A central scheme for shallow water flows along channels with irregular geometry

Jorge Balbás; Smadar Karni

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2009)

  • Volume: 43, Issue: 2, page 333-351
  • ISSN: 0764-583X

Abstract

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We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (i.e., it is well-balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness of the numerical algorithm.

How to cite

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Balbás, Jorge, and Karni, Smadar. "A central scheme for shallow water flows along channels with irregular geometry." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 43.2 (2009): 333-351. <http://eudml.org/doc/246108>.

@article{Balbás2009,
abstract = {We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (i.e., it is well-balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness of the numerical algorithm.},
author = {Balbás, Jorge, Karni, Smadar},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {hyperbolic systems of conservation and balance laws; semi-discrete schemes; Saint-Venant system of shallow water equations; non-oscillatory reconstructions; channels with irregular geometry; Saint-Venant equations},
language = {eng},
number = {2},
pages = {333-351},
publisher = {EDP-Sciences},
title = {A central scheme for shallow water flows along channels with irregular geometry},
url = {http://eudml.org/doc/246108},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Balbás, Jorge
AU - Karni, Smadar
TI - A central scheme for shallow water flows along channels with irregular geometry
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2009
PB - EDP-Sciences
VL - 43
IS - 2
SP - 333
EP - 351
AB - We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (i.e., it is well-balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness of the numerical algorithm.
LA - eng
KW - hyperbolic systems of conservation and balance laws; semi-discrete schemes; Saint-Venant system of shallow water equations; non-oscillatory reconstructions; channels with irregular geometry; Saint-Venant equations
UR - http://eudml.org/doc/246108
ER -

References

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