The Flux-Differencing Discontinuous Galerkin Method Applied to an
Idealized Fully Compressible Nonhydrostatic Dry Atmosphere
Abstract
Dynamical cores used to study the circulation of the atmosphere employ
various numerical methods ranging from finite-volume, spectral element,
global spectral, and hybrid methods. In this work, we explore the use of
Flux-Differencing Discontinuous Galerkin (FDDG) methods to simulate a
fully compressible dry atmosphere at various resolutions. We show that
the method offers a judicious compromise between high-order accuracy and
stability for large-eddy simulations and simulations of the atmospheric
general circulation. In particular, filters, divergence damping,
diffusion, hyperdiffusion, or sponge-layers are not required to ensure
stability; only the numerical dissipation naturally afforded by FDDG is
necessary. We apply the method to the simulation of dry convection in an
atmospheric boundary layer and in a global atmospheric dynamical core in
the standard benchmark of Held and Suarez (1994).