AN ENTROPY SATISFYING MUSCL SCHEME FOR SYSTEMS OF CONSERVATION-LAWS

For the high-order numerical approximation of hyperbolic systems of co nservation laws, we propose to use as a building principle an entropy diminishing criterion instead of the familiar total variation diminish ing 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 t he classical Van Leer's MUSCL scheme. Strong convergence of this secon d order, entropy satisfying scheme is proved for systems of two equati ons. Numerical tests demonstrate the interest of our theory.