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• W1975871360 startingPage "7959" @default.
• W1975871360 abstract "For most of the discretization schemes, the numerical approximation of shallow-water models is a delicate problem. Indeed, the coupling between the momentum and the continuity equations usually leads to the appearance of spurious solutions and to anomalous dissipation/dispersion in the representation of the fast (Poincaré) and slow (Rossby) waves. In order to understand these difficulties and to select appropriate spatial discretization schemes, Fourier/dispersion analyses and the study of the null space of the associated discretized problems have proven beneficial. However, the cause of spurious oscillations and reduced convergence rates, that have been detected for most of mixed-order finite element shallow-water formulations, in simulating classical problems of geophysical fluid dynamics, is still an open question. The aim of the present study is to show that when spurious inertial solutions are present, they are mainly responsible for the aforementioned problems. Further, a criterion is found which determines the existence and the number of spurious inertial solutions. As it is delicate to cure spurious inertial modes, a class of possible discretization schemes is proposed, that is not affected by such spurious solutions." @default.
• W1975871360 created "2016-06-24" @default.
• W1975871360 creator A5046810181 @default.
• W1975871360 date "2012-10-01" @default.
• W1975871360 modified "2023-09-26" @default.
• W1975871360 title "Spurious inertial oscillations in shallow-water models" @default.
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• W1975871360 doi "https://doi.org/10.1016/j.jcp.2012.04.052" @default.
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