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, Antonio Baptista

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)4359-4382
Number of pages24
JournalGeoscientific Model Development
Volume11
Issue number11
DOIs
StatePublished - Oct 30 2018
Externally publishedYes

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Hydrostatics
Discontinuous Galerkin
hydrostatics
Ocean
Discretization
Three-dimensional
ocean
Unstructured Grid
Time Integration
baroclinic motion
Strong Stability
Limiter
Model
Formulation
Splitting Method
Limiters
Advection
Finite Element Discretization
Estuaries
Monotonicity

ASJC Scopus subject areas

  • Modeling and Simulation
  • Earth and Planetary Sciences(all)

Cite this

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, Antonio.

In: Geoscientific Model Development, Vol. 11, No. 11, 30.10.2018, p. 4359-4382.

Research output: Contribution to journalArticle

Kärnä, Tuomas ; Kramer, Stephan C. ; Mitchell, Lawrence ; Ham, David A. ; Piggott, Matthew D. ; Baptista, Antonio. / Thetis coastal ocean model : Discontinuous Galerkin discretization for the three-dimensional hydrostatic equations. In: Geoscientific Model Development. 2018 ; Vol. 11, No. 11. pp. 4359-4382.
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