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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.
@article{M2AN_2014__48_3_665_0,
author = {Balb\'as, Jorge and Hernandez-Duenas, Gerardo},
title = {A positivity preserving central scheme for shallow water flows in channels with wet-dry states},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {665--696},
publisher = {EDP-Sciences},
volume = {48},
number = {3},
year = {2014},
doi = {10.1051/m2an/2013106},
mrnumber = {3177861},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013106/}
}
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 PY - 2014 SP - 665 EP - 696 VL - 48 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013106/ DO - 10.1051/m2an/2013106 LA - en ID - M2AN_2014__48_3_665_0 ER -
%0 Journal Article %A Balbás, Jorge %A Hernandez-Duenas, Gerardo %T A positivity preserving central scheme for shallow water flows in channels with wet-dry states %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 665-696 %V 48 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013106/ %R 10.1051/m2an/2013106 %G en %F M2AN_2014__48_3_665_0
Balbás, Jorge; Hernandez-Duenas, Gerardo. A positivity preserving central scheme for shallow water flows in channels with wet-dry states. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 3, pp. 665-696. doi: 10.1051/m2an/2013106
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