Modified time splitting scheme for shallow water equations

An alternating direction implicit scheme for the shallow water equations is considered. The truncation error related to application of splitting technique is separated and analyzed. An approach to reducing the splitting errors is considered and corresponding modified time splitting scheme is presented. An analysis of the linear stability shows that both schemes allow the same maximum time step, which is great enough for atmospheric modeling. Numerical experiments confirm extended stability of both schemes and evaluate their splitting errors as functions of time step. The results of integrations with increased time steps show a clear advantage of the modified version over the traditional scheme.