A Subsonic well-balanced reconstruction scheme for shallow water flows. Bouchut, F. & Morales de Luna, T. 48(5):1733. ![A Subsonic well-balanced reconstruction scheme for shallow water flows [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper abstract bibtex We consider the Saint-Venant system for shallow water flows with non-flat bottom. In the past years, efficient well-balanced methods have been proposed in order to well resolve solutions close to steady states at rest. Here we describe a strategy based on a local subsonic steady-state reconstruction that allows to derive a subsonic-well-balanced scheme, preserving exactly all the subsonic steady states. It generalizes the now wellknown hydrostatic solver, and as the latter it preserves nonnegativity of water height and satisfies a semi-discrete entropy inequality. An application to the Euler-Poisson system is proposed.
@article{bouchut_subsonic_2010,
title = {A Subsonic well-balanced reconstruction scheme for shallow water flows},
volume = {48},
url = {http://dx.doi.org/10.1137/090758416},
abstract = {We consider the Saint-Venant system for shallow water flows with non-flat bottom. In the past years, efficient well-balanced methods have been proposed in order to well resolve solutions close to steady states at rest. Here we describe a strategy based on a local subsonic steady-state reconstruction that allows to derive a subsonic-well-balanced scheme, preserving exactly all the subsonic steady states. It generalizes the now wellknown hydrostatic solver, and as the latter it preserves nonnegativity of water height and satisfies a semi-discrete entropy inequality. An application to the Euler-Poisson system is proposed.},
pages = {1733},
number = {5},
journaltitle = {{SIAM} Journal on Numerical Analysis},
author = {Bouchut, François and Morales de Luna, Tomás},
date = {2010},
keywords = {semi-discrete entropy inequality, shallow water, subsonic reconstruction, subsonic steady states, well-balanced scheme},
}
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