Runge-Kutta Methods for Hyperbolic Conservation Laws with Stiff Relaxation Terms

Abstract

Underresolved numerical schemes for hyperbolic conservation laws with stiff relaxation terms may generate unphysical spurious numerical results or reduce to lower order if the small relaxation time is not temporally well-resolved. We design a second-order Runge-Kutta type splitting method that possesses the discrete analogue of the continuous asymptotic limit, which thus is able to capture the correct physical behaviors with high order accuracy, even if the initial layer and the small relaxation time are not numerically resolved.