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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.

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