摘要
The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.
研究目的:实现Bessho型三维移动脉动源格林函数的快速数值计算创新要点:1.提出了综合采用变量代换和"最速下降法"计算振荡项;2.推导了变量代换后,被积函数出现"伪奇异性"点的快速数值求解方法;3.建立了参数域内的局部自适应数值积分方法。研究方法:1.采用"Gaussian quadrature rule"消除被积函数端点处的奇异性;2.结合变量代换和"最速下降法"的特点,采用分区方法处理振荡积分(见图6);3.采用参数域内局部自适应积分方法实现被积函数沿最速下降线积分的快速计算。重要结论:1.采用"Gaussian quadrature rule"能有效消除积分端点的奇异性;2.采用提出方法计算格林函数及其偏导数的耗时为4×10 3s–6×10 3s,能满足工程应用的需要。
基金
Project supported by the National Natural Science Foundation of China （No. 50879090）, and the Key Research Program of Hydrody- namics of China （No. 9140A 14030712JB 11044）
