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We present an integrated three-dimensional (3D) spillway model where the realistic and complicated river terrain is implemented by the platform CATIA (Computer Aided Three Dimensional Interactive Application). This integrated 3D spillway model allows for complicated topographic and geomorphic conditions and describes the spatial distribution of the spillway dam (upstream reservoir, downstream river channel and the spillway dam itself) precisely, thus making it a real alternative to the physical model. Furthermore, this model provides the premise and possibility of a full-scale simulation of the spillway flow, that is, it can not only be used to study the hydraulics on the spillway face, but also can be used to study the hydraulics along the downstream river channel and estimate the scour problem associated with both the spillway flow and downstream river channel. In this model, turbulence was simulated using RNG k−ɛ equations. The flow velocity and surface pressure from the numerical model were verified by the data from experiments. Moreover, the river flow was studied and flow velocities downstream were obtained. The scour formed downstream of a ski-jump was also studied in this study on the location and shape of a scour hole. In all, this study provides new approaches for solving relevant hydraulic engineering problems.

The hybrid radial boundary node method is applied to solve the biharmonic problems. Based on modified variational principle, the variational formula of the biharmonic problems is established. The radial basis point interpolation is employed to approximate the boundary variables, while the domain variables are interpolated by a combination of the fundamental solution of the laplace equation and the biharmonic equation. Compared to the regular hybrid boundary node method, as the shape function has the delta function property, the boundary conditions of the original problem can be easily implemented, and the fictitious source points are not involved. Numerical examples show that this method is efficient for solving the biharmonic equation.