Communications in Mathematical Sciences

Volume 13 (2015)

Number 8

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

Pages: 2119 – 2154



Christophe Berthon (Laboratoire de Mathématiques Jean Leray, Université de Nantes, France)

Bruno Dubroca (Institut de Mathématiques de Bordeaux, Centre Lasers Intenses et Applications, Université Bordeaux 1, Talence, France)

Afeintou Sangam (Laboratoire J.A. Dieudonné, Université Nice Sophia Antipolis, Nice, France, and INRIA Sophia Antipolis 2004, Sophia Antipolis, France)


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

65M12, 65M60

Published 3 September 2015