A FEM model with unstructured triangular elements based on the modified Boussinesq equations is developed in this paper. A local coordinate system at the reflecting boundary is introduced to improve the treatment of the oblique waves on the reflecting boundaries. The Adams-Bashforth-Moulton predictor-corrector scheme is used for time integration. The numerical model was used for the simulation for the multidirectional wave propagation through a pile group. The effects of the wave directionality on the wave run-up in the group are numerically investigated.


Boussinesq type equations which include also time dependence, weak nonlinearity and dispersion provide a means for studying wave propagation over a slowly varying bathymetry. The first such set of equations for variable water depth was derived by Peregrine(1967), which are referred to as the standard Boussinesq equations. To extend the standard equations to be adapted for deeper water, many modified forms of Boussinesq type equations are given, such as Madsen et al. (1992), Nwogu (1993), Beji and Nadaoka (1996) and so on. To simulate the wave transformation numerically, many numerical models had been established. But most of the models based on the modified forms of Boussinesq type equations are solved by the finite difference method which is easy to use, but is not versatile enough to deal with irregular boundaries. Based on Beji and Nadaoka's equations, we develop a FEM model with unstructured triangular elements. The internal wave maker embedded in an unstructured mesh is used so wave energy which is reflected from the structure would pass through the wave generation line without any numerical distortion. Typical cases are employed to validate the developed numerical model. Some calculated results show that the model is capable of giving satisfactory predictions and accuracy because of the improved treatment of the oblique boundaries.

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