Impact of mass lumping on gravity and Rossby waves in 2D finite-element shallow-water models

Le Roux, D.Y.;Hanert, Emmanuel;Rostand, V.;Pouillot, B.
(2009) International Journal for Numerical Methods in Fluids — Vol. 59, n° 7, p. 767-790 (2009)

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Authors
  • Le Roux, D.Y.Université Laval
    Author
  • Hanert, Emmanuelorcid-logoUCLouvain
    Author
  • Rostand, V.Université Laval
    Author
  • Pouillot, B.Université Laval
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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 P1NC−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.
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Le Roux, D. Y., Hanert, E., Rostand, V., & Pouillot, B. (2009). Impact of mass lumping on gravity and Rossby waves in 2D finite-element shallow-water models. International Journal for Numerical Methods in Fluids, 59(7), 767-790. https://doi.org/10.1002/fld.1837 (Original work published 2009)