SUMMARYA hybrid scheme composed of ÿnite-volume and ÿnite-di erence methods is introduced for the solution of the Boussinesq equations. While the ÿnite-volume method with a Riemann solver is applied to the conservative part of the equations, the higher-order Boussinesq terms are discretized using the ÿnite-di erence scheme. Fourth-order accuracy in space for the ÿnite-volume solution is achieved using the MUSCL-TVD scheme. Within this, four limiters have been tested, of which van-Leer limiter is found to be the most suitable. The Adams-Basforth third-order predictor and Adams-Moulton fourth-order corrector methods are used to obtain fourth-order accuracy in time. A recently introduced surface gradient technique is employed for the treatment of the bottom slope. A new model 'HYWAVE', based on this hybrid solution, has been applied to a number of wave propagation examples, most of which are taken from previous studies. Examples include sinusoidal waves and bi-chromatic wave propagation in deep water, sinusoidal wave propagation in shallow water and sinusoidal wave propagation from deep to shallow water demonstrating the linear shoaling properties of the model. Finally, sinusoidal wave propagation over a bar is simulated. The results are in good agreement with the theoretical expectations and published experimental results.

SUMMARYNumerical methods have become well established as tools for solving problems in hydraulic engineering. In recent years the ÿnite volume method (FVM) with shock capturing capabilities has come to the fore because of its suitability for modelling a variety of types of ow; subcritical and supercritical; steady and unsteady; continuous and discontinuous and its ability to handle complex topography easily.This paper is an assessment and comparison of the performance of ÿnite volume solutions to the shallow water equations with the Riemann solvers; the Osher, HLL, HLLC, ux di erence splitting (Roe) and ux vector splitting. In this paper implementation of the FVM including the Riemann solvers, slope limiters and methods used for achieving second order accuracy are described explicitly step by step. The performance of the numerical methods has been investigated by applying them to a number of examples from the literature, providing both comparison of the schemes with each other and with published results. The assessment of each method is based on ÿve criteria; ease of implementation, accuracy, applicability, numerical stability and simulation time. Finally, results, discussion, conclusions and recommendations for further work are presented.

The effects of the resistance caused by vegetation on flow velocity and water depth has become a major interest for ecologists and those who deal with river restoration projects. Some numerical and experimental works have been performed to analyse and formulate the drag effects induced by vegetation. Here we introduce a quasi-three-dimensional (Q3D) numerical solution, which is constructed by coupling the finite volume solution of the two-dimensional shallow water equations with a finite difference solution of Navier–Stokes equations for vertical velocity distribution. The drag forces are included in both sets of equations. Turbulence shear stresses are computed in two alternative ways: the parabolic eddy viscosity approach with a correction term introduced in this study, and a combination of the eddy viscosity and mixing length theories in the vertical direction. In order to deal with flexible vegetation, a cantilever beam theory is used to compute the deflection of the vegetation. The model COMSIM (complex flow simulations) has been developed and applied in experimental cases. The results are shown to be satisfactory.

SUMMARYThis paper describes development of an integrated shallow surface and saturated groundwater model (GSHAW5). The surface ow motion is described by the 2-D shallow water equations and groundwater movement is described by the 2-D groundwater equations. The numerical solution of these equations is based on the ÿnite volume method where the surface water uxes are estimated using the Roe shock-capturing scheme, and the groundwater uxes are computed by application of Darcy's law. Use of a shock-capturing scheme ensures ability to simulate steady and unsteady, continuous and discontinuous, subcritical and supercritical surface water ow conditions. Ground and surface water interaction is achieved by the introduction of source-sink terms into the continuity equations. Two solutions are tightly coupled in a single code. The numerical solutions and coupling algorithms are explained. The model has been applied to 1-D and 2-D test scenarios. The results have shown that the model can produce very accurate results and can be used for simulation of situations involving interaction between shallow surface and saturated groundwater ows.

Most of the methods developed for the prediction of bridge afflux are generally based on either energy or momentum equations. Recent studies have shown that the energy method, which is one of the four bridge subroutines within the commonly used program HEC-RAS for computing water surface profiles along rivers, produced more accurate results than three other methods (momentum, WSPRO and Yarnell's methods) when applied to bridge afflux data obtained from experiments conducted in a two-stage channel. This work developed three artificial intelligence models (the radial basis neural network, the multi-layer perceptron and the adaptive neurofuzzy inference system) as alternatives to the energy method. Multiple linear and multiple non-linear regression models were also used in the analysis. The results showed that the performance of the adaptive neuro fuzzy inference system in predicting bridge afflux was superior to the other models.