A minimum entropy principle of high order schemes for gas dynamics equations

The entropy solutions of the compressible Euler equations satisfy a minimum principle for the specific entropy [10]. First order schemes such as Godunov-type and Lax-Friedrichs schemes and the second order kinetic schemes [6] also satisfy a discrete minimum entropy principle. In this paper, we show an extension of the positivity-preserving high order schemes for the compressible Euler equations in [13, 14], to enforce the minimum entropy principle for high order finite volume and discontinuous Galerkin (DG) schemes. AMS subject classification: 65M60, 76N15