An Arbitrary Space-Time High-Order Finite Volume Scheme for Gas Dynamics Equations in Curvilinear Coordinates on Polar Meshes

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.