Comparison of unstructured, staggered grid methods for the shallow water equations

Unstructured grid models are receiving increased attention mainly because of their ability to provide a flexible spatial discretization. Hence, some areas can be resolved in great detail while not over-resolving other areas. Development of these models is an ongoing process with significant longstanding issues with spurious computational modes, efficiency, advection and Coriolis approximations, and so forth. However, many of these problems have been solved with the current generation of models which have much promise for coastal to global scale ocean modelling. Our purpose is to intercompare a class of unstructured grid models where the continuity equation reduces to a finite volume approximation. The momentum equations can be approximated with finite difference, finite element, or finite volume methods. Each of these methods can have advantages and disadvantages in different classes of problems that range from hydraulics to coastal and global ocean flows. Some of the more important differences are restrictions on grid irregularity and stability of the Coriolis term. The finite element version of the model has important advantages in the discretization of the Coriolis term and does not require a reconstruction of a tangential velocity component. The comparison is illustrated with a simple test case.