A positivity preserving central scheme for shallow water flows in channels with wet-dry states

Jorge Balbás; Gerardo Hernandez-Duenas

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 3, page 665-696
  • ISSN: 0764-583X

Abstract

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We present a high-resolution, non-oscillatory semi-discrete central scheme for one-dimensional shallow-water flows along channels with non uniform cross sections of arbitrary shape and bottom topography. The proposed scheme extends existing central semi-discrete schemes for hyperbolic conservation laws and enjoys two properties crucial for the accurate simulation of shallow-water flows: it preserves the positivity of the water height, and it is well balanced, i.e., the source terms arising from the geometry of the channel are discretized so as to balance the non-linear hyperbolic flux gradients. In addition to these, a modification in the numerical flux and the estimate of the speed of propagation, the scheme incorporates the ability to detect and resolve partially wet regions, i.e., wet-dry states. Along with a detailed description of the scheme and proofs of its properties, we present several numerical experiments that demonstrate the robustness of the numerical algorithm.

How to cite

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Balbás, Jorge, and Hernandez-Duenas, Gerardo. "A positivity preserving central scheme for shallow water flows in channels with wet-dry states." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.3 (2014): 665-696. <http://eudml.org/doc/273337>.

@article{Balbás2014,
abstract = {We present a high-resolution, non-oscillatory semi-discrete central scheme for one-dimensional shallow-water flows along channels with non uniform cross sections of arbitrary shape and bottom topography. The proposed scheme extends existing central semi-discrete schemes for hyperbolic conservation laws and enjoys two properties crucial for the accurate simulation of shallow-water flows: it preserves the positivity of the water height, and it is well balanced, i.e., the source terms arising from the geometry of the channel are discretized so as to balance the non-linear hyperbolic flux gradients. In addition to these, a modification in the numerical flux and the estimate of the speed of propagation, the scheme incorporates the ability to detect and resolve partially wet regions, i.e., wet-dry states. Along with a detailed description of the scheme and proofs of its properties, we present several numerical experiments that demonstrate the robustness of the numerical algorithm.},
author = {Balbás, Jorge, Hernandez-Duenas, Gerardo},
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},
language = {eng},
number = {3},
pages = {665-696},
publisher = {EDP-Sciences},
title = {A positivity preserving central scheme for shallow water flows in channels with wet-dry states},
url = {http://eudml.org/doc/273337},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Balbás, Jorge
AU - Hernandez-Duenas, Gerardo
TI - A positivity preserving central scheme for shallow water flows in channels with wet-dry states
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 3
SP - 665
EP - 696
AB - We present a high-resolution, non-oscillatory semi-discrete central scheme for one-dimensional shallow-water flows along channels with non uniform cross sections of arbitrary shape and bottom topography. The proposed scheme extends existing central semi-discrete schemes for hyperbolic conservation laws and enjoys two properties crucial for the accurate simulation of shallow-water flows: it preserves the positivity of the water height, and it is well balanced, i.e., the source terms arising from the geometry of the channel are discretized so as to balance the non-linear hyperbolic flux gradients. In addition to these, a modification in the numerical flux and the estimate of the speed of propagation, the scheme incorporates the ability to detect and resolve partially wet regions, i.e., wet-dry states. Along with a detailed description of the scheme and proofs of its properties, we present several numerical experiments that demonstrate the 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
UR - http://eudml.org/doc/273337
ER -

References

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