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Discussion papers | Copyright
https://doi.org/10.5194/hess-2018-242
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 25 Jun 2018

Research article | 25 Jun 2018

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Hydrology and Earth System Sciences (HESS).

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

Ben R. Hodges Ben R. Hodges
  • National Center for Infrastructure Modeling and Management, University of Texas at Austin

Abstract. New finite-volume forms of the Saint-Venant equations for one-dimensional (1D) open-channel flow are derived. The new equations are in the flux-gradient conservation form and serve to transfer portions of both the hydrostatic pressure force and the gravitational force from the source term to the conservative flux term. The derivation introduces an analytical approximation of the free surface across a finite volume element (e.g. linear, parabolic) as well as an analytical approximation of the bottom topography. Integration of the product of these provides an approximation of a piezometric pressure gradient term that can be split between the source and the conservative flux terms without introducing new variables within the discretization. The resulting finite-volume equations are written entirely in terms of flow rates, cross-sectional areas, water surface elevations, and the channel bottom elevation (but without using any volume-averaged bottom slope). The new conservative form should be more tractable for large-scale simulations of river networks and urban drainage systems than the traditional conservative form of the Saint-Venant equations where it is difficult to maintain a well-balanced discretization for highly-variable topography.

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Ben R. Hodges
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Latest update: 19 Jul 2018
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Short summary
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 of 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 mega-cities. 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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