Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

Steve Bryson; Yekaterina Epshteyn; Alexander Kurganov; Guergana Petrova

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

  • Volume: 45, Issue: 3, page 423-446
  • ISSN: 0764-583X

Abstract

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We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples.

How to cite

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Bryson, Steve, et al. "Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system." ESAIM: Mathematical Modelling and Numerical Analysis 45.3 (2011): 423-446. <http://eudml.org/doc/197429>.

@article{Bryson2011,
abstract = { We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples. },
author = {Bryson, Steve, Epshteyn, Yekaterina, Kurganov, Alexander, Petrova, Guergana},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Hyperbolic systems of conservation and balance laws; semi-discrete central-upwind schemes; Saint-Venant system of shallow water equations; hyperbolic systems of conservation and balance laws; Saint-Venant system of shallow water equations},
language = {eng},
month = {1},
number = {3},
pages = {423-446},
publisher = {EDP Sciences},
title = {Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system},
url = {http://eudml.org/doc/197429},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Bryson, Steve
AU - Epshteyn, Yekaterina
AU - Kurganov, Alexander
AU - Petrova, Guergana
TI - Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2011/1//
PB - EDP Sciences
VL - 45
IS - 3
SP - 423
EP - 446
AB - We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples.
LA - eng
KW - Hyperbolic systems of conservation and balance laws; semi-discrete central-upwind schemes; Saint-Venant system of shallow water equations; hyperbolic systems of conservation and balance laws; Saint-Venant system of shallow water equations
UR - http://eudml.org/doc/197429
ER -

References

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