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Two‐dimensional dispersion analyses of finite element approximations to the shallow water equations
Author(s) -
Atkinson J. H.,
Westerink J. J.,
Luettich R. A.
Publication year - 2004
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.701
Subject(s) - shallow water equations , dispersion (optics) , mathematics , finite element method , grid , mathematical analysis , waves and shallow water , galerkin method , geometry , physics , optics , thermodynamics
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 2Δ x 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 2Δ x noise in the solution. Copyright © 2004 John Wiley & Sons, Ltd.