Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows (Q1815894)

This paper is concerned with time-stepping numerical methods for computing stiff semi-discrete systems of ordinary differential equations for transient hypersonic flows with thermo-chemical nonequlibrium. We study three different semi-implicit Runge-Kutta methods for additively split differential equations in the form of \(u'= f(u)+ g(u)\), where \(f\) is treated by explicit Runge-Kutta methods and \(g\) is simultaneously treated by three implicit Runge-Kutta methods: a diagonally implicit Runge-Kutta method and two linearized implicit Runge-Kutta methods. The results of two numerical tests on the stability and accuracy properties of these methods are also presented in the paper.