势流问题边界积分方程的几种解法对比

Comparison of solving methods for boundary integral equation of potential flow

为了求解势流问题边界积分方程,以简单格林函数为基函数建立了势流问题边界积分方程,并对求解积分方程的几种数值方法一直接法,迭代法和多极子方法进行了理论分析和介绍,通过无限静水面下一偶极子作用问题的数值计算,对上述几种方法的运算速度和内存消耗进行了分析对比,结果表明快速多极子方法比另外两种计算方法在计算量和计算机存储量方面更加优越,可以分别降低到近似O(N)数量级,建议将快速多极子方法应用于大型计算问题中。

In order to solve the boundary integral equation of potential flow, based on the simple Green function, the boundary integral equation for potential problem is established in this paper. Several numerical solving methods for boundary integral equations, including direct method, iterative method and fast multipole method （FMM） are theoretically introduced. The calculation results, on a dipole below an infinite flat plane, show that FMM is superior to the others in the computation cost and the storage of the computer, and they can be decreased to about O（N） respectively. FMM is suggested for use in large-scale problems.