强非线性时域水弹性问题的MPS方法改进研究

The large-scale and high speed tendency of modern ships means that the hydroelasticity effect plays a more significant role during the fluid-structure interaction process. It can greatly affect the overall and fatigue strengths of the structure. MPS method consists of mesh-less spatial discretization and Lagrangian-type time stepping. It breaks the limitation of simulating violent free surface deformation in potential flow theory and avoids the difficulty of mesh manipulation in mesh-based CFD method respectively, which makes the MPS method very suitable for the simulation of the highly non-linear time domain hydroelasticity problems with complex boundary changing. However, it also confronts the problems of relatively low accuracy especially the non-physical pressure fluctuation issue and low computational efficiency. In this study, the Numerical-Manifold-Method-based Poisson equation solving and particle shifting technique will be used to improve the computational accuracy of MPS method; the domain decomposition method and parallel computation technique will be adopted to increase the efficiency of the fluid simulation; modal superposition method will be modified and applied for the simulation of structure dynamic response. The fluid and structure solvers will be coupled in an iterative manner to achieve strong fluid and structure interaction computation, which will be validated against water entry and exist experiments of typical flexible structure models. The developed numerical model in this project is aiming to provide an accurate and efficient numerical tool for the computation of highly non-linear hydroelasticity problems based on MPS method.

现代船舶日趋呈现大型化、高速化等特点，使得结构物水弹性效应在流固耦合作用中越发重要，已成为影响总体和疲劳强度的重要因素。MPS方法采用无网格空间离散形式和拉格朗日形式的时间步进格式，突破了势流理论无法模拟自由面剧烈变形和网格类CFD方法网格处理困难的限制，十分适合强非线性时域水弹性计算中涉及的边界大变形问题的模拟。针对其压强非物理性震荡等精度和较低的计算效率问题，本项目将采用基于数值流形法的Poisson方程求解和粒子动态重排方法提高MPS方法的计算精度；通过区域分割技术以及并行化算法提高整体的流体求解效率；改进模态叠加方法来高效计算结构物动态响应并通过迭代方式与流体求解器进行强耦合。所发展数值模型将以典型结构物的出入水实验进行验证，最终给出基于MPS方法的准确高效强非线性时域水弹性计算模型。

本项目针对现代舰船大型化、高速化的背景，力求解决强非线性水弹性响应计算问题，将MPS方法引入强非线性时域水弹性问题的计算，针对其精度和效率问题，分别提出基于数值流形思想的高精度压力Poisson方程求解方法，新的自由液面和固体边界条件，基于CPU的并行化方法以及空间多分辨率方法的快速计算策略。在此基础上，发展改进的模态叠加方法进行结构动力响应计算，并采用迭代方式与流体部分进行强流固耦合运算。通过以上的研究，为船舶与海洋结构物的强非线性时域水弹性问题提供高效准确的数值方法，为相关结构物的设计提供技术支撑。