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Raviart–Thomas and Brezzi–Douglas–Marini finite‐element approximations of the shallow‐water equations
Author(s) -
Rostand V.,
Le Roux D. Y.
Publication year - 2007
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.1668
Subject(s) - discretization , shallow water equations , spurious relationship , polygon mesh , finite element method , mathematics , multigrid method , geostrophic wind , equilateral triangle , mathematical analysis , inertia , geometry , calculus (dental) , classical mechanics , mechanics , physics , partial differential equation , medicine , statistics , dentistry , thermodynamics
An analysis of the discrete shallow‐water equations using the Raviart–Thomas and Brezzi–Douglas–Marini finite elements is presented. For inertia–gravity waves, the discrete formulations are obtained and the dispersion relations are computed in order to quantify the dispersive nature of the schemes on two meshes made up of equilateral and biased triangles. A linear algebra approach is also used to ascertain the possible presence of spurious modes arising from the discretization. The geostrophic balance is examined and the smallest representable vortices are characterized on both structured and unstructured meshes. Numerical solutions of two test problems to simulate gravity and Rossby modes are in good agreement with the analytical results. Copyright © 2007 John Wiley & Sons, Ltd.