A nonnegative and shape‐preserving global transport model on cubed sphere using high‐order conservative collocation scheme

Abstract

A numerical model for global tracer transport is implemented by using Gauss–Legendre‐point conservative collocation (GLPCC) scheme on cubed sphere. Three‐point GLPCC scheme can achieve fifth‐order accuracy in the spherical geometry. To remove the spurious oscillations in the regions with strong gradients or discontinuities, the hierarchical reconstruction (HR) is applied to the “troubled cells” identified by a smoothness indicator based on the WENO concept. To assure the positivity‐preserving property, a flux correction operation is adopted to impose the restriction on the mass reduction due to the fluxes leaving the cell edges. The proposed numerical scheme aims to remove the nonphysical oscillations while preserving the accuracy in the smooth regions and maintain the compact spatial stencil as far as possible by making full use of degrees of freedom. The proposed schemes are evaluated by simulating the widely used benchmark tests for advection equation in one dimension and multidimensions of spherical geometry. Numerical results show that the fifth‐order accuracy is well preserved for smooth problems, while numerical oscillations can be effectively removed and the nonnegativity of the solutions is strictly guaranteed. It is very promising to develop the practical numerical model for tracer transport computation in atmospheric general circulation models using the proposed numerical framework.