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

Wen Yan, Michael Shelley

Research output: Contribution to journalArticlepeer-review


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 (1971) [8]. 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 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.

Original languageEnglish (US)
Pages (from-to)263-270
Number of pages8
JournalJournal of Computational Physics
StatePublished - Dec 15 2018


  • Image method
  • Periodic boundary condition
  • Rotne–Prager–Yamakawa tensor
  • Stokeslet in half-space

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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