Simple and efficient representations for the fundamental solutions of Stokes flow in a half-space

Z. Gimbutas, Leslie Greengard, S. Veerapaneni

Research output: Contribution to journalArticle

Abstract

We derive new formulae for the fundamental solutions of slow viscous flow, governed by the Stokes equations, in a half-space. They are simpler than the classical representations obtained by Blake and collaborators, and can be efficiently implemented using existing fast solver libraries. We show, for example, that the velocity field induced by a Stokeslet can be annihilated on the boundary (to establish a zero-slip condition) using a single reflected Stokeslet combined with a single Papkovich-Neuber potential that involves only a scalar harmonic function. The new representation has a physically intuitive interpretation.

Original languageEnglish (US)
Article number302
JournalJournal of Fluid Mechanics
Volume776
DOIs
StatePublished - Jul 2 2015

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Harmonic functions
Stokes flow
Viscous flow
half spaces
harmonic functions
viscous flow
slip
velocity distribution
scalars

Keywords

  • boundary integral methods
  • low-Reynolds-number flows
  • Stokesian dynamics

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

Simple and efficient representations for the fundamental solutions of Stokes flow in a half-space. / Gimbutas, Z.; Greengard, Leslie; Veerapaneni, S.

In: Journal of Fluid Mechanics, Vol. 776, 302, 02.07.2015.

Research output: Contribution to journalArticle

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