Asymptotic‐preserving Godunov‐type numerical schemes for hyperbolic systems with stiff and nonstiff relaxation terms

We devise a new class of asymptotic‐preserving Godunov‐type numerical schemes for hyperbolic systems with stiff and nonstiff relaxation source terms governed by a relaxation time ε. 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 ε and second, to make optional the choice of the numerical scheme in the asymptotic regime ε tends to zero. The latter property may be of particular interest to make easier and more efficient the coupling at a fixed spatial interface of two models involving very different values of ε. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013