预修正快速傅里叶变换方法在多浮体结构水动力问题中的应用研究

发布时间：2019-03-09 20:49

【摘要】：边界元方法具有高精度和降维等优点,被广泛应用于波浪与结构物相互作用的水动力问题的研究中。但在离散边界积分方程所形成的线性方程组中,系数矩阵为大型非对称的稠密矩阵,方程组的求解耗费大量计算机资源,严重限制了该方法所能处理的问题的规模。探索可用于大型复杂多浮体结构水动力分析的预修正快速傅里叶变换(precorrected Fast Fourier Transform,简称pFFT)边界元方法是本研究的主要目标。预修正快速傅里叶变换(pFFT)方法可以处理任意形式格林函数问题,该方法将面元之间的相互影响分为近场和远场两部分,远场积分的计算采用将面元投影到位于均匀网格的等效奇点来近似计算,近场积分则采用直接积分方法进行计算。事实上,所有的点状奇点都位于均匀网格上。该特性使得由点状奇点所产生的速度势可以通过快速傅里叶变换方法快速求得。结合基于广义最小残量法(GMRES)的迭代方法求解线性方程组,pFFT方法可以将边界元方法的计算复杂度由O(N3)降低至O(N log N),其中N为边界控制点个数。经过科学严谨的算例验证,本研究发展的pFFT边界单元方法完全可以解决大型复杂结构水动力问题。为了能够求解复杂三维结构的水动力问题,本文探索了一种基于有限元和边界元耦合的建模及数据提取方法。针对结构物中常见的模型几何奇异性问题,提出了双重以及多重节点重置法,有效解决了典型高阶边界元方法中加权平均所导致的几何奇异性,进一步提高了水动力问题的计算精度。对于流场问题,采用了可以直接对边界高阶奇异积分方程求解的解析方法,计算结果具有很高的精度。应用Newman的广义运动模态分解方法和拉格朗日乘子法,基于波浪辐射和绕射理论建立了多浮体结构水动力响应的运动方程,应用pFFT方法分别对自由漂浮、刚性连接或铰接约束条件下,由多个浮式、潜式极薄板组成的多浮体结构水动力问题进行了分析,得到了结构的透射系数、反射系数、附加质量、阻尼系数、波浪力、运动响应RAO以及域内速度场分布。数值结果表明该pFFT方法计算精度和计算速度很高,可以用于任意结构形式,任意约束条件下多浮体系统的水动力分析。
[Abstract]:The boundary element method (BEM), which has the advantages of high accuracy and dimension reduction, has been widely used in the study of hydrodynamic problems of wave-structure interaction. However, in the linear equations formed by discrete boundary integral equations, the coefficient matrix is a large asymmetric dense matrix, and the solution of the equations consumes a lot of computer resources, which seriously limits the scale of the problems that this method can deal with. It is the main objective of this study to explore the pre-revised Fast Fourier transform (precorrected Fast Fourier Transform,) pFFT boundary element method which can be used in hydrodynamic analysis of large complex multi-floating structures. The pre-revised Fast Fourier transform (pFFT) method can deal with any form of Green's function problem. In this method, the interaction between surface elements is divided into two parts: near-field and far-field. The far-field integral is approximately calculated by projecting the surface element onto the equivalent singular point on the uniform grid, while the near-field integral is calculated by the direct integration method. In fact, all the pointwise singularities are on the uniform mesh. This property enables the velocity potential generated by the point singularity to be quickly obtained by the Fast Fourier transform (FFT) method. Combined with the iterative method based on the generalized minimum residual method (GMRES) to solve the linear equations, the pFFT method can reduce the computational complexity of the BEM from O (N3) to O (N log N), where N is the number of boundary control points. The numerical results show that the pFFT boundary element method developed in this paper can solve the hydrodynamic problems of large and complex structures. In order to solve the hydrodynamic problem of complex three-dimensional structure, a method of modeling and data extraction based on the coupling of finite element and boundary element is explored in this paper. In order to solve the geometric singularity problem of model in structures, a double and multiple node rearrangement method is proposed, which effectively solves the geometric singularity caused by weighted averaging in the typical high order boundary element method. The calculation precision of hydrodynamic problem is further improved. For the flow field problem, the analytical method which can directly solve the higher order singular integral equation with boundary is adopted, and the calculation results have high accuracy. Based on the theory of wave radiation and diffraction, the equations of motion for hydrodynamic response of multi-floating structures are established by using Newman's generalized motional mode decomposition method and Lagrangian multiplier method. The pFFT method is applied to free floating respectively. Under the condition of rigid connection or hinged constraint, the hydrodynamic problem of multi-floating structure composed of several floating and submerged polar plates is analyzed. The transmission coefficient, reflection coefficient, additional mass, damping coefficient and wave force of the structure are obtained. The motion response RAO and the velocity field distribution in the domain. The numerical results show that the pFFT method can be used for hydrodynamic analysis of multi-floating system under arbitrary structure and constraint conditions because of its high calculation accuracy and calculation speed.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TV131.2

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