Extension of centered hydrodynamical schemes to unstructured deforming conical meshes : the case of circles

In a prior work (CEMRACS10), a curvilinear bi-dimensional nite volume extension of Lagrangian centered schemes GLACE (GLACE) on unstructured cells, whose edges are parame- terized by rational quadratic B ezier curves was proposed and we showed numerical results for this scheme. Now, we extend the EUCCLHYD scheme (EUCCLHYD) to these cells. To simulate ows with evolving large deformations, we write a formalism allowing the time evolution of the conic pa- rameter. 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 xed 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 rst step toward general conical deformation. R esum e.