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).
© 2023 The Authors. Journal of Advances in Modeling Earth Systems published by Wiley Periodicals LLC on behalf of American Geophysical Union. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. We thank Keaton Burns and Greg L. Wagner for their encouragement and advice throughout the writing of this manuscript and Pedram Hassanzadeh for suggesting a modification to the title of the manuscript. The authors would also like to thank the two anonymous reviewers and the associate editor for their detailed comments and suggestions. Our work is supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program, and by the National Science Foundation under AGS Grants 1835860, 1835576, and 1835881. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Data Availability Statement: The software to plot all the figures is found in the GitHub repository (https://github.com/sandreza/DryAtmosphereFluxDifferencingVisualization) archived at Zenodo (A. Souza, 2022a). The data files are found via figshare at (A. Souza, 2022b) along with the software used to produce the data.
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