Computation of periodic Green’s functions of Stokes flow

Abstract

Methods of computing periodic Green’s functions of Stokes flow representing the flow due to triply-, doubly-, and singly-periodic arrays of three-dimensional or two-dimensional point forces are reviewed, developed, and discussed with emphasis on efficient numerical computation. The standard representation in terms of Fourier series requires a prohibitive computational effort for use with singularity and boundary-integral-equation methods; alternative representations based on variations of Ewald’s summation method involving various types of splitting between physical and Fourier space with partial sums that decay in a Gaussian or exponential manner, allow for efficient numerical computation. The physical changes undergone by the flow in deriving singly- and doubly- periodic Green’s functions from their triply-periodic counterparts are considered.