Audusse, E. and Klein, R. and Nguyen, D.D. and Vater, S. (2011) Preservation of the discrete geostrophic equilibrium in shallow water flows. In: Finite Volumes for Complex Applications VI  Problems& Perspectives, 6.6.10.6. 2011, Prague, Czech Republic.

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Official URL: http://dx.doi.org/10.1007/9783642206719_7
Abstract
We are interested in the numerical simulation of large scale phenomena in geophysical flows. In these cases, Coriolis forces play an important role and the circulations are often perturbations of the socalled geostrophic equilibrium. Hence, it is essential to design a numerical strategy that preserves a discrete version of this equilibrium. In this article we work on the shallow water equations in a finite volume framework and we propose a first step in this direction by introducing an auxiliary pressure that is in geostrophic equilibrium with the velocity field and that is computed thanks to the solution of an elliptic problem. Then the complete solution is obtained by working on the deviating part of the pressure. Some numerical examples illustrate the improvement through comparisons with classical discretizations.the deviating part of the pressure. Some numerical examples illustrate the improvement when compare with classical finite volume methods.
Item Type:  Conference or Workshop Item (Paper) 

Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group 
ID Code:  1034 
Deposited By:  Ulrike Eickers 
Deposited On:  09 Feb 2011 16:03 
Last Modified:  03 Mar 2017 14:41 
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