A conservative slide line method for cell-centered semi-Lagrangian and ALE schemes in 2D

Abstract

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. Acad. Sci. Paris, Ser. I 348 (2010) 1027–1032]. We introduce the notion of slide lines thanks to a mortar-like approach. We propose and analyze a P 1 − 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.