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

The 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. Plain Language Summary Computing powers and architectures historically influence the numerical algorithm designs of global atmospheric simulations at the fundamental levels. The next generation of the global circulation models can push its resolution to kilometer horizontal scales, which requires vital capabilities in a balanced representation of all motion modes and handling sharp discontinuities such as topography. Here, we demonstrate a new framework of a dynamical core that inherits advantages in both traditional geophysical fluid dynamics (GFD) modelings and versatile general computational fluid dynamics (CFD) techniques. This new development introduces several innovations, including the unified grid description, numerical optimization, stability enhancement, and a newly designed test to illustrate specific numerical properties cleanly. The desirable results of this work increase our confidence in creating a unique global circulation model to leverage next-generation highperformance computing and to improve our fundamental understanding of the atmospheric processes.

Automated summary

This study introduces a Low Mach number Approximate Riemann Solver (LMARS) based model for solving shallow-water equations on arbitrary gnomonic cubed-sphere grids. By utilizing a novel grid-generation process and improving the pressure gradient algorithm with LMARS viscous term, the model demonstrates stability and organic diffusion control for various numerical applications. The solver's dispersion properties and consistent performance among different grid types are validated through a newly introduced splash on the sphere test, laying a solid foundation for a new generation of global circulation models with kilometer horizontal scales.