A Precorrected Fast Fourier Transform Method For Hydrodynamic Analysis Of Multi-Bodies

Boundary element method has been widely used in hydrodynamic analysis of marine structures because of the reduction of spatial dimensions and high accuracy. However, the discretization of the boundary integral equation leads to a large, unsymmetrical and fully populated system of linear equations, which are computationally expensive to solve, and this will limits the complexity of problems that can be analyzed. This paper aims to study the precorrected Fast Fourier Transform (pFFT) method, which can be used to analyze the hydrodynamic interactions of floating multi-body system.The pFFT algorithm is quite independent of the Green functions. In this method, the interactions between boundary elements are divided into near-field and far-field. The far-field integration is approximated by representing far elements with point singularities residing on a uniform grid. And the near-field integration is computed by direct integral method. The fact that all the point singularities are on a uniform grid makes it possible to rapidly calculate potentials owing to those point singularities using the Fast Foutier Transform method. Together with the iterative solver based on the generalized minimal residual algorithm (GMRES), pFFT method can reduces the computation complexity for the boundary element method from order O(N3) to O(N log N), where N represents the number of computational elements. By strict numerical verification, the pFFT method developed in this paper can be used in the hydrodynamic analysis of multi-bodies.For solving the hydrodynamic problems of complex 3-D structures, a method of modeling and data extraction and export was established based on the combination of FEM and BEM. A newly developed multiple and double nodes relocation method coupled with FEM and BEM data transformation is applied along complicated sharp edges and corners of the structures. With this method, the geometric singularity caused by the weighted average of the typical higher-order boundary element method can be removed, the precision of hydrodynamic calculation can be improved sufficiently. For the wave flow field problem, a hyper-singular integral equation is derived with high precision.Based on the wave radiation and diffraction theory, the motion equations of hinged multi-bodies are established according to the Lagrangian multiplier method and the generalized mode expansion method proposed by Newman. The pFFT method is utilized to analysis the hydrodynamics of multi-bodies that consists of horizontal or inclined thin plates with rigid, hinge connection or freely floating. The results of transmission coefficients, reflection coefficients, added mass, damping, wave force, motion RAO and wave flow field are given. Numerical results show that this pFFT method has a high precision and can be used in the hydrodynamic analysis of complex multi-bodies with arbitrary shape and constraint conditions.