A simple robust and accurate a posteriori sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes

The new a posteriori sub-cell stabilization approach is developed within a high order accurate one-step ADER-DG framework on multidimensional unstructured meshes for hyperbolic systems of conservation laws as well as for hyperbolic PDE with non-conservative products. The method is applied to the Euler equations of compressible gas dynamics, to the ideal magneto-hydrodynamics equations (MHD) as well as to the seven-equation Baer-Nunziato model of compressible multi-phase flows. A large set of standard test problems is solved in order to assess the accuracy and robustness of the new limiter.