A synchronized co-volume scheme for the large-scale shallow water equations

Abstract:

The co-volume scheme specifies the mass at cell centers and cell vertices, and both of the normal and tangential velocity components at cell edges. This scheme is extremely flexible, applicable to unstructured meshes, and avoids the need to reconstruct the tangential velocity component, as the classical C-grid scheme does. But the co-volume has been shown to be a generalization of the E-grid scheme, and therefore inherits all the known defects of the latter. From another point of view, a recent study shows that, for the co-volume scheme on the f-plane, the mass-vorticity-divergence fields on the primary mesh are completely decoupled from the mass-vorticity-divergence fields on the dual mesh. We propose to periodically synchronize the fields on the primary mesh and the fields on the dual mesh. In this presentation, we explore approaches for the synchronization, and the effects of them.