Abstract
We are interested in the study of numerical schemes for the resolution of gas dynamics equations which preserve symmetric (or axisymmetric) flows. A simple way to achieve this is to derive a numerical scheme whose mesh and coordinates system are aligned with the flow. Typically, for the simulation of cylindrical implosions of gas, the cylindrical coordinate system and a polar mesh are well-suited. But such coordinates systems introduce geometrical singularities as well as geometrical source terms. In this paper, we investigate an arbitrary high-order space-time Finite Volume (FV) scheme in cylindrical coordinates. Test-cases with and without polar symmetries are studied in order to confirm the order of the scheme as well as its robustness.
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