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A self-adaptive domain decomposition for the viscous/inviscid coupling. I: Burgers equation. (English) Zbl 0768.76041

A new formulation of the viscous/inviscid coupling, termed \(\chi\)- formulation, has been applied to the Burgers equation: the equation is modified in such a way that the viscous terms are neglected in dependence of their magnitude. We consider a domain decomposition method, based on the \(\chi\)-formulation, by splitting the original problem into an inviscid Burgers equation and a \(\chi\)-viscous Burgers equation. The interface between the subdomains is automatically adjusted by the proposed method, yielding an optimal resolution of the boundary-layer structure.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
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