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

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). Plain Language Summary Numerical models cannot explicitly represent all degrees of freedom that characterize atmospheric flows due to limitations in computing power. One must allocate the available computational degrees of freedom to reduce the degradation of the solution. In this work, we explore the use of the discontinuous Galerkin numerical method, a hybrid approach that combines the accuracy of spectral methods with the flexibility of finite volume methods. We apply it to idealized dry atmospheric simulations and show that the method is robust and incorporates physical principles to best account for unresolved processes. Key Points The Flux‐Differencing Discontinuous Galerkin (FDDG) method is a robust numerical discretization for geophysically relevant configurations FDDG allows for a computationally stable total energy formulation of the compressible Euler equations with gravity and rotation FDDG simulates a dry convective boundary layer and the atmospheric general circulation using only numerical dissipation