A computationally efficient Riemann solver based shallow water model on the cubed-sphere

A cubed-sphere grid system provides much better uniform grid point distribution compared to the conventional lat-lon grid system. A finite volume method could be used to solve the flux form shallow water equations. However, due to the non-orthogonal cubed-sphere grid, extra metric terms are necessary in the momentum equations, which requires more computational steps compared to their counterpart on an orthogonal grid. In this model, the vector-invariant shallow water equations are implemented, which has fewer non-orthogonal terms. A fast Riemann solver is derived to calculate the values of the prognostic variables at control volume interfaces for the momentum equations and to compute the fluxes for the continuity equation.