An entropy preserving relaxation scheme for ten-moments equations with source terms

Abstract : The present paper concerns the derivation of finite volume methods to approximate weak solutions of Ten-Moments equations with source terms. These equations model compressible anisotropic flows. A relaxation-type scheme is proposed to approximate such flows. Both robustness and stability conditions of the suggested finite volume methods are established. To prove discrete entropy inequalities, we derive a new strategy based on local minimum entropy principle and never use some approximate PDE's auxiliary model as usually recommended. Moreover, numerical simulations in 1D and in 2D illustrate our approach.
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Communications in Mathematical Sciences, International Press, 2015, Communications in Mathematical Sciences, 13 (8), pp. 2119-2154. 〈10.4310/CMS.2015.v13.n8.a7〉
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Christophe Berthon, Bruno Dubroca, Afeintou Sangam. An entropy preserving relaxation scheme for ten-moments equations with source terms. Communications in Mathematical Sciences, International Press, 2015, Communications in Mathematical Sciences, 13 (8), pp. 2119-2154. 〈10.4310/CMS.2015.v13.n8.a7〉. 〈hal-01255069〉

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