International Journal for Numerical Methods in Fluids · 2008 · 17 citations · 21 references
Mass Lumping TechniqueEngineeringSurface WaveFluid MechanicsMass LumpingShallow Water HydrodynamicsWave MotionCoastal HydrodynamicsDispersionWave AnalysisWave HydrodynamicsDispersion PropertiesWave DynamicsOcean Wave MechanicsPhysicsWave PropagationHydromechanicsShip HydrodynamicsFinite‐element Shallow‐water ModelsHydrodynamicsApplied PhysicsRossby Waves
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 − 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.
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