有势流边界积分方程奇点的简洁处理法

Simple Procedure to Remove the Singularities of Boundary Integral Equations for Potential Flows

本文结合笔者所做的多种流体在线混合的研究课题讨论了有势流直接数字积分的一般方法。为了使高斯积分法或其它的数字积分法能简单的直接用于求积分值 ,从而推导出了一个更简洁的计算公式 ,在该公式中格林函数中的奇点从理论上被消除。在本文中可以不用插值函数求解未知变量 ,因此 ,该方法比传统方法更为简单。

This paper presents a general simple integral formulation for potential flows in the light of the author's research on fluid mixture.The singularities of Green's functions in the formulation are desingularized theoretically, so that Gaussian quadrature or any other numerical integration methods can be applied directly to evaluate all the integrals easily.It is unnecessary for unknown variables to use interpolation functions.Therefore, the present method is much simpler and more efficient than the conventional one.