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Unstructured grid ocean models are advantageous for simulating the coastalocean and river-estuary-plume systems. However, unstructured grid models tendto be diffusive and/or computationally expensive which limits theirapplicability to real life problems. In this paper, we describe a noveldiscontinuous Galerkin (DG) finite element discretization for the hydrostaticequations. The formulation is fully conservative and second-order accurate inspace and time. Monotonicity of the advection scheme is ensured by using astrong stability preserving time integration method and slope limiters.Compared to previous DG models advantages include a more accurate modesplitting method, revised viscosity formulation, and new second-order timeintegration scheme. We demonstrate that the model is capable of simulatingbaroclinic flows in the eddying regime with a suite of test cases. Numericaldissipation is well-controlled, being comparable or lower than in existingstate-of-the-art structured grid models.

Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations