An unconditionally stable semi-Lagrangian method for the spherical atmospherical shallow water equations

A semi-implicit, semi-Lagrangian, mixed finite difference-finite volume model for the shallow water equations on a rotating sphere is introduced and discussed. Its main features are the vectorial treatment of the momentum equation and the finite volume approach for the continuity equation. Pressure and Coriolis terms in the momentum equation and velocity in the continuity equation are treated semi-implicitly. Moreover, a splitting technique is introduced to preserve symmetry of the numerical scheme. An alternative asymmetric scheme (without splitting) is also introduced and the efficiency of both is discussed. The model is shown to be conservative in geopotential height and unconditionally stable for 0.5 less than or equal to theta less than or equal to 1. Numerical experiments on two standard test problems confirm the performance of the model.