Computational Science – ICCS 2009

Volume 5545 of the series Lecture Notes in Computer Science pp 243-252

A Fully Implicit Jacobian-Free High-Order Discontinuous Galerkin Mesoscale Flow Solver

  • Amik St-CyrAffiliated withNational Center for Atmospheric Research (NCAR)
  • , David NeckelsAffiliated withPreviously NCAR now Beckman Coulter Inc.

* Final gross prices may vary according to local VAT.

Get Access


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.