Comparison between TVD-MacCormack and ADI-type solvers of the shallow water equations

Liang, Dongfang, Falconer, Roger Alexander ORCID: https://orcid.org/0000-0001-5960-2864 and Lin, BinLiang ORCID: https://orcid.org/0000-0001-8622-5822 2006. Comparison between TVD-MacCormack and ADI-type solvers of the shallow water equations. Advances in Water Resources 29 (12) , pp. 1833-1845. 10.1016/j.advwatres.2006.01.005

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Abstract

A total variation diminishing (TVD) modification of the MacCormack scheme is developed for simulating shallow water dynamics on a uniform Cartesian grid. Results obtained using conventional and deviatoric forms of the conservative non-linear shallow water equations (SWEs) are compared for cases where the bed has a varying topography. The comparisons demonstrate that the deviatoric form of the SWEs gives more accurate results than the conventional form, in the absence of numerical balancing of the flux-gradient and source terms. A further comparison is undertaken between the TVD-MacCormack model and an alternating direction implicit (ADI) model for cases involving steep-fronted shallow flows. It is demonstrated that the ADI model is unable to predict trans-critical flows correctly, and artificial viscosity has to be introduced to remove spurious oscillations. The TVD-MacCormack model reproduces all flow regimes accurately. Finally, the TVD-MacCormack model is used to predict a laboratory-scale dyke break undertaken at Delft University of Technology. The predictions agree closely with the experimental data, and are in excellent agreement with results from an alternative Godunov-type model

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Uncontrolled Keywords:	Shallow water ; Dam break ; Flood routing ; River modelling ; TVD scheme ; MacCormack scheme ; Shock capturing
ISSN:	0309-1708
Last Modified:	17 Oct 2022 09:05
URI:	https://orca.cardiff.ac.uk/id/eprint/2005

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