Two‐dimensional dispersion analyses of finite element approximations to the shallow water equations |
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| Authors: | J. H. Atkinson J. J. Westerink R. A. Luettich Jr |
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| Affiliation: | 1. Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN 46556, U.S.A.;2. Institute of Marine Sciences, University of North Carolina at Chapel Hill, 3431 Arendell Street, Morehead City, NC 28557, U.S.A. |
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| Abstract: | Dispersion analysis of discrete solutions to the shallow water equations has been extensively used as a tool to define the relationships between frequency and wave number and to determine if an algorithm leads to a dual wave number response and near 2Δx oscillations. In this paper, we explore the application of two‐dimensional dispersion analysis to cluster based and Galerkin finite element‐based discretizations of the primitive shallow water equations and the generalized wave continuity equation (GWCE) reformulation of the harmonic shallow water equations on a number of grid configurations. It is demonstrated that for various algorithms and grid configurations, contradictions exist between the results of one‐dimensional and two‐dimensional dispersion analysis as a result of subtle changes in the mass matrix. Numerical experiments indicate that the two‐dimensional dispersion analysis correctly predicts the existence and onset of near 2Δx noise in the solution. Copyright © 2004 John Wiley & Sons, Ltd. |
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| Keywords: | dispersion analysis shallow water equations finite element models |
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