Repository: Freie Universit├Ąt Berlin, Math Department

A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows

Audusse, E. and Bouchut, F. and Bristeau, M.O. and Klein, R. and Perthame, B. (2004) A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. Journal of Scientific Computation, 25 (6). pp. 2050-2065.



We consider the Saint-Venant 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 so-called well-balanced schemes. We describe a general strategy, based on a local hydrostatic reconstruction, that allows us to derive a well-balanced 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 well-balanced 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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