Editorial Type:
Article
Article Type:
Research Article

A Semi-implicit Semi-Lagrangian Finite-Element Shallow-Water Ocean Model

Daniel Y. Le Roux Department of Atmospheric and Oceanic Sciences, and Centre for Climate and Global Change Research, McGill University, and Centre de Recherche en Calcul Appliqué, Montreal, Quebec, Canada

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Charles A. Lin Department of Atmospheric and Oceanic Sciences, and Centre for Climate and Global Change Research, McGill University, and Centre de Recherche en Calcul Appliqué, Montreal, Quebec, Canada

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Andrew Staniforth Meteorological Research Branch, Environment Canada, Dorval, Quebec, Canada

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Print Publication:
01 May 2000
DOI:
https://doi.org/10.1175/1520-0493(2000)128<1384:ASISLF>2.0.CO;2
Page(s):
1384–1401
Restricted access

Abstract

The finite-element, semi-implicit, and semi-Lagrangian methods are combined together to solve the shallow-water equations using unstructured triangular meshes. Triangular finite elements are attractive for ocean modeling because of their flexibility for representing irregular boundaries and for local mesh refinement. A kriging interpolator is used for the semi-Lagrangian advection, leading to an accurate representation of the slow Rossby modes. The terms that govern fast gravitational oscillations are discretized using the semi-implicit scheme, thereby circumventing a severe time step restriction. A low-order velocity–surface-elevation finite-element basis-function pair is used for the spatial discretization. Results of test problems to simulate slowly propagating Rossby modes illustrate the promise of the proposed approach for ocean modeling.

* Current affiliation: National Center for Atmospheric Research, Advanced Study Program, Boulder, Colorado.

Current affiliation: U.K. Meteorological Office, Bracknell, Berkshire, United Kingdom.

Corresponding author address: Dr. Daniel Y. Le Roux, Dept. of Atmospheric and Oceanic Sciences, McGill University, Centre for Climate and Global Change Research, Montreal PQ H3A 2K6, Canada.

Email: dleroux@cerca.umontreal.ca

Abstract

The finite-element, semi-implicit, and semi-Lagrangian methods are combined together to solve the shallow-water equations using unstructured triangular meshes. Triangular finite elements are attractive for ocean modeling because of their flexibility for representing irregular boundaries and for local mesh refinement. A kriging interpolator is used for the semi-Lagrangian advection, leading to an accurate representation of the slow Rossby modes. The terms that govern fast gravitational oscillations are discretized using the semi-implicit scheme, thereby circumventing a severe time step restriction. A low-order velocity–surface-elevation finite-element basis-function pair is used for the spatial discretization. Results of test problems to simulate slowly propagating Rossby modes illustrate the promise of the proposed approach for ocean modeling.

* Current affiliation: National Center for Atmospheric Research, Advanced Study Program, Boulder, Colorado.

Current affiliation: U.K. Meteorological Office, Bracknell, Berkshire, United Kingdom.

Corresponding author address: Dr. Daniel Y. Le Roux, Dept. of Atmospheric and Oceanic Sciences, McGill University, Centre for Climate and Global Change Research, Montreal PQ H3A 2K6, Canada.

Email: dleroux@cerca.umontreal.ca

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