Finite Volume Model for Shallow Water Equations with Improved Treatment of Source Terms
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VIEW THE REPLYPublication: Journal of Hydraulic Engineering
Volume 134, Issue 2
Abstract
A simple yet precise relation between the flux gradient and the bed slope source term is presented, which produces a net force within the cell with an inclined water surface, but ensures still water condition when there is no flow across the boundaries. The proposed method consists of calculating the pressure term based on the water depths at the cell vertices, which may be computed by a higher order scheme and the bed slope source term by a centered discretization technique. The methodology is demonstrated with a Godunov-type upwind finite volume formulation. The inviscid fluxes are calculated using Roe’s approximate Riemann solver and a second-order spatial accuracy is obtained by implementing multidimensional gradient reconstruction and slope limiting techniques. The accuracy and applicability of the numerical model is verified with a couple of test problems and a real flow example of tidal water movement in a stretch of River Hooghly in India.
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Acknowledgments
The writers wish to express their sincere appreciation to Jonathan Richard Shewchuk for allowing the use of the mesh generator program triangle.c, which is freely available for downloading at http://www-2.cs.cmu.edu/∼quake/triangle.html. The Kolkata Port Trust (KoPT), India is greatly acknowledged for providing necessary field data for the River Hooghly case study. The many helpful suggestions provided by the anonymous reviewers are also thankfully acknowledged.
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Published In
Journal of Hydraulic Engineering
Volume 134 • Issue 2 • February 2008
Pages: 231 - 242
Copyright
© 2008 ASCE.
History
Received: Aug 21, 2006
Accepted: Apr 16, 2007
Published online: Feb 1, 2008
Published in print: Feb 2008
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