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

Abstract

Designing dynamical cores that meet the challenges imposed by simulating the continuous equations that govern geophysical flows has a long history (Williamson, 2007). Various numerical methods are employed to achieve accuracy, efficiency, and stability. However, careful compromises are required because these goals are often in conflict: significant dissipation helps with stability at the cost of accuracy, and high-order schemes deliver accuracy at the expense of computing cost. This work explores the discontinuous Galerkin (DG) method for simulating atmospheric motions.

A New WENO‐Based Momentum Advection Scheme for Simulations of Ocean Mesoscale Turbulence

“…Diffusive numerical schemes have seen application in various computational fluid dynamics fields, especially in combination with the conservative (or "flux-form") formulation of the advection operator (Karaca et al, 2012;Maulik & San, 2018;Zeng et al, 2021), including in atmospheric models (Norman et al, 2023;Smolarkiewicz & Margolin, 1998;Souza et al, 2023) and regional ocean models (Holland et al, 1998;Mohammadi-Aragh et al, 2015;Shchepetkin & McWilliams, 1998a). However, finite-volume general circulation models (GCMs) often favor the rotational formulation of the advection operator due to its ease of implementation with non-regular grids, such as the cubed sphere grid (Ronchi et al, 1996), the latitudelongitude capped grid (Fenty & Wang, 2020), or the tripolar grid (Madec & Imbard, 1996).…”