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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.

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)
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