Impact of mass lumping on gravity and Rossby waves in 2D finite‐element shallow‐water models |
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| Authors: | D. Y. Le Roux E. Hanert V. Rostand B. Pouliot |
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| Affiliation: | 1. Département de Mathématiques et de Statistique, Université Laval, Québec, Que., Canada G1K 7P4;2. Department of Meteorology, The University of Reading, Earley Gate, P.O. Box 243, Reading RG6 6BB, U.K. |
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| 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 P0?P1, RT0 and P ?P1 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. |
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| Keywords: | shallow‐water equations finite elements mass lumping gravity waves Rossby waves |
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