Arina, Renzo; Canuto, Claudio A self-adaptive domain decomposition for the viscous/inviscid coupling. I: Burgers equation. (English) Zbl 0768.76041 J. Comput. Phys. 105, No. 2, 290-300 (1993). 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. Cited in 6 Documents MSC: 76M25 Other numerical methods (fluid mechanics) (MSC2010) 65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs Keywords:chi-formulation; boundary-layer structure PDFBibTeX XMLCite \textit{R. Arina} and \textit{C. Canuto}, J. Comput. Phys. 105, No. 2, 290--300 (1993; Zbl 0768.76041) Full Text: DOI