基于Laguerre函数对圆柱面绕射势的数值逼近

无限深圆柱表面绕射势沿水深方向的变化是连续的、不断衰减的。基于无穷区间Laguerre多项式并引入的伸缩系数s定义了Laguerre函数,既保证了函数在无穷区间的正交性,又使函数具有灵活性。绕射势的变化,可以用一系列Laguerre函数表示成级数形式。文中对该方法的收敛性进行了证明,并以一条FPSO为例对其在圆柱面的绕射势进行了逼近。求解级数展开式的系数时会遇到无穷积分问题,采用多次使用Gauss-Legendre积分和Gauss-Laguerre积分相结合的方法代替传统的Gauss-Laguerre积分方法,获得更高的积分精度。利用Laguerre函数可以对Rankine源法或者Rankine-Kelvin法的控制面上速度势进行逼近。

Numerical approximation of diffraction waves on cylinder surface based on Laguerre function

The vertical variation of water diffraction waves on vertical infinite circular cylinder is consid-ered to be continuous and descending. The variation can be represented by a series of Laguerre functions using Laguerre polynomials. A scale parameter s is introduced to the function which ensures orthogonali-ty and flexibility. The convergence of Laguerre series is proved and diffraction wave of a FPSO on a circu-lar cylinder surface is approximated for instance. The Gauss-Legendre integration is combined with Gauss-Laguerre integration to alternate traditional Gauss-Laguerre integration. This integration method can obtain higher numerical precision. The Laguerre series can be applied to approximate the velocity potential on the control surface in Rankine source method or Rankine-Kelvin source method.