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]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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