Localized artificial viscosity stabilization of discontinuous Galerkin methods for nonhydrostatic mesoscale atmospheric modeling

Abstract

Gibbs oscillation can show up near flow regions with strong temperature gradients in the numerical simulation of nonhydrostatic (NH) mesoscale atmospheric flows when using the high-order discontinuous Galerkin (DG) method. We propose to incorporate localized Laplacian artificial viscosity in the DG framework to suppress the spurious oscillation in the vicinity of sharp thermal fronts, while not contaminating the smooth flow features elsewhere. The resulting numerical formulation is then validated on several benchmark test cases, including a shock discontinuity problem with the 1D Burger’s equation, and two test cases for the compressible Euler equations: a rising thermal bubble and density current. The results indicate that the proposed DG-localized Laplacian artificial viscosity method works robustly with a wide range of grid sizes and polynomial orders.