Maximum principle on the entropy and second-order kinetic schemes

Khobalatte, Brahim; Perthame, Benoît

doi:10.1090/S0025-5718-1994-1208223-4

Maximum principle on the entropy and second-order kinetic schemes
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by Brahim Khobalatte and Benoît Perthame PDF

Math. Comp. 62 (1994), 119-131 Request permission

Abstract:

We consider kinetic schemes for the multidimensional inviscid gas dynamics equations (compressible Euler equations). We prove that the discrete maximum principle holds for the specific 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 exhibit stability and strong convergence of the scheme.

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