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.

doi:10.5194/gmd-11-4359-2018

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.

Authors

Tuomas Kärnä

Stephan C. Kramer

Lawrence Mitchell

David A. Ham

Matthew D. Piggott

António M. Baptista

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
Related Public URLs	https://arxiv.org/pdf/1711.08552.pdf