Asymptotic-preserving Godunov-type numerical schemes for hyperbolic systems with stiff and nonstiff relaxation terms (Q2846177)

The paper deals with the numerical approximation of the strictly hyperbolic system NEWLINE\[NEWLINE\partial_t u+\partial_x v=0,NEWLINE\]NEWLINE NEWLINE\[NEWLINE\partial_t v+\partial_x g(u,v)=\frac{1}{\varepsilon(t,x,u)}S(u,v),NEWLINE\]NEWLINE with relaxation-type source-term, where the state vector \(W=(u,v)^T\) belongs to a convex subset \(\Omega\) of \(\mathbb{R}^2\) and the function \(g:\Omega \to \mathbb{R}\) is smooth enough. The system admits various asymptotic regimes for various values of \(\varepsilon\). The authors propose a class of asymptotic-preserving Godunov-type numerical schemes and confirm their functionality by the number of numerical experiments.