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

Abstract

AbstractThe rapidly increasing computing powers allow global atmospheric simulations with aggressively high resolutions, challenging traditional model design principles. This study presents a Low Mach number Approximate Riemann Solver (LMARS) based unstaggered finite‐volume model for solving the shallow‐water equations on arbitrary gnomonic cubed‐sphere grids. Using a novel reference line‐based grid‐generation process, it unifies the representation of arbitrary gnomonic cubed‐sphere grid projections and permits high‐efficiency 1D reconstruction in the halo regions. The numerical discretization also extends a widely used pressure gradient algorithm with the LMARS viscous term, thus improves the model's stability for various numerical applications. The solver demonstrates a broad range of organic diffusion control without any explicit filters, validated by a comprehensive set of test cases. Lastly, a newly introduced splash on the sphere test verifies the solver's desirable dispersion properties and consistent performance among different grid types. This study paves a solid foundation for a new generation of global circulation models with kilometer horizontal scales.