Implementation of the Semi-Lagrangian Advection Scheme on a Quasi-Uniform Overset Grid on a Sphere

The semi-Lagrangian advection scheme is implemented on a new quasi-uniform overset （Yin-Yang） grid on the sphere. The Yin-Yang grid is a newly developed grid system in spherical geometry with two perpendicularly-oriented latitude-longitude grid components （called Yin and Yang respectively） that overlapp each other, and this effectively avoids the coordinate singularity and the grid convergence near the poles. In this overset grid, the way of transferring data between the Yin and Yang components is the key to maintaining the accuracy and robustness in numerical solutions. A numerical interpolation for boundary data exchange, which maintains the accuracy of the original advection scheme and is computationally efficient, is given in this paper. A standard test of the solid-body advection proposed by Williamson is carried out on the Yin-Yang grid. Numerical results show that the quasi-uniform Yin-Yang grid can get around the problems near the poles, and the numerical accuracy in the original semi-Lagrangian scheme is effectively maintained in the Yin-Yang grid.

Application of the Characteristic CIP Method to a Shallow Water Model on the Sphere

Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directly using a semi-Lagrangian advection scheme instead of the semi-implicit method in a shallow water model, to avoid expensive matrix inversions. Adoption of the semi-Lagrangian scheme renders the numerical model always stable for any Courant number, and which saves CPU time. To illustrate the effciency of the characteristic constrained interpolation profile （CIP） method, some numerical results are shown for idealized test cases on a sphere in the Yin-Yang grid system.