@Article{CiCP-22-3,
author = {},
title = {Numerical Computation of Doubly-Periodic Stokes Flow Bounded by a Plane with Applications to Nodal Cilia},
journal = {Communications in Computational Physics},
year = {2017},
volume = {22},
number = {3},
pages = {620--642},
abstract = {<p style="text-align: justify;">A numerical method is presented for the computation of externally forced
Stokes flows bounded by the plane z=0 and satisfying periodic boundary conditions
in the x and y directions. The motivation for this work is the simulation of flows
generated by cilia, which are hair-like structures attached to the surface of cells that
generate flows through coordinated beating. Large collections of cilia on a surface can
be modeled using a doubly-periodic domain. The approach presented here is to derive
a regularized version of the fundamental solution of the incompressible Stokes
equations in Fourier space for the periodic directions and physical space for the z direction.
This analytical expression for <strong>û</strong>(k,m;z) can then be used to compute the fluid
velocity <strong>u</strong>(x,y,z) via a two-dimensional inverse fast Fourier transform for any fixed
value of z. Repeating the computation for multiple values of z leads to the fluid velocity
on a uniform grid in physical space. The zero-flow condition at the plane z =0
is enforced through the use of images. The performance of the method is illustrated
by numerical examples of particle transport by nodal cilia, which verify optimal particle
transport for parameters consistent with previous studies. The results also show
that for two cilia in the periodic box, out-of-phase beating produces considerable more
particle transport than in-phase beating.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0151},
url = {https://global-sci.com/article/80154/numerical-computation-of-doubly-periodic-stokes-flow-bounded-by-a-plane-with-applications-to-nodal-cilia}
}