三维浮体二阶辐射问题的实时模拟

Real time simulation of second-order radiation of 3D bodies

采用二阶时域理论对任意三维物体的非线性波浪问题进行了研究。对自由表面边界条件和物面边界条件进行了Taylor级数展开 ,Stokes摄动展开用于建立相应的一阶和二阶边值问题 ,而且此边值问题的计算域不随时间变化。使用基于B -样条的边界元方法计算每一时刻的二阶波浪场 ,二阶自由表面边界条件在时间上进行数值积分。在自由表面加一个人工阻尼层以避免波浪的反射。对二阶物面边界条件采用数学手段 ,推导出一个没有二阶空间导数的表达式 ,以便于计算。本文对强迫正弦垂荡和纵荡运动的截断圆柱进行了计算 ,讨论了漂浮结构的二阶水动压力影响 。

The nonlinear wave rediation of a surface-piercing body of arbitrary shape in three dimensions is investigated by time-domain second-order method. In this approach, Taylor series expansions are applied to the body surface boundary condition and the free surface boundary conditions, and Stokes perturbation procedure is then used to establish corresponding boundary value problems at the first and the second order of waves steepness with time-independent boundaries. A boundary element method based on B-splines is used to calculate the wave field at each time step, and the free-surface boundary condition is satisfied to the second order by a numerical integration in time. An artificial damping layer is adopted on the free surface to avoid the wave reflection. Additionally, a mathematical manipulation is adopted to remove the second-order spacial derivatives in the body surface boundary condition. Numerical results including hydrodynamic forces are presented for the case of a truncated surface-piercing cylinder undergoing specified sinusoidal surge and heave motions. It is found that the numerical results in this paper agree well others’results.