NDLI: Dispersion Relation Analysis of the $P^NC_1 - P^_1$ Finite-Element Pair in Shallow-Water Models

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Le Roux, Daniel Y.
Copyright Year	2005
Abstract	Shallow-water models typically employ gridpoint, finite, and spectral-element techniques. For most of these methods the coupling between the momentum and continuity equations is a delicate problem and usually leads to spurious solutions in the representation of inertia-gravity waves. The spurious modes have a wide range of characteristics and may take the form of pressure (surface-elevation), velocity, and/or Coriolis modes. The modes usually cause aliasing and an accumulation of energy in the smallest-resolvable scale, leading to noisy solutions. The triangular finite-element pair $P^{NC}_{1}-P^{}_{1}$ is shown to "properly" model the dispersion of the inertia-gravity waves, and this is achieved at a reasonable computational cost compared to traditional finite-difference schemes. Two tests are proposed. The first test examines the propagation and dispersion of fast surface gravity waves in a circular basin and their reflection at the lateral boundary. In the second test, results of the Stommel problem are presented using the proposed finite-element pair and are compared with those obtained with the C- and CD-finite-difference grids. They illustrate the promise of the proposed approach.
Starting Page	394
Ending Page	414
Page Count	21
File Format	PDF
ISSN	10648275
DOI	10.1137/030602435
e-ISSN	10957197
Issue Number	2
Volume Number	27
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	linear waves Linear waves partial differential equations Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods finite difference method finite elements Finite difference methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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