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Improved Treatment of Source Terms in Upwind Schemes for the Shallow Water Equations in Channels with Irregular Geometry

✍ Scribed by Marı́a Elena Vázquez-Cendón

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
311 KB
Volume
148
Category
Article
ISSN
0021-9991

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✦ Synopsis

This paper deals with the numerical solution of the shallow water equations in channels with irregular geometry but with a locally rectangular cross section. This type of channel leads to the presence of source terms involving the gradient of the depth and the breadth of the channel. Extensions of the Q-scheme of van Leer and Roe are proposed which generate natural upwind discretizations of the source terms. The consistency of the proposed schemes is analyzed. A stationary solution that emphasizes the source terms considered is obtained which is used to test the proposed extensions in terms of a "conservation" property. A low-order asymptotic unsteady analytical solution for a small Froude number is also obtained. The numerical results presented confirm the improved properties of the proposed schemes for a transient test problem.

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