[M-GI30] Computational sciences on the universe, galaxies, stars, planets and their environments

[MGI30-07] Shallow-water models using cubed-sphere projection and radial basis functions

*Takeshi Enomoto^1,2, Koji Ogasawara³ (1.Disaster Prevention Research Institute, Kyoto University, 2.Application Laboratory, Japan Agency for Marine-Earth Science and Technology, 3.Graduate School of Science, Kyoto University )

Keywords:dynamical core, meshless method, radial basis function, cubed sphere

Radial Basis Function generated Finite Difference (RBF-FD) is a meshless method that does not require all-to-all communication in parallel computation, easily achieves high-order convergence, and whose p-refinement does not impose stricter CFL conditions. Although RBF-FD previously struggled with parameter tuning for accuracy, the recently proposed PHS + Poly method eliminates this difficulty. In atmospheric science, PHS + Poly has thus far been applied only to the transport scheme. In this study, we develop the shallow water equation model and evaluate its performance as the next step toward developing a GCM.
In this presentation, we describe the study in which PHS + Poly is applied to the shallow water equations in cubed sphere coordinates. Cubed sphere coordinates are obtained by projecting an inscribed cube onto a sphere and dividing the sphere into six regions, with each face having a two-dimensional curvilinear coordinate system. Cubed sphere coordinates have lower computational cost compared to the three-dimensional Cartesian coordinate system, which is widely used in RBF-FD.
The results of standard test cases for the shallow water equation model demonstrate that high-order algebraic convergence is confirmed in the nonlinear zonal geostrophic flow test case, and show that accuracy of RBF-FD is comparable to other spectral methods in the Rossby-Haurwitz wave test case.