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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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Volume 11, issue 11 | Copyright
Geosci. Model Dev., 11, 4359-4382, 2018
https://doi.org/10.5194/gmd-11-4359-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Model description paper 30 Oct 2018

Model description paper | 30 Oct 2018

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

Tuomas Kärnä1,a, Stephan C. Kramer3, Lawrence Mitchell2,4,b, David A. Ham2, Matthew D. Piggott3, and António M. Baptista1 Tuomas Kärnä et al.
  • 1Center for Coastal Margin Observation & Prediction, Oregon Health & Science University, Portland, OR, USA
  • 2Department of Mathematics, Imperial College London, London, UK
  • 3Department of Earth Science and Engineering, Imperial College London, London, UK
  • 4Department of Computing, Imperial College London, London, UK
  • apresent address: Finnish Meteorological Institute, Helsinki, Finland
  • bpresent address: Department of Computer Science, Durham University, Durham, UK

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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Unstructured meshes are attractive for coastal ocean modeling, as they allow more accurate representation of complex coastal topography. Unstructured mesh models are, however, often perceived as slow and inaccurate. We present a novel discontinuous Galerkin ocean model: Thetis. We demonstrate that the model is able to simulate baroclinic ocean flows with high accuracy on a triangular prismatic mesh. This work paves the way for highly accurate and efficient three-dimensional coastal ocean models.
Unstructured meshes are attractive for coastal ocean modeling, as they allow more accurate...
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