Geodesic
Extension of centered hydrodynamical schemes to unstructured deforming conical meshes : the case of circles
Aude Bernard-Champmartin1 ; Erwan Deriaz2 ; Philippe Hoch3 ; Gerald Samba3 ; Michael Schaefer4
1 CMLA, ENS Cachan / LRC MESO, ENS Cachan and CEA, DAM, DIF, 61 av du Président Wilson, 94235 Cachan 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 CEA, DAM, DIF, Bruyères-le-Chatel, F-91297 Arpajon Cedex, France
4 University of Muenster, Orléans-Ring 10, 48149 Münster, Germany
ESAIM. Proceedings, Tome 38 (2012), pp. 135-162.

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In a prior work [CEMRACS10], a curvilinear bi-dimensional finite volume extension of Lagrangian centered schemes GLACE [GLACE] on unstructured cells, whose edges are parameterized by rational quadratic Bézier curves was proposed and we showed numerical results for this scheme. Now, we extend the EUCCLHYD scheme [EUCCLHYD] to these cells. To simulate flows with evolving large deformations, we write a formalism allowing the time evolution of the conic parameter. As an example, this allows an edge changing from an ellipse segment to a hyperbolic one. In this framework, we consider the case of a mesh whose edges are circle segments with non fixed centers. We show that this formalism extends also the previous work [GLACE CIRCLE] (which is equivalent to [CEMRACS10] when conic edges are all circles). This is a necessary first step toward general conical deformation.
DOI : 10.1051/proc/201238008

Aude Bernard-Champmartin 1 ; Erwan Deriaz 2 ; Philippe Hoch 3 ; Gerald Samba 3 ; Michael Schaefer 4

1 CMLA, ENS Cachan / LRC MESO, ENS Cachan and CEA, DAM, DIF, 61 av du Président Wilson, 94235 Cachan 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 CEA, DAM, DIF, Bruyères-le-Chatel, F-91297 Arpajon Cedex, France
4 University of Muenster, Orléans-Ring 10, 48149 Münster, Germany 
@article{EP_2012_38_a7,
     author = {Aude Bernard-Champmartin and Erwan Deriaz and Philippe Hoch and Gerald Samba and Michael Schaefer},
     title = {Extension of centered hydrodynamical schemes to unstructured deforming conical meshes : the case of circles},
     journal = {ESAIM. Proceedings},
     pages = {135--162},
     publisher = {mathdoc},
     volume = {38},
     year = {2012},
     doi = {10.1051/proc/201238008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201238008/}
}
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Aude Bernard-Champmartin; Erwan Deriaz; Philippe Hoch; Gerald Samba; Michael Schaefer. Extension of centered hydrodynamical schemes to unstructured deforming conical meshes : the case of circles. ESAIM. Proceedings, Tome 38 (2012), pp. 135-162. doi : 10.1051/proc/201238008. http://geodesic.mathdoc.fr/articles/10.1051/proc/201238008/

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