Study And Improvement Of The Conservative Constraint Algorithm On The Yin-Yang Grid

As a new quasi-uniform overset grid on the sphere,Yin-Yang grid could avoid the two numerical problem of the coordinate singularity and the grid convergence near the poles over the latitude-longitude grid.However,Yin-Yang grid dose not ensure mass conservation for global transport,the mass conservation algorithm on the Yin-Yang grid is of important significance to the construction and application of Yin-Yang grid in global atmospheric modeling.It's also an important index of model performance to ensure the long-term stable model integration and high computational effect.In this study,a new algorithm is devolped to ensure exact conservation and improve the computational effect.We suggest a mass conservation algorithm of cell-wise bi-linear mass distribution and piece-wise linear flux distribution over boundary.In contrast to the conservative constraint which defines cell-wise constant mass distribution,the new algorithm improves the accuracy of advection computation on the Yin-Yang grid and stability of model integration.The flux-form advection equation is solved by using the CIP-CSLR scheme.Several idealized tests,including a solid cosine-bell advection with non-divergent flow,global transport of a sine-wave test,a test with smooth deformational flow,a test with global steady state nonlinear zonal geostrophic flow,a test of zonal flow over an isolated mountain and Rossby-Haurwitz wave test are conducted to compare the impact of cell-wise bi-linear distribution with that of the cell-wise constant distribution.The error norms and spatial distribution of scalars all suggested that the new scheme is capable of refining the global conservation status in model application,which could effectively improve the computational effect of the conservative constraint on the Yin-Yang grid without obviously increasing of computational cost.In addition,we managed to use a third-order Runge-Kutta temporal integration scheme in the CIP-CSLR advection scheme,the numerical experiments are given to verify the proposed algorithm.The numerical results show that the second algorithm is a high order numerical scheme with enforcing local and global conservation.