@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},
volume = {33},
year = {1999},
pages = {547-571},
mrnumber = {1713238},
zbl = {0938.65110},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_1999__33_3_547_0}
}
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, Tome 33 (1999) pp. 547-571. http://gdmltest.u-ga.fr/item/M2AN_1999__33_3_547_0/
[1] , and , 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] and , 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 1320837 | Zbl 0831.65091
[3] , and , A Finite Volume Extension of the Lax-Friedrichs and Nessyahu-Tadmor Schemes for Conservation Laws on Unstructured Grids. IJCFD 9 (1997) 1-22. | MR 1609613 | Zbl 0913.76063
[4] , , and , 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] , and , High Order Central Schemes for Hyperbolic Systems of Conservation Laws. SIAM J. Sci. Comp. (to appear.). | MR 1722134 | Zbl 0940.65093
[6] and , Systems of Conservation Equations with a Convex Extension. Proc Nat. Acad. Sci. 68 (1971) 1686-1688. | MR 285799 | Zbl 0229.35061
[7] and , Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer, New York (1996). | MR 1410987 | Zbl 0860.65075
[8] , , and , Uniformly High Order Accurate Essentially Non-oscillatory Schemes III. JCP 71 (1987) 231-303. | MR 897244 | Zbl 0652.65067
[9] , A Piecewise-parabolic Dual-mesh Method for the Euler Equations. AIAA-95-1739-CP, The 12th AIAA CFD conference (1995).
[10] , , , and , High-Resolution Non-Oscillatory Central Schemes with Non-Staggered Grids for Hyperbolic Conservation Laws. SINUM 35 (1998) 2147-2168. | MR 1655841 | Zbl 0920.65053
[11] and , Efficient Implementation of Weighted ENO Schemes. JCP 126 (1996) 202-228. | MR 1391627 | Zbl 0877.65065
[12] and , Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws. SIAM J. Sci. Comp. 19 (1998) 1892-1917. | MR 1638064 | Zbl 0914.65095
[13] and , The Relaxation Schemes for Systems of Conservation Laws in Arbitrary Space Dimensions.CPAM 48 (1995) 235-277. | MR 1322811 | Zbl 0826.65078
[14] , Weak Solutions of Non-Linear Hyperbolic Equations and Their Numerical Computation. CPAM 7 (1954) 159-193. | MR 66040 | Zbl 0055.19404
[15] , Towards the Ultimate Conservative Difference Scheme, V. A. Second-Order Sequel to Godunov's Method. JCP 32 (1979) 101-136. | Zbl 0939.76063
[16] , Numerical Methods for Conservation Laws. Lectures in Mathematics, Birkhauser Verlag, Basel (1992). | Zbl 0723.65067
[17] , A Third-order 2D Central Schemes for Conservation Laws, Vol. I. INRIA School on Hyperbolic Systems (1998) 489-504.
[18] , and , Central WENO Schemes for Multi-Dimensional Hyperbolic Systems of Conservation Laws (in preparation).
[19] and , Non-oscillatory Central Schemes for the Incompressible 2-D Euler Equations. Math. Res. Lett. 4 (1997) 1-20. | MR 1453063 | Zbl 0883.76057
[20] and , Nonoscillatory High Order Accurate Self-Similar Maximum Principle Satisfying Shock Capturing Schemes I. SINUM 33 (1996) 760-779. | MR 1388497 | Zbl 0859.65091
[21] , and , Weighted Essentially Non-oscillatory Schemes. JCP 115 (1994) 200-212. | MR 1300340 | Zbl 0811.65076
[22] and , Third Order Nonoscillatory Central Scheme for Hyperbolic Conservation Laws.Numer Math. 79 (1998) 397-425. | MR 1626324 | Zbl 0906.65093
[23] and , Non-oscillatory Central Differencing for Hyperbolic Conservation Laws. JCP 87 (1990) 408-463. | MR 1047564 | Zbl 0697.65068
[24] , Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes. JCP 43 (1981) 357-372. | MR 640362 | Zbl 0474.65066
[25] and , A High Resolution Staggered Mesh Approach for Nonlinear Hyperbolic Systems of Conservation Laws. JCP 1010 (1992) 314-329. | MR 1174626 | Zbl 0756.65112
[26] , Numerical experiments on the accuracy of ENO and modified ENO schemes. J. Sci. Comp 5 (1990) 127-149. | Zbl 0732.65085
[27] and , Efficient Implementation of Essentially Non-Oscillatory Shoek-Capturing Schemes, II. JCP 83 (1989) 32-78. | MR 1010162 | Zbl 0674.65061
[28] , A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws. JCP 22 (1978) 1-31. | MR 495002 | Zbl 0387.76063
[29] , High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws. SINUM 21 (1984) 995-1011. | MR 760628 | Zbl 0565.65048
[30] , Approximate Solutions of Nonlinear Conservation Laws. CIME Lecture notes (1997), UCLA CAM Report 97-51. | MR 1728853 | Zbl 0927.65110
[31] and , The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks. JCP 54 (1984) 115-173. | MR 748569 | Zbl 0573.76057
[32] , An Artificial Compression Method for ENO schemes : the SLOpe Modification Method. JCP 89 (1990) 125-160. | MR 1063150 | Zbl 0705.65062
[33] , Natural Continuous Extensions of Runge-Kutta Methods. Math. Comp. 46 (1986) 119-133. | MR 815835 | Zbl 0608.65043