# Analytical solutions for two-dimensional singly periodic Stokes flow singularity arrays near walls

## TL;DR

This paper derives new analytical solutions for two-dimensional periodic Stokes flows near walls, enabling efficient and accurate numerical computations without complex summation techniques.

## Contribution

The authors introduce novel analytical representations for periodic Stokes flows near walls using conformal mapping and complex variables, simplifying numerical calculations.

## Key findings

- Analytical solutions for 2D periodic Stokes flows near walls.
- Solutions are suitable for fast, accurate numerical computation.
- Elimination of Ewald summation in flow calculations.

## Abstract

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.