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Conservative finite-volume forms of the Saint-Venant equations for hydrology and urban drainage
| Content Provider | Scilit |
|---|---|
| Author | Hodges, Ben R. |
| Copyright Year | 2018 |
| Description | 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. |
| DOI | 10.5194/hess-2018-242 |
| Volume Number | 2018 |
| Language | English |
| Publisher | Copernicus GmbH |
| Publisher Date | 2018-06-25 |
| Access Restriction | Open |
| Subject Keyword | Interdisciplinary Mathematics Finite Volume Venant Equations Conservative Form |
| Content Type | Text |
| Resource Type | Article |
