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An Antidiffusive Entropy Scheme for Monotone Scalar Conservation Laws
Authors:F Bouchut
Affiliation:(1) Département de Mathématiques et Applications, École Normale Supérieure et CNRS, UMR 8553, 45 rue d'Ulm, 75230 Paris cedex 05, France
Abstract:In a recent work J. Sci. Comput. 16, 479–524 (2001), B. Després and F. Lagoutière introduced a new approach to derive numerical schemes for hyperbolic conservation laws. Its most important feature is the ability to perform an exact resolution for a single traveling discontinuity. However their scheme is not entropy satisfying and can keep nonentropic discontinuities. The purpose of our work is, starting from the previous one, to introduce a new class of schemes for monotone scalar conservation laws, that satisfy an entropy inequality, while still resolving exactly the single traveling shocks or contact discontinuities. We show that it is then possible to have an excellent resolution of rarefaction waves, and also to avoid the undesirable staircase effect. In practice, our numerical experiments show second-order accuracy.
Keywords:scalar conservation laws  entropy scheme  entropy indicator  self-adaptive antidiffusion  step functions  smoothness indicator
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