Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
https://doi.org/10.5194/gmd-2017-292
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Model description paper
02 Feb 2018
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Geoscientific Model Development (GMD).
Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations
Tuomas Kärnä1, Stephan C. Kramer3, Lawrence Mitchell2,4, David A. Ham2, Matthew D. Piggott3, and António M. Baptista1 1NSF Science and Technology Center for Coastal Margin Observation & Prediction, Oregon Health & Science University, Portland, Oregon, USA
2Department of Mathematics, Imperial College London, London, United Kingdom
3Department of Earth Science and Engineering, Imperial College London, London, United Kingdom
4Department of Computing, Imperial College London, London, United Kingdom
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.

Citation: Kärnä, T., Kramer, S. C., Mitchell, L., Ham, D. A., Piggott, M. D., and Baptista, A. M.: Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations, Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2017-292, in review, 2018.
Tuomas Kärnä et al.
Tuomas Kärnä et al.

Model code and software

Thetis coastal ocean model Thetis https://doi.org/10.5281/zenodo.1050306 A Compiler for Fast Expression Evaluation COFFEE https://doi.org/10.5281/zenodo.573267 The Finite Element Automated Tabulator FIAT https://doi.org/10.5281/zenodo.1043841 A smarter library of finite elements FInAT https://doi.org/10.5281/zenodo.1039605 An automated finite element system Firedrake https://doi.org/10.5281/zenodo.1043843 Portable, Extensible Toolkit for Scientific Computation PETSc https://doi.org/10.5281/zenodo.1022071 The Python interface to PETSc petsc4py https://doi.org/10.5281/zenodo.1022068 Framework for performance-portable parallel computations on unstructured meshes PyOP2 https://doi.org/10.5281/zenodo.1043839 The Two Stage Form Compiler TSFC https://doi.org/10.5281/zenodo.1043837 The Unified Form Language UFL https://doi.org/10.5281/zenodo.1043842
Tuomas Kärnä et al.

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Short summary
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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