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Maximum principle on the entropy and second-order kinetic schemes


Authors: Brahim Khobalatte and Benoît Perthame
Journal: Math. Comp. 62 (1994), 119-131
MSC: Primary 65M06; Secondary 35L65, 76M25, 76N15
DOI: https://doi.org/10.1090/S0025-5718-1994-1208223-4
MathSciNet review: 1208223
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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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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1994-1208223-4
Keywords: Compressible Euler equations, upwind schemes, kinetic schemes, entropy property, second-order schemes
Article copyright: © Copyright 1994 American Mathematical Society

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