Universal image systems for non-periodic and periodic Stokes flows above a no-slip wall
arXiv:1803.02424 · doi:10.1016/j.jcp.2018.08.041
Abstract
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.
To appear in Journal of Computational Physics
References in corpus (5)
- Hydrodynamics of self-propulsion near a boundary: predictions and accuracy of far-field approximations
- Brownian Dynamics of Confined Suspensions of Active Microrollers
- Sedimentation of spheroidal bodies near walls in viscous fluids: glancing, reversing, tumbling, and sliding
- Flexibly imposing periodicity in kernel independent FMM: A Multipole-To-Local operator approach
- Ewald sum for hydrodynamic interactions with periodicity in two dimensions
Cited by in corpus (8)
- An integral-based spectral method for inextensible slender fibers in Stokes flow
- A fast spectral method for electrostatics in doubly-periodic slit channels
- Computing hydrodynamic interactions in confined doubly-periodic geometries in linear time
- Fast Ewald summation for Stokes flow with arbitrary periodicity
- Kernel Aggregated Fast Multipole Method: Efficient summation of Laplace and Stokes kernel functions
- A numerical method for suspensions of articulated bodies in viscous flows
- Rheology of moderated dilute suspensions of star colloids: the shape factor
- Mapping flagellated swimmers to surface-slip driven swimmers