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.
: An adaptive nonhydrostatic atmospheric dynamical core was developed on a Cartesian grid and extended to spherical geometry with the application of a cubed‐sphere grid. To assure a practical Courant‐Friedrichs‐Lewy number for stability, a horizontally explicit and vertically implicit algorithm was applied in this model through a third‐order implicit–explicit Runge–Kutta scheme. A two‐dimensional adaptive grid was applied in the horizontal directions to generate the computational meshes, with variable resolutions according to the evolution of the predicted variables during the simulations, while the vertical grid is fixed considering the characteristics of atmospheric flows and the computational efficiency in practical applications. The Berger–Oliger block‐structured adaptive algorithm was adopted in this study. Blocks with different resolutions can be constructed straightforwardly on each patch of the cubed sphere and an algorithm to exchange both solution and block information between adjacent patches was designed in order to implement a global model. The nonhydrostatic governing equations are solved by a three‐point multimoment constrained finite‐volume scheme. Using the compact stencil for spatial reconstructions, the interpolation operations between coarse–fine blocks can be implemented efficiently and the local‐based scheme is also helpful to suppress the computational modes around the coarse–fine interfaces due to the abrupt change of grid resolution. Additionally, flux corrections were conducted along the block boundaries and the resulting dynamical core is rigorously conservative. The proposed model was evaluated by calculating several idealized benchmark tests, and the effectiveness of the adaptive model in saving computational costs was verified in this study.
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