New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from a concentric annulus (or a disc) to a rectangle and a complex variable formulation of Stokes flow to derive the solutions. The form of the solutions is amenable to fast and accurate numerical computation without the need for Ewald summation or other fast summation techniques.

中文翻译：

---

近壁二维单周期斯托克斯流奇点阵列的解析解

由于二维无滑移通道和靠近无滑移壁的半平面中点奇点的周期性阵列，斯托克斯流的新解析表示被推导出来。该分析利用从同心环（或圆盘）到矩形的共形映射和斯托克斯流的复杂变量公式来推导出解。解的形式适用于快速准确的数值计算，无需 Ewald 求和或其他快速求和技术。