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ADER schemes for the shallow water equations in channel with irregular bottom elevation

✍ Scribed by G. Vignoli; V.A. Titarev; E.F. Toro

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
460 KB
Volume
227
Category
Article
ISSN
0021-9991

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✦ Synopsis

This paper deals with the construction of high-order ADER numerical schemes for solving the one-dimensional shallow water equations with variable bed elevation. The non-linear version of the schemes is based on ENO reconstructions. The governing equations are expressed in terms of total water height, instead of total water depth, and discharge. The ENO polynomial interpolation procedure is also applied to represent the variable bottom elevation. ADER schemes of up to fifth order of accuracy in space and time for the advection and source terms are implemented and systematically assessed, with particular attention to their convergence rates. Non-oscillatory results are obtained for discontinuous solutions both for the steady and unsteady cases. The resulting schemes can be applied to solve realistic problems characterized by nonuniform bottom geometries.

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