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

Z. Gimbutas, L. 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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Keywords

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

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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