一种处理高阶面元法中奇异积分的方法

A scheme dealing with the singular integrals in high order panel method

对高阶面元法中奇异积分问题进行数值研究,根据面元的大小以及面元到场点的距离,把整个曲面积分分为远场、近场两类,分别对其使用不同的方法以处理Rankine源项所引起的积分奇异问题,对三维球体、椭球体进行数值计算,将结果与解析解和其他方法的计算值的比较表明此计算方法是有效的。

A numerical scheme is developed for the singular integrals in high order panel method. Considering the singularity of the integrand due to the Rankine terms, the integrals are classed into two categories according to the characteristic length of the panel and its distance to the field point： the far-field and near-field integrals. Different methods are applied for different cases to deal with the singular integrals. The numerical resuits for three-dimensional sphere and ellipsoids are compared with the analytical results and other numerical results, showing that the present method is valid.