Central WENO Subcell Finite Volume Limiters for ADER Discontinuous Galerkin Schemes on Fixed and Moving Unstructured Meshes (Communications in Computational Physics, 2018)
We present a novel a posteriori subcell finite volume limiter for high orderdiscontinuous Galerkin (DG) finite element schemes for the solution of nonlinear hyperbolicPDE systems in multiple space dimensions on fixed and moving unstructuredsimplex meshes. The numerical method belongs to the family of high order fully discreteone-step ADER-DG schemes [12, 45] and makes use of an element-local space-timeGalerkin finite element predictor. Our limiter is based on the MOOD paradigm, inwhich the discrete solution of the high order DG scheme is checked a posteriori againsta set of physical and numerical admissibility criteria, in order to detect spurious oscillationsor unphysical solutions and in order to identify the so-called troubled cells.Within the detected troubled cells the discrete solution is then discarded and recomputedlocally with a more robust finite volume method on a fine subgrid.In this work, we propose for the first time to use a high order ADER-CWENO finitevolume scheme as subcell finite volume limiter on unstructured simplex meshes, insteadof a classical second order TVD scheme. Our new numerical scheme has beendeveloped both for fixed Eulerian meshes as well as for moving Lagrangian grids. Ithas been carefully validated against a set of typical benchmark problems for the compressibleEuler equations of gas dynamics and for the equations of ideal magnetohydrodynamics(MHD).