Comparison between TVD-MacCormack and ADI-type solvers of the shallow water equations
- 作者：Dongfang Liang ; Roger A. Falconer and Binliang Lin
- 关键词：Shallow water ; Dam break ; Flood routing ; River modelling ; TVD scheme ; MacCormack scheme ; Shock capturing
- 刊名：Advances in Water Resources
- 出版年：2006
- 期刊代码：4_03091708
- 类别：env
- 出版时间：December 2006
- 卷：29
- 期：12
- 页码：1833-1845
- 文件大小：1242 K
摘要
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.