Ewald summation for the rotlet singularity of Stokes flow

TL;DR

This paper develops an Ewald summation method for efficiently computing the rotlet singularity in Stokes flow with periodic boundary conditions, including error estimates, by relating it to electrostatic force calculations.

Contribution

It introduces a novel Ewald summation technique specifically for the rotlet in Stokes flow, with derivations based on electrostatic analogies.

Findings

Provides explicit Ewald summation formulas for the rotlet

Includes truncation error estimates for practical computations

Enhances computational efficiency for periodic Stokes flow simulations

Abstract

Ewald summation is an efficient method for computing the periodic sums that appear when considering the Green's functions of Stokes flow together with periodic boundary conditions. We show how Ewald summation, and accompanying truncation error estimates, can be easily derived for the rotlet, by considering it as a superposition of electrostatic force calculations.