A fast solver of the shallow water equations on a sphere using a combined compact difference scheme

The spectral-like three-point combined compact difference (sp-CCD) scheme is developed for the shallow water models on a sphere, which is originally proposed by Chu and Fan (J. Comput. Phys. 140 (1998) 370). A standard test set proposed by Williamson et al. (J. Comput. Phys. 102 (1992) 211) is used to evaluate the accuracy of the new method. It is shown that the accuracy of the method is comparable to that of the spherical harmonics model as a whole. The relative efficiency of the method with respect to the spherical harmonics model appears from the resolution of 512×256, and it becomes significant for the higher resolutions. The test results suggest that the method could be extended to numerical atmospheric models.