A fully implicit Jacobian-free high-order discontinuous galerkin mesoscale flow solver

Abstract

In this work it is shown how to discretize the compressible Euler equations around a vertically stratified base state using the discontinuous Galerkin approach on collocated Gauss type grids. A stiffly stable Rosenbrock W-method is combined with an approximate evaluation of the Jacobian to integrate in time the resulting system of ODEs. Simulations with fully compressible equations for a rising thermal bubble are performed. Also included are simulations of an inertia gravity wave in a periodic channel. The proposed time-stepping method accelerates the simulation times with respect to explicit Runge-Kutta time stepping procedures having the same number of stages. © 2009 Springer Berlin Heidelberg.