Variational Multiscale Stabilization and p-adaptivity of High-Order Spectral Elements for the Convection-Diffusion Equation

Abstract

Adaptive mesh refinement generally serves to increase computational efficiency without compromising the accuracy of the numerical solution. However it is an open question in which regions the spatial resolution can actually be coarsened without affecting the accuracy of the result. This question is investigated for a specific meteorological problem, namely the simulation of atmospheric convection. For this purpose a novel numerical model is developed that is tailored towards this specific meteorological problem. The compressible Euler equations are solved with a Discontinuous Galerkin method. Time integration is done with a semi- implicit approach and the dynamic grid adaptivity uses space filling curves via the AMATOS function library. So far the model is able to simulate dry flow in two-dimensional geometry without subgrid-scale modeling. The model is validated with three standard test cases.