We present a new high-resolution, non-oscillatory semi-discrete central-upwind scheme for one-dimensional two-layer shallow-water flows with friction and entrainment along channels with arbitrary cross sections and bottom topography. These flows are described by a conditionally hyperbolic balance law with non-conservative products. A detailed description of the properties of the model is provided, including entropy inequalities and asymptotic approximations of the eigenvalues of the corresponding coefficient matrix. The scheme extends existing central-upwind semi-discrete numerical methods for hyperbolic conservation and balance laws and it satisfies two properties crucial for the accurate simulation of shallow-water flows: it preserves the positivity of the water depth for each layer, 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. Along with the description of the scheme and proofs of these two properties, we present several numerical experiments that demonstrate the robustness of the numerical algorithm.
Keywords: Hyperbolic systems of conservation and balance laws, semi-discrete schemes, Saint-Venant system of shallow-water equations with friction, non-oscillatory reconstructions, channels with irregular geometry
@article{M2AN_2021__55_5_2185_0,
author = {Hernandez-Duenas, Gerardo and Balb\'as, Jorge},
title = {A central-upwind scheme for two-layer shallow-water flows with friction and entrainment along channels},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2185--2210},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {5},
doi = {10.1051/m2an/2021052},
mrnumber = {4323402},
zbl = {1485.76057},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021052/}
}
TY - JOUR AU - Hernandez-Duenas, Gerardo AU - Balbás, Jorge TI - A central-upwind scheme for two-layer shallow-water flows with friction and entrainment along channels JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 2185 EP - 2210 VL - 55 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021052/ DO - 10.1051/m2an/2021052 LA - en ID - M2AN_2021__55_5_2185_0 ER -
%0 Journal Article %A Hernandez-Duenas, Gerardo %A Balbás, Jorge %T A central-upwind scheme for two-layer shallow-water flows with friction and entrainment along channels %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 2185-2210 %V 55 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021052/ %R 10.1051/m2an/2021052 %G en %F M2AN_2021__55_5_2185_0
Hernandez-Duenas, Gerardo; Balbás, Jorge. A central-upwind scheme for two-layer shallow-water flows with friction and entrainment along channels. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 5, pp. 2185-2210. doi: 10.1051/m2an/2021052
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