Geodesic
Extension of ALE methodology to unstructured conical meshes
Benjamin Boutin1 ; Erwan Deriaz2 ; Philippe Hoch3 ; Pierre Navaro4
1 IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France
2 M2P2 - UMR-6181 CNRS IMT La Jetée Technopôle de Château-Gombert, 38 Rue Frédéric Joliot-Curie, 13451 MARSEILLE Cedex 20, France
3 Corresponding author: CEA, DAM, DIF, Bruyères-le-Chatel, F-91297 Arpajon Cedex, France
4 IRMA, 7 rue René Descartes, 67084 Strasbourg Cedex, France
ESAIM. Proceedings, Tome 32 (2011), pp. 31-55.

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We propose a bi-dimensional finite volume extension of a continuous ALE method on unstructured cells whose edges are parameterized by rational quadratic Bezier curves. For each edge, the control point possess a weight that permits to represent any conic (see for example [LIGACH]) and thanks to [WAGUSEDE,WAGU], we are able to compute the exact area of our cells. We then give an extension of scheme for remapping step based on volume fluxing [MARSHA] and self-intersection flux [ALE2DHAL]. For the rezoning phase, we propose a three step process based on moving nodes, followed by control point and weight re-adjustment. Finally, for the hydrodynamic step, we present the GLACE scheme [GLACE] extension (at first-order) on conic cell using the same formalism. We only propose some preliminary first-order simulations for each steps: Remap, Pure Lagrangian and finally ALE (rezoning and remapping).
DOI : 10.1051/proc/2011011

Benjamin Boutin 1 ; Erwan Deriaz 2 ; Philippe Hoch 3 ; Pierre Navaro 4

1 IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France
2 M2P2 - UMR-6181 CNRS IMT La Jetée Technopôle de Château-Gombert, 38 Rue Frédéric Joliot-Curie, 13451 MARSEILLE Cedex 20, France
3 Corresponding author: CEA, DAM, DIF, Bruyères-le-Chatel, F-91297 Arpajon Cedex, France
4 IRMA, 7 rue René Descartes, 67084 Strasbourg Cedex, France 
@article{EP_2011_32_a4,
     author = {Benjamin Boutin and Erwan Deriaz and Philippe Hoch and Pierre Navaro},
     title = {Extension of {ALE} methodology to unstructured conical meshes},
     journal = {ESAIM. Proceedings},
     pages = {31--55},
     publisher = {mathdoc},
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     year = {2011},
     doi = {10.1051/proc/2011011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2011011/}
}
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Benjamin Boutin; Erwan Deriaz; Philippe Hoch; Pierre Navaro. Extension of ALE methodology to unstructured conical meshes. ESAIM. Proceedings, Tome 32 (2011), pp. 31-55. doi : 10.1051/proc/2011011. http://geodesic.mathdoc.fr/articles/10.1051/proc/2011011/

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