Geodesic
A conservative slide line method for cell-centered semi-Lagrangian and ALE schemes in 2D
Bertoluzza, Silvia1  ; Del Pino, Stéphane2  ; Labourasse, Emmanuel3 
1 Istituto di Matematica Applicata e Tecnologie Informatiche del CNR, Pavia, Italy.
2 CEA, DAM, DIF 91297, Arpajon France.
3 CEA, DAM, DIF 91297, Arpajon France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 1, pp. 187-214

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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.

DOI : 10.1051/m2an/2015037
Classification : 65Z05, 35L65, 65N08, 65N30, 76N15
Keywords: Compressible gas, Lagrange, ALE, slide lines, finite-volumes, finite-elements, mortar

Bertoluzza, Silvia 1 ; Del Pino, Stéphane 2 ; Labourasse, Emmanuel 3

1 Istituto di Matematica Applicata e Tecnologie Informatiche del CNR, Pavia, Italy.
2 CEA, DAM, DIF 91297, Arpajon France.
3 CEA, DAM, DIF 91297, Arpajon France. 
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     title = {A conservative slide line method for cell-centered {semi-Lagrangian} and {ALE} schemes in {2D}},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {187--214},
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Bertoluzza, Silvia; Del Pino, Stéphane; Labourasse, Emmanuel. A conservative slide line method for cell-centered semi-Lagrangian and ALE schemes in 2D. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 1, pp. 187-214. doi: 10.1051/m2an/2015037

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