1 research outputs found
Fast Ewald summation for Stokes flow with arbitrary periodicity
A fast and spectrally accurate Ewald summation method for the evaluation of
stokeslet, stresslet and rotlet potentials of three-dimensional Stokes flow is
presented. This work extends the previously developed Spectral Ewald method for
Stokes flow to periodic boundary conditions in any number (three, two, one, or
none) of the spatial directions, in a unified framework. The periodic potential
is split into a short-range and a long-range part, where the latter is treated
in Fourier space using the fast Fourier transform. A crucial component of the
method is the modified kernels used to treat singular integration. We derive
new modified kernels, and new improved truncation error estimates for the
stokeslet and stresslet. An automated procedure for selecting parameters based
on a given error tolerance is designed and tested. Analytical formulas for
validation in the doubly and singly periodic cases are presented. We show that
the computational time of the method scales like O(N log N) for N sources and
targets, and investigate how the time depends on the error tolerance and window
function, i.e. the function used to smoothly spread irregular point data to a
uniform grid. The method is fastest in the fully periodic case, while the run
time in the free-space case is around three times as large. Furthermore, the
highest efficiency is reached when applying the method to a uniform source
distribution in a primary cell with low aspect ratio. The work presented in
this paper enables efficient and accurate simulations of three-dimensional
Stokes flow with arbitrary periodicity using e.g. boundary integral and
potential methods.Comment: 54 pages, 15 figure