Application of a coupled discontinuous-continuous Galerkin finite element shallow water model to coastal ocean dynamics

A coupled discontinuous-continuous Galerkin (DG-CG) shallow water model is compared to a continuous Galerkin generalized wave-continuity equation (GWCE) based model for the coastal ocean, whereby local mass imbalance typical of GWCE-based solutions is eliminated using the coupled DG-CG approach. Two mass imbalance indicators for the GWCE-based model are presented and analyzed. The indicators motivate discussion on the suitability of using a GWCE-based model versus the locally conservative coupled DG-CG model. Both realistic and idealized test problems for tide, wind, and wave-driven circulation form the basis of the study. For the problems studied, coupled DG-CG solutions retain the robustness of well-documented solutions from GWCE-based models and also capture the dynamics driven by small-scale, highly advective processes which are problematic for GWCE-based models. Issues associated with the coupled DG-CG model are explored, including increased cost due to increased degrees of freedom, the necessary application of slope limiters, as well as the actual coupling process.