Revisiting Compressible Vortex Test Cases for Numerical Method Assessment

Several 2D compressible vortex models, proposed in the literature to investigate vorticity dynamics or to assess the accuracy of numerical methods, are reviewed and reformulated with a common non-dimensional notation. Two vortex types may be distinguished, namely the zero-global circulation vortex and the finite-global circulation vortex, where the global circulation amounts to the circulation value around a far-field path enclosing the vortex core. Numerical experiments carried out on the convected and stationary vortex benchmark tests are analyzed to clarify the error dynamics during the flow evolution in time. It is shown that both classes of compressible vortex models are affected, on the long term, by a flow instability of acoustic type. It is then concluded that this classical problem may be used to assess the spatial accuracy of a numerical scheme, through a standard h-refinement approach, only with the necessary caution.