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Fourier analysis of a class of upwind schemes in shallow water systems for gravity and Rossby waves
Author(s) -
Mohammadian A. M.,
Le Roux D. Y.
Publication year - 2008
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.1617
Subject(s) - upwind scheme , rossby wave , shallow water equations , limiter , dispersion (optics) , physics , fourier transform , mechanics , fourier analysis , finite volume method , mathematics , mathematical analysis , meteorology , engineering , atmospheric sciences , optics , telecommunications , discretization
A Fourier analysis has been performed for a class of upwind finite volume schemes, including the study of phase speed, group velocity, damping and dispersion. In the first part, pure gravity waves are investigated. As expected, most upwind schemes lead to a significant damping, but they exhibit a better phase behavior than most centered schemes. In the second part, the Coriolis parameter is considered and the Rossby modes are studied. In this case, all selected upwind schemes lead to a severe damping. The numerical results are also compared with those obtained by using a slope limiter approach. It is concluded that most upwind schemes with or without slope limiters present poor results for an accurate calculation of the Rossby modes. Copyright © 2008 John Wiley & Sons, Ltd.