Consider a two dimensional steady low Reynolds number flow past a circular cylinder. A boundary integral representation that matches an outer Oseen flow and inner Stokes flow is given, and the matching error is shown to be smallest when the outer domain is as close as possible to the body. Also, it is shown that as the Greenâs function is approached, the oseenlet becomes the stokeslet to leading order and has the same order of magnitude error as the matching error. This means a novel boundary integral representation in terms of oseenlets is possible. To test this, a corresponding boundary element code is developed which uses point collocation weighting functions, linear shape functions, two-point Gaussian quadrature with analytic removal of the Greenâs function singularity for the integrations. The method is compared against various methods for the benchmark problem of flow past a circular cylinder. In particular, the drag coefficient is used for the comparison. The advantage of this method over existing ones is demonstrated and discussed particularly in the Reynolds number range $Re=1\sim 4$.

考虑通过圆柱的二维稳定低雷诺数流。给出了与外部Oseen流和内部Stokes流相匹配的边界积分表示，并且当外部域尽可能靠​​近身体时，匹配误差显示为最小。此外，还表明，随着接近格林函数的出现，oseenlet变成了前导顺序的stokeslet，并且其大小误差与匹配误差相同。这意味着可以用立体图表示新颖的边界积分表示。为了测试这一点，开发了一个相应的边界元素代码，该代码使用点搭配加权函数，线性形状函数，两点高斯求积，并对积分进行了格林函数奇点的解析去除。将该方法与各种方法进行比较，以解决流过圆柱的基准问题。特别地，阻力系数用于比较。特别是在雷诺数范围内，证明并讨论了该方法相对于现有方法的优势$\mathrm{[R}Ë=\mathrm{1个}〜4$。