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Impact of mass lumping on gravity and Rossby waves in 2D finite element shallow-water models. (English) Zbl 1156.76035
Summary: The goal is to evaluate the effect of mass lumping on 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 consistent schemes (without lumping) and the continuous case. The \(P_{0}-P_{1}, RT_{0}\) and \(P_1^{\text{NC}}-P_{1}\) 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 analytical results.

76M10 Finite element methods applied to problems in fluid mechanics
76B65 Rossby waves (MSC2010)
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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