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Transport of Pollutant in Shallow WaterA Two Time Steps Kinetic Method

Published online by Cambridge University Press:  15 November 2003

Emmanuel Audusse  and
Marie-Odile Bristeau
Emmanuel Audusse
Affiliation:
Projet M3N, INRIA, Domaine de Voluceau, 78153 Le Chesnay, France. Emmanuel.Audusse@inria.fr., Marie-Odile.Bristeau@inria.fr.
Marie-Odile Bristeau
Affiliation:
Projet M3N, INRIA, Domaine de Voluceau, 78153 Le Chesnay, France. Emmanuel.Audusse@inria.fr., Marie-Odile.Bristeau@inria.fr.
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Abstract

The aim of this paper is to present a finite volume kinetic method to compute the transport of a passive pollutant by a flow modeled by the shallow water equations using a new time discretization that allows large time steps for the pollutant computation. For the hydrodynamic part the kinetic solver ensures – even in the case of a non flat bottom – the preservation of the steady state of a lake at rest, the non-negativity of the water height and the existence of an entropy inequality. On an other hand the transport computation ensures the conservation of pollutant mass, a non-negativity property and a maximum principle for the concentration of pollutant and the preservation of discrete steady states associated with the lake at rest equilibrium. The interest of the developed method is to preserve these theoretical properties with a scheme that allows to disconnect the hydrodynamic time step – related to a classical CFL condition – and the transport one – related to a new CFL condition – and further the hydrodynamic calculation and the transport one. The CPU time is very reduced and we can easily solve different transport problems with the same hydrodynamic solution without large storage. Moreover the numerical results exhibit a better accuracy than with a classical method especially when using 1D or 2D regular grids.

Keywords

Shallow water equationsSaint-Venant systemfinite volume methodkinetic schemetransport of pollutanttime discretization.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 2 , March 2003 , pp. 389 - 416
Copyright
© EDP Sciences, SMAI, 2003

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