Article Type:
Research Article

A Mass-Conserving Semi-Lagrangian Scheme for the Shallow-Water Equations

Sylvie Gravel Recherche en prévision numérique, Service de l'environnement atmosphérique, Dorval, Quebec, Canada

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Andrew Staniforth Recherche en prévision numérique, Service de l'environnement atmosphérique, Dorval, Quebec, Canada

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Print Publication:
01 Jan 1994
DOI:
https://doi.org/10.1175/1520-0493(1994)122<0243:AMCSLS>2.0.CO;2
Page(s):
243–248
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Abstract

By generalizing the algorithm of Priestley for passively advected fields, a mass-conserving scheme for the coupled shallow-water equations is obtained. It is argued that the interpolation step of semi-Lagrangian schemes is the principal reason for their lack of formal conservation. The corrections introduced by the proposed algorithm to achieve conservation appropriately reflect the localized nature of the interpolation errors that induce its violation.

Abstract

By generalizing the algorithm of Priestley for passively advected fields, a mass-conserving scheme for the coupled shallow-water equations is obtained. It is argued that the interpolation step of semi-Lagrangian schemes is the principal reason for their lack of formal conservation. The corrections introduced by the proposed algorithm to achieve conservation appropriately reflect the localized nature of the interpolation errors that induce its violation.

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