常数分布Rankine源法与二阶绕射问题精度研究

Numerical investigation of second-order wave diffraction based on the Rankine source method

为了准确地预报作用在浮体上的非线性水动力,采用时域二阶理论对非线性波物相互作用问题进行了研究.对自由面条件和物面条件进行Taylor级数展开和Stokes摄动展开得到一阶和二阶边值问题.使用基于Rankine源的边界元法计算每一时刻的流场,并在自由面上采用积分格式的自由面条件(IFBC);在远方控制面上采用多次透射边界条件(MTF).以圆球绕流和直立圆柱桩的二阶绕射问题为例,研究了所述方法的数值精度,经过对数值结果的比较与分析,得出了该方法精度较低的原因,并且得到MTF和IFBC可以有效地用于时域二阶问题的数值模拟,在远方人工边界上达到无反射的效果.

In order to exactly predict hydrodynamic forces acting on a floating body,a time-domain second-order method was formulated to simulate a three-dimensional nonlinear wave-body interaction problem.In this approach,Taylor series expansions were applied to the body surface boundary condition and the free surface boundary conditions.The Stokes perturbation procedure was then used to establish a corresponding first and second order boundary value problem on the time-independent surfaces.A boundary element method（BEM）,based on the Rankine source,was used to calculate the wave field at each time step.A multi-transmitting formula（MTF） method,with an artificial wave speed,was then employed to satisfy the radiation condition and minimize wave reflections.A stable form,an integral form of free-surface boundary condition（IFBC） was used to update velocity potentials on the free surface.This method was applied to compute uniform flow over a sphere and surface-piercing circular cylinder causing second-order wave diffraction.The numerical precision of the method was then investigated.The results were also compared with analytical solutions and the differences between them were analyzed.It was shown that MTF and IFBC can be used to simulate second-order time domain problems.It was also seen that long-time simulations can be done almost without reflecting waves.