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AMM

Seminar

Discrete analyses and numerical simulation of the shallow-water system

Le Roux, D (Université Claude Bernard Lyon 1)
Thursday 15 November 2012, 10:00-11:00

Seminar Room 1, Newton Institute

Abstract

The shallow-water system, obtained from the Navier-Stokes equations by vertical averaging, is extensively used in environmental studies (ocean, atmosphere, rivers) to simulate the propagation of inertia-gravity and Rossby waves. For most of the discretization schemes, the numerical approximation of shallow-water models is a delicate problem leading to the appearance of spurious (non physical) solutions in the representation of the fast (inertia-gravity) 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. The aim of this talk is to present such results and to propose a class of possible discretization schemes that is not affected by the spurious modes. Both discrete analyses and numerical simulations involving the eddy propagation in an oceanic context will be presented.

Presentation

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