Communications in Mathematical Sciences
Volume 13 (2015)
An entropy preserving relaxation scheme for ten-moments equations with source terms
Pages: 2119 – 2154
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 a 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.
hyperbolic system, ten-moments equations, source terms, godunov type schemes, discrete entropy inequalities, discrete entropy minimum principle
2010 Mathematics Subject Classification