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Central WENO schemes for hyperbolic systemsof conservation laws

Published online by Cambridge University Press:  15 August 2002

Doron Levy ,
Gabriella Puppo  and
Giovanni Russo
Doron Levy
Affiliation:
Département de Mathématiques et d'Informatique, École Normale Supérieure, 45 rue d'Ulm, 75230 Paris Cedex 05, France.
Gabriella Puppo
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy. puppo@polito.it.
Giovanni Russo
Affiliation:
Dipartimento di Matematica, Università dell'Aquila, Via Vetoio, loc. Coppito, 67100 L'Aquila, Italy. russo@univaq.it.
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Abstract

We present a family of high-order, essentially non-oscillatory, central schemes for approximating solutions of hyperbolic systems of conservation laws. These schemes are based on a new centered version of the Weighed Essentially Non-Oscillatory (WENO) reconstruction of point-valuesfrom cell-averages, which is then followed by an accurate approximationof the fluxes via a natural continuous extension of Runge-Kutta solvers.We explicitly construct the third and fourth-order scheme and demonstrate theirhigh-resolution properties in several numerical tests.

Keywords

Hyperbolic conservation lawscentral difference schemeshigh-order accuracynon-oscillatory schemesWENO reconstructionRunge-Kutta.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 3 , May 1999 , pp. 547 - 571
Copyright
© EDP Sciences, SMAI, 1999

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