Godunov-type schemes for hyperbolic systems with parameter-dependent source. The case of Euler system with friction. (English summary) Math. Models Methods Appl. Sci. 20 (2010), no. 11, 2109–2166. The authors have developed a methodology to derive well-balanced and asymptotic preserving schemes which is detailed on the model problem of an Euler system with gravity and friction for the gas dynamics. The problem is presented in both the Eulerian and Lagrangian frameworks and the possible stationary solutions are computed before the study of the asymptotic behaviour. This study can be extended to a wider class of problems and, in this context, all the notions have been given a precise definition. A simple solver is derived which, by construction, preserves discrete equilibrium and reproduces at the discrete level the same asymptotic behaviour as that of the solutions of the continuous system. Numerical illustrations show that the corresponding schemes behave very well on two test problems: convergence in time to a stationary state with null velocity, and sensitivity with respect to the mesh size for large friction. Reviewed by Luis Vázque
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