Résumé
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 (C) 2008 John Wiley & Sons, Ltd.