A High-Order Discontinuous Galerkin Solver with Dynamic Adaptive Mesh Refinement to Simulate Cloud Formation Processes

Abstract

We present a high-order discontinuous Galerkin (DG) solver of the compressible Navier-Stokes equations for cloud formation processes. The scheme exploits an underlying parallelized implementation of the ADER-DG method with dynamic adaptive mesh refinement. We improve our method by a PDE-independent general refinement criterion, based on the local total variation of the numerical solution. While established methods use numerics tailored towards the specific simulation, our scheme works scenario independent. Our generic scheme shows competitive results for both classical CFD and stratified scenarios. We focus on two dimensional simulations of two bubble convection scenarios over a background atmosphere. The largest simulation here uses order 6 and 6561 cells which were reduced to 1953 cells by our refinement criterion.