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

Abstract

AbstractA numerical constraint was developed to improve the global and local conservation for the Yin‐Yang grid system, which has been known as one of the quasi‐uniform grids on a sphere. Two‐dimensional cubic mass distribution within an individual mesh was assumed, to describe the subgrid‐scale structure of local properties and to ensure high‐order‐accuracy mass flux specification for the Yin‐Yang boundary. A three‐point Multi‐moment Constrained finite Volume scheme, in cooperation with a fourth‐order Runge–Kutta scheme, was selected for numerical transport with the help of Boundary Gradient Switching for oscillation suppression. The new scheme was tested with a couple of idealized numerical experiments in advection and shallow‐water models on the Yin‐Yang grid to verify its performance. Numerical results confirmed the exact mass conservation in spherical advection problems, and the numerical convergence rate reached fourth order in both advection and shallow‐water models. Computational stability, shape‐preserving and numerical oscillation‐free properties were also revealed in the nonlinear testing problems.