Numerische Mathematik

, Volume 74, Issue 1, pp 1-33

First online:

An entropy satisfying MUSCL scheme for systems of conservation laws

  • Frédéric CoquelAffiliated withLaboratoire d'Analyse Numérique, Université Paris VI, F-75252 Paris, France
  • , Philippe G. LeFlochAffiliated withCentre de Mathématiques Appliquées and CNRS UA756, Ecole Polytechnique, F-91128 Palaiseau, France

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For the high-order numerical approximation of hyperbolic systems of conservation laws, we propose to use as a building principle an entropy diminishing criterion instead of the familiar total variation diminishing criterion introduced by Harten for scalar equations. Based on this new criterion, we derive entropy diminishing projections that ensure, both, the second order of accuracy and all of the classical discrete entropy inequalities. The resulting scheme is a nonlinear version of the classical Van Leer's MUSCL scheme. Strong convergence of this second order, entropy satisfying scheme is proved for systems of two equations. Numerical tests demonstrate the interest of our theory.

Mathematics Subject Classification (1991): 65M05, 65M12, 35L65