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

Published

July 2, 2015

Author(s)

Zydrunas Gimbutas, Leslie Greengard, Shravan Veerapaneni

Abstract

We derive new formulas 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 solvers 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.

Citation

Journal of Fluid Mechanics

Volume

776

Issue

R1

Pub Type

Journals

Download Paper

https://doi.org/10.1017/jfm.2015.302

Keywords

Stokes flow, Blake’s formulas, Papkovich-Neuber solution

Citation

Gimbutas, Z. , Greengard, L. and Veerapaneni, S. (2015), Simple and efficient representations for the fundamental solutions of Stokes flow in a half-space, Journal of Fluid Mechanics, [online], https://doi.org/10.1017/jfm.2015.302 (Accessed October 11, 2025)