Maximum principle on the entropy and minimal limitations for kinetic schemes
Abstract
We consider kinetic schemes for the multidimensional inviscid gaz dynamics equations (compressible Euler equations). We prove that the discrete maximum principle holds for a special convex entropy. This fixes the choice of the equilibrium functions necessary for kinetic schemes. We use this property to perform a second order oscillation free scheme where only one slope limitation (for three conserved quantities in 1d) is necessary. Numerical results assert the strong convergence of the scheme.