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 language | English (US) |
|---|---|
| Article number | 302 |
| Journal | Journal of Fluid Mechanics |
| Volume | 776 |
| DOIs | |
| State | Published - Jul 2 2015 |
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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 journal › Article
}
TY - JOUR
T1 - Simple and efficient representations for the fundamental solutions of Stokes flow in a half-space
AU - Gimbutas, Z.
AU - Greengard, Leslie
AU - Veerapaneni, S.
PY - 2015/7/2
Y1 - 2015/7/2
N2 - 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.
AB - 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.
KW - boundary integral methods
KW - low-Reynolds-number flows
KW - Stokesian dynamics
UR - http://www.scopus.com/inward/record.url?scp=84942910108&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84942910108&partnerID=8YFLogxK
U2 - 10.1017/jfm.2015.302
DO - 10.1017/jfm.2015.302
M3 - Article
AN - SCOPUS:84942910108
VL - 776
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
M1 - 302
ER -