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Impact of mass lumping on gravity and Rossby waves in 2D finite‐element shallow‐water models
Author(s) -
Le Roux D. Y.,
Hanert E.,
Rostand V.,
Pouliot B.
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1837
Subject(s) - rossby wave , dispersion (optics) , dispersion relation , finite element method , mechanics , waves and shallow water , shallow water equations , mathematical analysis , physics , surface gravity , mathematics , classical mechanics , thermodynamics , optics , atmospheric sciences , astronomy , spectral line
Abstract The goal of this study is to evaluate the effect of mass lumping on the dispersion properties of four finite‐element velocity/surface‐elevation pairs that are used to approximate the linear shallow‐water equations. For each pair, the dispersion relation, obtained using the mass lumping technique, is computed and analysed for both gravity and Rossby waves. The dispersion relations are compared with those obtained for the consistent schemes (without lumping) and the continuous case. The P 0 − P 1 , RT 0 and P NC 1 − P 1 pairs are shown to preserve good dispersive properties when the mass matrix is lumped. Test problems to simulate fast gravity and slow Rossby waves are in good agreement with the analytical results. Copyright © 2008 John Wiley & Sons, Ltd.