@Article{bouchut2010subsonic,
  author   = {Bouchut, Fran{\c{c}}ois and Morales de Luna, Tom{\'a}s},
  title    = {{A} {S}ubsonic well-balanced reconstruction scheme for shallow water flows},
  journal  = {SIAM Journal on Numerical Analysis},
  year     = {2010},
  volume   = {48},
  number   = {5},
  pages    = {1733},
  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.},
  keywords = {shallow water, subsonic reconstruction, subsonic steady states, well-balanced scheme, semi-discrete entropy inequality},
  url      = {http://dx.doi.org/10.1137/090758416},
}

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