A p-Adaptive Discontinuous Galerkin Method with hp-Shock Capturing

Abstract In this work, we present a novel hybrid Discontinuous Galerkin scheme with hp-adaptivity capabilities for the compressible Euler equations. smooth regions, an efficient and accurate discretization is achieved via local p-adaptation. At strong discontinuities shocks, finite volume on h-refined element-local subgrid gives robustness. Thus, obtain hp-adaptive that exploits both high convergence rate efficiency of p-adaptive order as well stable shock capturing abilities low scheme, but avoids inherent resolution loss through h-refinement. A single priori indicator, based modal decay polynomial solution representation, used to distinguish between discontinuous regions control p-refinement. Our method implemented extension open source software FLEXI. Hence, implementation performance computers was important criterion during development. The our adaptive demonstrated variety test cases, where results are compared against non simulations. findings suggest proposed produces comparable or even better significantly less computational costs.