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arXiv · 1711.08552

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

Tuomas Kärnä·Stephan C. Kramer·Lawrence Mitchell·David A. Ham·Matthew D. Piggott·António M. Baptista
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Abstract

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.

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Tuomas Kärnä, Stephan C. Kramer, Lawrence Mitchell, David A. Ham, Matthew D. Piggott, António M. Baptista. 2017-11-23. Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations. https://doi.org/10.5194/gmd-11-4359-2018

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