A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows

A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows. Bouchut, F. & Morales de Luna, T. SIAM Journal on Numerical Analysis, 48(5):1733–1758, 2010.

Paper doi 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{bouchut2010subsonic,
  Title                    = {A {Subsonic-Well-Balanced} Reconstruction Scheme for Shallow Water Flows},
  Author                   = {Bouchut, Francois and Morales de Luna, Tomas},
  Journal                  = {{SIAM} Journal on Numerical Analysis},
  Year                     = {2010},
  Number                   = {5},
  Pages                    = {1733--1758},
  Volume                   = {48},

  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.},
  Category                 = {MATHEMATICS, APPLIED},
  Comment                  = {�ndice de impacto: 1.664, Num. revistas en cat.: 236, Revista dentro del 25%: S�, Categor�a: MATHEMATICS, APPLIED, Fuente de impacto: WOS (JCR), Posici�n: 24},
  Doi                      = {10.1137/090758416},
  File                     = {:bouchut2010subsonic-well-balanced.pdf:PDF},
  Impactfactor             = {1.664},
  ISSN                     = {00361429},
  Keywords                 = {shallow water, subsonic reconstruction, subsonic steady states, well-balanced scheme, semi-discrete entropy inequality},
  Position                 = {24},
  Revincat                 = {236},
  Url                      = {http://link.aip.org/link/SJNAAM/v48/i5/p1733/s1&Agg=doi}
}

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