A comparison of the GWCE and mixed P − P1 formulations in finite‐element linearized shallow‐water models |
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| Authors: | D Y Le Roux R Walters E Hanert J Pietrzak |
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| Institution: | 1. Universit é de Lyon, CNRS, Universit é Lyon 1, Institut Camille Jordan, 43, blvd du 11 novembre 1918, 69622 Villeurbanne Cedex, France;2. Hydrodynamics, O/RM, 6051 Hunt Rd, Vic., Canada BC V8Y 3H7;3. Earth and Life Institute, Universit é catholique de Louvain, Croix du Sud 2/16, B‐1348 Louvain‐la‐Neuve, Belgium;4. Faculteit CiTG, TU Delft, Stevinweg 1, 2628 CN Delft, The Netherlands |
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| Abstract: | The appearance of spurious pressure modes in early shallow‐water (SW) models has resulted in two common strategies in the finite element (FE) community: using mixed primitive variable and generalized wave continuity equation (GWCE) formulations of the SW equations. One FE scheme in particular, the P ? P1 pair, combined with the primitive equations may be advantageously compared with the wave equation formulations and both schemes have similar data structures. Our focus here is on comparing these two approaches for a number of measures including stability, accuracy, efficiency, conservation properties, and consistency. The main part of the analysis centres on stability and accuracy results via Fourier‐based dispersion analyses in the context of the linear SW equations. The numerical solutions of test problems are found to be in good agreement with the analytical results. Copyright © 2011 John Wiley & Sons, Ltd. |
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| Keywords: | shallow‐water equations generalized wave continuity equation finite elements dispersion analysis gravity waves |
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