Asymptotic-preserving Godunov-type numerical schemes for hyperbolic systems with stiff and non-stiff relaxation terms

International audienceWe devise a new-class of asymptotic-preserving Godunov-type numerical schemes for hyperbolic systems with sti ff and non-sti ff relaxation source terms governed by a relaxation time epsilon. As an alternative to classical operator-splitting techniques, the objectives of these schemes are twofold: first, to give accurate numerical solutions for large, small and in-between values of epsilon and second, to make optional the choice of the numerical scheme in the asymptotic regime epsilon tends to zero. The latter property may be of particular interest to make easier and more e fficient the coupling at a fi xed spatial interface of two models involving very di fferent values of epsilon