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HESS | Articles | Volume 23, issue 3
Hydrol. Earth Syst. Sci., 23, 1281-1304, 2019
https://doi.org/10.5194/hess-23-1281-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
Hydrol. Earth Syst. Sci., 23, 1281-1304, 2019
https://doi.org/10.5194/hess-23-1281-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 07 Mar 2019

Research article | 07 Mar 2019

Conservative finite-volume forms of the Saint-Venant equations for hydrology and urban drainage

Ben R. Hodges
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Cited articles  
Abbott, M. B. and Ionescu, F.: On The Numerical Computation Of Nearly Horizontal Flows, J. Hydraul. Res., 5, 97–117, https://doi.org/10.1080/00221686709500195, 1967. a
Aricò, C. and Tucciarelli, T.: A marching in space and time (MAST) solver of the shallow water equations. Part I: The 1D model, Adv. Water Resour., 30, 1236–1252, https://doi.org/10.1016/j.advwatres.2006.11.003, 2007. a
Audusse, E., Bouchut, F., Bristeau, M.-O., Klein, R., and Perthame, B.: A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows, SIAM J. Scient. Comput., 25, 2050–2065, https://doi.org/10.1137/S1064827503431090, 2004. a, b
Audusse, E., Bouchut, F., Bristeau, M.-O., and Sainte-Marie, J.: Kinetic Entropy Inequality and Hydrostatic Reconstruction Scheme for the Saint-Venant System, Math. Comput., 85, 2815–2837, https://doi.org/10.1090/mcom/3099, 2016. a
Blanckaert, K. and Graf, W.: Momentum transport in sharp open-channel bends, J. Hydraul. Eng.-ASCE, 130, 186–198, https://doi.org/10.1061/(ASCE)0733-9429(2004)130:3(186), 2004. a
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A new derivation of the equations for one-dimensional open-channel flow in rivers and storm drainage systems has been developed. The new approach solves some long-standing problems for obtaining well-behaved solutions with conservation forms of the equations. This research was motivated by the need for highly accurate models of large-scale river networks and the storm drainage systems in megacities. Such models are difficult to create with existing equation forms.
A new derivation of the equations for one-dimensional open-channel flow in rivers and storm...
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