Boundary Element Simulation of Three-Dimensional Nonlinear Waves in the Time Domain

• Main Authors: Cheng-TsungChen, 陳誠宗
• Other Authors: Jaw-Fang Lee
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/37651227039678986434

博士 === 國立成功大學 === 水利及海洋工程學系碩博士班 === 100 === In this thesis, a boundary element numerical model for the simulation of generating three-dimensional nonlinear waves was developed. The model is an extension of two-dimensional nonlinear model in the time domain developed by Chen (1990) and a seady periodic three-dimensional model developed by Huang (1988). To verify the present numerical model, the problem of wave acting on marine structures is solved. The present results then were compared with the diffraction theory of MacCamy and Fuchs (1954). The comparisons show favorable agreements indicating the accuracy of the present model. Then, the results from the calculation of wave passing submerged circular shoal were compared with experimental results of circular shoal conducted by Williams et al. (1980). It shows considerable consistency. Meanwhile, the wave diffraction passing a submerged rectangular cuboid with the ratio of width to length of the rectangular cuboid being 3:1 was computed. Results demonstrate that wave reflection at the centerline in front of the structure can be duplicated by the two-dimensional results. However, wave diffraction and focusing behind the structure cannot be calculated by the two-dimensional model. Furthermore, based on the numerical model of the two-dimensional nonlinear wave, wherein the free surface boundary was nonlinear and the wave generation boundary was moving with time. A combined initial and boundary value problem was posed to solve the corresponding unsteady flow problems. A boundary element method with constant element was used to model the problems of time varying, moving boundaries, i.e., the free surface and the structural boundaries. The dynamic free surface boundary condition was considered by applying the Galerkin weighted residual method and then incorporated into the boundary element model. In the dynamic analysis, an incremental expression and Hirt and Harlow’s (1967) error correction procedures were used to solve the nonlinear dynamic problem. Then, with the confirmed framework of three-dimensional boundary element method, the dimension of the problem extends to three dimension model. For the deep-water wave example, the central results of the linear-normal wave profile generated by piston-type and flap-type wave-maker in the time domain were compared to those of two-dimensional linear analytical solution and two-dimensional boundary element method. It shows that the wave heights and phases are consistent. But due to the increasing error cumulated by lengthening time, the error of the peak and the trough increased slightly and the phase started to shift. Moreover, the central results of non-linear normal wave profile generated by piston-type wave-maker were compared to those of two dimensional linear analytical solution and two-dimensional non-linear viscous finite difference method. It shows that the trends were consistent, but the wave peak and trough from the present study were smaller than that from two dimension modeling. When computing time increased the wave phases gradually shifted. However, compared to linear-normal wave, the cumulative error of non-linear normal wave was larger and therefore the differences of the peak, the trough and the offset of the phase were greater. Finally, we further simulated the linear directional waves in the time domain. Since the wave decays to both sides of the plane tank, its water level was smaller than that of the linear normal waves in the time-domain. In conclusion, the present boundary element model in simulating three-dimensional linear directional wave can provide reasonable good results.