Discontinuous Galerkin methods for axisymmetric flows

In this article, high order discontinuous Galerkin methods for axisymmetric flows are developed. A first work is performed to put the equations in a so called canonical form to gather terms of similar nature, and also for ensuring the three dimensional conservativity. Then the numerical scheme is developed. Instead of relying on the strong axisymmetric formulation, we rely on the -averaged form of the standard three-dimensional discontinuous Galerkin method for the Navier-Stokes system. This allows to derive a numerical scheme without ambiguity on the source terms. The numerical scheme is new and makes link between different formulations previously proposed. A wide and progressive set of test cases, especially designed for axisymmetric problems is proposed. The numerical scheme is tested using these cases and the optimal order of accuracy is obtained.