Fem Wave Model Of Boussinesq Equations With Unstructured Element And Research On The Multidirectional Wave Diffraction By A Cylinder Array

As Boussinesq type equations include some weak nonlinearity and dispersion, which can stimulate phenomenon of nonlinear movement of wave and the evolvement of waves group caused by topographical changes, in recent years, people pay more and more attention to them. Based on various methods, many researchers modified the classical Boussinesq equations to adapt for the need of the simulation of wave movement in actual project. This paper will begin with the introduction of the related researches about Boussinesq type equations.In order to easily handle the solve of the wave propagates in geometrically complex boundaries, the paper adopts unstructured triangle element and constructs a numerical model using finite element method, which can be used to calculate the weaves propagate in near shore, based on the improved Boussinesq equations first developed by Beji and Nadaoka. In the model, the time integration is performed by using the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme. The first spatial derivatives of the water surface elevation at node are determined by the weighted average of the corresponding derivatives in elements surrounding the node. So the third derivatives in the equations are effectively dealt with, which makes the model adopt the linear unit. The programming model employs the index storage method, in which only the non-zero elements of the two-dimensional matrices are stored to save computer storage. At the same time, a locally rotated coordinate system is introduced to improve the treatment for the fully reflective boundaries whose orientation does not coincide with the coordinate system. The numerical results shows that the numerical model based on unstructured triangle gridding is suit to the calculation of wave propagates in irregularly shaped areas and the fine results are obtained.Because of the limitation of the computation domain, the wave reflected from the structure in the domain can be re-reflected at the incident boundary, which may pollute the computation domain and affect the numerical results. To deal with this problem, the method to generate waves in the computation domain and absorb the outgoing waves at the incident boundary is introduced in the present model, which avoids the reflecting waves at the incident boundary. Typical numerical results show that the suitable regular, uni-and multidirectional irregular and multidirectional focusing waves can be effectively generated in the computation domain, which makes the numerical model to simulate the wave and structure interaction possible.The actual waves are multidirectional waves. However, due to the complexity of their spreading, most of the researches associated with wave propagation and their actions on structures are focused on unidirectional waves. Little work mentions the affect caused by the directional distribution of the multidirectional waves on wave propagation and their actions on structures of. In this paper, the multidirectional irregular waves and the multidirectional focusing waves are first simulated with the developed numerical model. The numerical results were compared with the theoretical solutions or experimental results. The agreement between the results can illustrate the validity and applicability of the numerical model.Take advantage of the numerical model developed in this paper, the multidirectional wave diffraction by the cylinder groups are numerically investigated. The numerical results show that the directional spreading of the multidirectional waves has a definite effect on the wave distribution in the cylinder group. The wave height in the cylinder group increases along with the decreasing of the directional concentration parameter s, which means that the wider the directional spreading becomes, the higher the height of waves around the cylinder group is, and the multidirectional wave may give more effect on the cylinder than the unidirectional wave. The results provide referential basis for the practical design of project.Further, the multidirectional focusing wave diffraction around and big size cylinder and cylinder group is numerically simulated. The effects of the wave directional spreading, focusing wave amplitude and the dimension of the cylinder are investigated. The results show that the directional spreading of the multidirectional focusing waves also has big effects on the wave conditions by the cylinder and in the cylinder group. Generally, when the directional spreading concentration parameter s is on the small side, that is the directional distribution is relatively wider, the effects of the directional spreading is on the big side. But when s is bigger than about30-40, the change of the directional spreading has small affect on run up.