Two-dimensional dispersion analyses of finite element approximations to the shallow water equations

J. H. Atkinson, J. J. Westerink, R. A. Luettich
2004 International Journal for Numerical Methods in Fluids  
Dispersion analysis of discrete solutions to the shallow water equations has been extensively used as a tool to deÿne the relationships between frequency and wave number and to determine if an algorithm leads to a dual wave number response and near 2 x oscillations. In this paper, we explore the application of two-dimensional dispersion analysis to cluster based and Galerkin ÿnite element-based discretizations of the primitive shallow water equations and the generalized wave continuity equation
more » ... (GWCE) reformulation of the harmonic shallow water equations on a number of grid conÿgurations. It is demonstrated that for various algorithms and grid conÿgurations, 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 2 x noise in the solution.
doi:10.1002/fld.701 fatcat:yabuvofrnvgthiooxmpum2b3xm