Pressure forcing and dispersion analysis for discontinuous Galerkin approximations to oceanic fluid flows

This paper is part of an effort to examine the application of discontinuous Galerkin (DG) methods to the numerical modeling of the general circulation of the ocean. One step performed here is to develop an integral weak formulation of the lateral pressure forcing that is suitable for usage with a DG method and with a generalized vertical coordinate that includes level, terrain-fitted, isopycnic, and hybrid coordinates as examples. This formulation is then tested, in special cases, with analyses of dispersion relations and numerical stability and with some computational experiments. These results suggest that the advantages of DG methods may significantly outweigh their disadvantages, in the settings tested here. This paper also outlines some other issues that need to be addressed in future work.