A high-accurate IDO (Interpolated Differential Operator) Scheme[1] has been applied to shallow water equations in spherical geometry represented by Williamson's test cases[2]. The IDO scheme required not only the discretized physical value on the grid point, but also its spatial derivatives as independent variables. The additional variables require solving more equations derived from the given equations, so that it makes possible to construct a high-accurate interpolation function around the local area of the grid point. The interpolation function reduces to an approximation solution of the given partial differential equation. For Williamson's test case 2, our result keeps the initial balance much better than 4th-order finite difference scheme. The result of the test case 5 has good agreement with that of Pseudo-Spectral method.

In order to avoid the singularities at the poles, we introduce two overset grids to replace the area around the poles. For the communication between the grid boundaries, third-order interpolated is used due to making use of spatial derivatives. Rossby-Haurwitz wave of the test case 6 propagates across the grid overset region without any oscillations, and is in good agreement with the case of a single grid. Any problems will not expected to apply to massively parallel computers.