Analysis and comparison of multi-conservation difference schemes

The spherical shallow water equations without the effects of any outer frictions and forcing source have many remarkable features, such as the energy conservation, the mass conservation, the potential vorticity conservation, the potential vorticity enstrophy conservation and the absolute angular momentum conservation. Once the equations are discretized, however, these important features can hardly be maintained. Focusing on the multi-conservation problem of numerical method, two new difference schemes developed recently are discussed and compared in this paper. One is the improved energy-conservation scheme, by which four of the aforesaid conservation properties can be kept well. The other is the symplectic-like scheme, which can conserve all of the five physical integrals approximately. Numerical tests show that both of the schemes are with good multi-conservation features and worth generalizing and applying.