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The Flux-Differencing Discontinuous Galerkin Method Applied to an Idealized Fully Compressible Nonhydrostatic Dry Atmosphere

Souza, A.N.; He, J.; Bischoff, T.; Waruszewski, MacIej; Novak, L.; Barra, V.; Gibson, T.; Sridhar, A.; Kandala, S.; Byrne, S.; Wilcox, L.C.; Kozdon, J.; Giraldo, F.X.; Knoth, O.; Marshall, J.; Ferrari, R.; Schneider, T.

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, https://doi.org/10.1175/1520-0477(1994)075〈1825:apftio〉2.0.co;2).