  It is well-known that by placing judiciously chosen image point forces and
doublets to the Stokeslet above a flat wall, the no-slip boundary condition can
be conveniently imposed on the wall [Blake, J. R. Math. Proc. Camb. Philos.
Soc. 70(2), 1971: 303.]. However, to further impose periodic boundary
conditions on directions parallel to the wall usually involves tedious
derivations because single or double periodicity in Stokes flow may require the
periodic unit to have no net force, which is not satisfied by the well-known
image system. In this work we present a force-neutral image system. This
neutrality allows us to represent the Stokes image system in a universal
formulation for non-periodic, singly periodic and doubly periodic geometries.
This formulation enables the black-box style usage of fast kernel summation
methods. We demonstrate the efficiency and accuracy of this new image method
with the periodic kernel independent fast multipole method in both non-periodic
and doubly periodic geometries. We then extend this new image system to other
widely used Stokes fundamental solutions, including the Laplacian of the
Stokeslet and the Rotne-Prager-Yamakawa tensor.
