The LMARS Based Shallow‐Water Dynamical Core on Generic Gnomonic Cubed‐Sphere Geometry

Abstract

Building a dynamical core for the atmospheric model is an art of balancing the requirements between accuracy and efficiency. Although a model's accuracy can be more definitive to measure in benchmark experiments-at least for smooth solutions, computational efficiency is a relative concept that strongly associates with the computing platform characteristics. In a way, the available computational power and machine architectures have been dictating the scope of the research topics and the design of the numerical simulation. For example, coming out of the wide adoption of the massively parallel computing, many modern models prefer quasi-uniform computational grids, such as the icosahedral (

Implementation of the Novel Duo‐Grid in GFDL's FV3 Dynamical Core

“…In some cases, we will in fact find that the interior solution is improved with the Duo-Grid. To quantify these errors, we use error norm measures as defined in Williamson (1992), Chen (2021). We also plot error maps to show the spatial distribution of these errors relative to the flow and grid configurations in different cases.…”

“…In this work, we implement an extension of the Duo-Grid developed by Chen (2021) in their Low Mach number Approximate Riemann Solver (LMARS). LMARS with the Duo-Grid is a highly efficient unstaggered finite-volume solver for the horizontal advection equations on arbitrary gnomonic cubed-sphere grids.…”

“…The Duo‐Grid implements two grids on each face of the cubed‐sphere: a “kinked” grid which follows the coordinate on the facing grids and includes the discontinuous coordinate, and an “extended” grid which extends the face's coordinates onto the facing grids along great circle lines. Chen (2021) applied the Duo‐Grid to their unstaggered dynamics to reduce the amplitude of grid imprinting into imperceptibility. Other researchers have investigated a similar approach as well, but these methods only apply to the equiangular gnomonic cubed‐sphere grid, and not optimized for performance (Katta et al., 2015; Ullrich et al., 2010).…”

High‐order conservative transport on Yin‐Yang grids using the multi‐moment constrained finite volume method

“…A two‐dimensional splash test on the sphere (Chen, 2021) is also carried out with three resolutions to investigate the shallow‐water model in short‐wave representation. A sinusoidal droplet is splashed at the Arctic point, which propagates freely southward on the non‐rotating globe.…”

“…icosahedral grid (Sadourny et al ., 1968; Tomita et al ., 2001), cubed‐sphere grid (Sadourny, 1972; Harris and Lin, 2013; Lin et al, 2017) and the overlapped Yin‐Yang grid (Kageyama and Sato, 2004). Among the quasi‐uniform grid systems, cubed‐sphere and geodesic grids bear several weak singular points (Chen, 2021). On the other hand, the Yin‐Yang grid, briefly described in the next section, successfully avoids the trouble of singular points entirely with two identical zones on a sphere (Kageyama and Sato, 2004), which are described with orthogonal latitude–longitude coordinates.…”