Order Nonoscillatory Central Scheme for Hyperbolic Conservation Laws.Numer Math. 79 (1998) 397-425. | MR | Zbl

[23] H. Nessyahu and E. Tadmor, Non-oscillatory Central Differencing for Hyperbolic Conservation Laws. JCP 87 (1990) 408-463. | MR | Zbl

[24] P.L. Roe, Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes. JCP 43 (1981) 357-372. | MR | Zbl

[25] R. Sanders and A. Weiser, A High Resolution Staggered Mesh Approach for Nonlinear Hyperbolic Systems of Conservation Laws. JCP 1010 (1992) 314-329. | MR | Zbl

[26] C.-W. Shu, Numerical experiments on the accuracy of ENO and modified ENO schemes. J. Sci. Comp 5 (1990) 127-149. | Zbl

[27] C.-W. Shu and S. Osher, Efficient Implementation of Essentially Non-Oscillatory Shoek-Capturing Schemes, II. JCP 83 (1989) 32-78. | MR | Zbl

[28] G. Sod, A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws. JCP 22 (1978) 1-31. | MR | Zbl

[29] P.K. Sweby, High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws. SINUM 21 (1984) 995-1011. | MR | Zbl

[30] E. Tadmor, Approximate Solutions of Nonlinear Conservation Laws. CIME Lecture notes (1997), UCLA CAM Report 97-51. | MR | Zbl

[31] P. Woodward and P. Colella, The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks. JCP 54 (1984) 115-173. | MR | Zbl

[32] H. Yang, An Artificial Compression Method for ENO schemes : the SLOpe Modification Method. JCP 89 (1990) 125-160. | MR | Zbl

[33] M. Zennaro, Natural Continuous Extensions of Runge-Kutta Methods. Math. Comp. 46 (1986) 119-133. | MR | Zbl