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.
Highlights
In this paper we address the resolution of basic cloud formation processes on modern super computer systems
– We extend the ExaHyPE Engine to allow viscous terms. – We provide an implementation of the compressible Navier-Stokes equations
We emphasize that we use a standard formulation of the Navier-Stokes equations as seen in the field of computational fluid mechanics and only use small modifications of the governing equations, in contrast to a equation set that is tailored exactly to the application area. – We present a general amr-criterion that is based on the detection of outlier cells w.r.t. their total variation
Summary
The simulation of cloud formations, as part of convective processes, is expected to play an important role in future numerical weather prediction [1] This requires both suitable physical models and effective computational realizations. We focus on the simulation of simple benchmark scenarios [10] They contain relatively small scale effects which are well approximated with the compressible Navier-Stokes equations. We use the ader-dg method of [5], which allows us to simulate the Navier-Stokes equations with a space-time-discretization of arbitrary high order. We use the numerical flux for the compressible Navier-Stokes equations of Gassner et al [8] This flux has already been applied to the ader-dg method in [4]. We use adaptive mesh refinement (amr) to increase the spatial resolution in areas of interest This has been shown to work well for the simulation of cloud dynamics [12]. Whether our proposed general implementation can achieve results that are competitive with the state-of-the-art models that rely on heavily specified equations and numerics
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