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A conservative slide line method for cell-centered semi-Lagrangian and ALE schemes in 2D. (English) Zbl 1382.76181
Summary: In this paper, we propose a new cell-center method to treat sliding of compressible fluid domains. We describe at first the theoretical framework based on [S. Del Pino, C. R., Math., Acad. Sci. Paris 348, No. 17–18, 1027–1032 (2010; Zbl 1426.76652)]. We introduce the notion of slide lines thanks to a mortar-like approach. We propose and analyze a \(\mathbb{P}_{1}-\mathbb{P}_{0}\) discretization of the theoritical method. We also describe a simple ALE procedure that preserves the slide line Lagrangian so that no mixed-cells model is necessary. Finally we present a set of representative numerical tests.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76N15 Gas dynamics (general theory)
Software:
SuperLU
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