Improvements And Applications Of Pre-corrected FFT Method For Wave-structure Interaction

Boundary Element Method (BEM) has become one of the most common numerical methods for wave-structure interaction. Comparing to other numerical methods, such as Finite Element Method (FEM) and Finite Volume Method (FVM), it has one advantage that the problem domain can be reduced to two dimensions which lowers the difficulty in meshing. When using the free-surface Green function, meshing can only be required on body surface, making further improvement in meshing.Nevertheless, the matrix equation is a dense system in BEM. When handling large-scale problems, it requires large memory space and powerful computational capacity that normal computers cannot meet at the moment. A couple of methods have been developed to reduce the computational time and required memory for traditional BEM, based on iterative methods. One of suitable approaches for such purposes is the pre-corrected Fast Fourier Transform (pFFT) method.For the pFFT method, previous research demonstrates the effectiveness in wave-structure interaction that it can dramatically improve computational efficiency and reduce required memory as well with little accuracy loss. However, there are still several weaknesses for the pFFT method, which have been handled in the dissertation. They are summarized as follows:In the first place, for the previous work of the pFFT method is all based on the case of infinite depth, we propose a decomposition method for the free-surface Green function to overcome the difficulty of achievement in the case of finite depth. The numerical results demonstrate the effectiveness of the decomposition method, where accurate results are obtained at all computation frequency. Meanwhile, it has the advantages in reducing computing time and saving computer memory space, as it does in the case of infinite depth.Secondly, we discuss the relationship between grid-based approximations and controlled input parameters by Rankine source, obtaining recommended ranges of these parameters. Then, the previous conclusion about the contribution of the infinite integral to error of approximation, is verified by numerical examples. They show that Rankine source is the majority of error, while the infinite integral contributes little, comparing to Rankine source. Also, the demand for area of precorrection of the image of Rankine source to plain sea bed, can be satisfied meanwhile if the area meets the demand of Rankine source. Thus, the conclusion by Rankine source can be extended to the case of the Green function involved without any change. The later analysis of wave-structure interaction by the pFFT method can be guided with enough accuracy.Finally, for the pre-corrected Fast Fourier Transform method applied in the analysis of wave-structure interaction, a technique is applied to remove the "irregular frequencies" in the integral equation to guaranty the solution is unique and correct, which is derived by arranging more source points on the inner water plane. By combining with an integral equation established for the interior problem of the body, a square matrix can be obtained which makes the equation easier to be solved. The numerical results illustrate that this method can remove the effect of irregular frequencies, and obtain accuracy results at all computation frequency. Comparing to the higher-order boundary element method, it has the advantages in reducing computing time and saving computer memory space.