Numerical results are presented and compared for four conservative upwind difference schemes for the shallow water equations when applied to a standard test problem This includes consideration of the effect of treating part of the flux balance as a source, and a comparison of square-root and arithme
Conservative upwind difference schemes for the shallow water equations
β Scribed by P. Glaister
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 466 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0898-1221
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β¦ Synopsis
A study of a number of current numerical schemes for the shallow water equations leads to the establishment of relationships between these schemes. Further analysis then suggests new formulations of the schemes, as well as an alternative scheme having the same key properties.
π SIMILAR VOLUMES
A multidimensional discretisation of the shallow water equations governing unsteady free-surface flow is proposed. The method, based on a residual distribution discretisation, relies on a characteristic eigenvector decomposition of each cell residual, and the use of appropriate distribution schemes.
Numerical results are presented and compared for three conservative upwind difference schemes for the Euler equations when applied to two standard test problems. This includes consideration of the effect of treating part of the flux balance as a source, and a comparison of different averaging of the
The classical nonlinear shallow-water model (SWM) of an ideal fluid is considered. For the model, a new method for the construction of mass and total energy conserving finite difference schemes is suggested. In fact, it produces an infinite family of finite difference schemes, which are either linea
In recent years upwind differencing has gained acceptance as a robust and accurate technique for the numerical approximation of the one-dimensional shallow water equations. In two dimensions the benefits have been less marked due to the reliance of the methods on standard operator splitting techniqu