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

Universal image systems for non-periodic and periodic Stokes flows above a no-slip wall