A second-order semi-implicit hybrid scheme for one-dimensional Boussinesq-type waves in rectangular channels
✍ Scribed by Sandra Soares-Frazão; Vincent Guinot
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 313 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0271-2091
- DOI
- 10.1002/fld.1679
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✦ Synopsis
Abstract
A numerical procedure is proposed for the solution of the Boussinesq equations in rectangular channels over a horizontal bed. The Boussinesq equations account for non‐hydrostatic effects in free‐surface flows. The proposed approach is a predictor–corrector procedure where the hyperbolic part of the equations is treated using a higher‐order estimate of the variable slope of the Godunov‐type, MUSCL scheme. The proposed slope estimate is third‐order accurate on irregular grids and fourth‐order accurate on regular grids. The dispersive, non‐hydrostatic terms are treated using a semi‐implicit discretization. A stability analysis of the proposed predictor–corrector procedure shows that optimal accuracy is achieved when the implicitation parameter is set equal to 0.5. This analysis is confirmed by numerical experiments, whereby the propagation of a solitary wave and the development of an undular bore are reproduced and compared successfully with the available analytical solutions. The proposed method is shown to be of a good level of accuracy without being too sensitive to the numerical parameters. Its applicability in practical problems is illustrated by a comparison with laboratory experiments. Copyright © 2008 John Wiley & Sons, Ltd.