基于高阶面元法的浅水域中船-船水动力相互作用数值预报

摘要

A three-dimensional high order panel method based on Non-Uniform Rational B-Spline (NURBS) is developed for predicting the ship-ship hydrodynamic interaction forces during meeting and overtaking in shallow water. A NURBS surface is used to precisely represent the body geometry. Velocity potential on the body surface is described by B-spline after the source density distribution on the boundary surface is determined. A collocation approach is applied to the boundary integral e-quation discretization. Under the assumption of low passing speed, the effect of free surface elevation is neglected in the numerical calculation, and the infinite image method is used to deal with the fi-nite water depth effect. The time stepping method is used to solve the velocity potential at each time step. The present results of hydrodynamic interaction forces are compared with those obtained by slender body theory and CFD-based RANS method to show the validity of the proposed numerical method. Calculations are conducted for different water depths, lateral distances between ships and ships’ speeds, and the detailed results are presented to demonstrate the effects of these factors. The results show that interaction forces are much larger and much more susceptible to water depth, but less susceptible to lateral distance in meeting case than those in overtaking case.%文章开发了一种基于非均匀有理B样条（NURBS）的三维高阶面元法对浅水域中两船会遇和追越时的船-船水动力相互作用进行预报。该方法采用NURBS精确表达船体曲面，采用配置点法满足离散的边界积分方程，在边界面上的源强分布确定之后采用B样条表达物面速度势分布。基于低速假设，忽略了自由面的兴波效应，采用无穷镜像法处理刚性自由面和浅水效应，采用时间步进法在时域内求解速度势。将文中计算结果与基于RANS方程求解的CFD方法和细长体理论方法计算结果比较，验证了该方法的有效性。在此基础上，分别在不同水深、船间横向间距和船速下进行了系列的计算，分析了这些因素对船-船水动力相互作用影响。结果表明，在相同的工况下，船-船会遇时相互作用力比追越时更大，对水深变化更敏感，而对横向间距不如追越时敏感。