Audusse, E. and Bouchut, F. and Bristeau, M.O. and Klein, R. and Perthame, B. (2004) A fast and stable wellbalanced scheme with hydrostatic reconstruction for shallow water flows. Journal of Scientific Computation, 25 (6). pp. 20502065.

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Abstract
We consider the SaintVenant system for shallow water flows, with nonflat bottom. It is a hyperbolic system of conservation laws that approximately describes various geophysical flows, such as rivers, coastal areas, and oceans when completed with a Coriolis term, or granular flows when completed with friction. Numerical approximate solutions to this system may be generated using conservative finite volume methods, which are known to properly handle shocks and contact discontinuities. However, in general these schemes are known to be quite inaccurate for near steady states, as the structure of their numerical truncation errors is generally not compatible with exact physical steady state conditions. This difficulty can be overcome by using the socalled wellbalanced schemes. We describe a general strategy, based on a local hydrostatic reconstruction, that allows us to derive a wellbalanced scheme from any given numerical flux for the homogeneous problem. Whenever the initial solver satisfies some classical stability properties, it yields a simple and fast wellbalanced scheme that preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group 
ID Code:  478 
Deposited By:  Ulrike Eickers 
Deposited On:  25 Jun 2009 12:42 
Last Modified:  03 Mar 2017 14:40 
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