  Unstructured grid ocean models are advantageous for simulating the coastal
ocean and river-estuary-plume systems. However, unstructured grid models tend
to be diffusive and/or computationally expensive which limits their
applicability to real life problems. In this paper, we describe a novel
discontinuous Galerkin (DG) finite element discretization for the hydrostatic
equations. The formulation is fully conservative and second-order accurate in
space and time. Monotonicity of the advection scheme is ensured by using a
strong stability preserving time integration method and slope limiters.
Compared to previous DG models advantages include a more accurate mode
splitting method, revised viscosity formulation, and new second-order time
integration scheme. We demonstrate that the model is capable of simulating
baroclinic flows in the eddying regime with a suite of test cases. Numerical
dissipation is well-controlled, being comparable or lower than in existing
state-of-the-art structured grid models.
