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

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

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., & Baptista, A. M. (2018). Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations. Geoscientific Model Development, 11(11), 4359-4382. https://doi.org/10.5194/gmd-11-4359-2018

• Journal Article Type: Article
• Acceptance Date: Oct 9, 2018
• Online Publication Date: Oct 30, 2018
• Publication Date: Oct 30, 2018
• Deposit Date: Oct 30, 2018
• Publicly Available Date: Oct 30, 2018
• Journal: Geoscientific Model Development
• Print ISSN: 1991-959X
• Electronic ISSN: 1991-9603
• Publisher: European Geosciences Union
• Peer Reviewed: Peer Reviewed
• Volume: 11
• Issue: 11
• Pages: 4359-4382
• DOI: https://doi.org/10.5194/gmd-11-4359-2018
• Public URL: https://durham-repository.worktribe.com/output/1315103
• Related Public URLs: https://arxiv.org/pdf/1711.08552.pdf