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Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows. (English) Zbl 0861.76057
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.

76M20 Finite difference methods applied to problems in fluid mechanics
76V05 Reaction effects in flows
76K05 Hypersonic flows
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