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

Published online by Cambridge University Press:  02 July 2015

Z. Gimbutas ,
L. Greengard  and
S. Veerapaneni
Z. Gimbutas
Affiliation:
Information Technology Laboratory, National Institute of Standards and Technology, 325 Broadway, Mail Stop 891.01, Boulder, CO 80305-3328, USA
L. Greengard
Affiliation:
Simons Center for Data Analysis, Simons Foundation, 160 Fifth Avenue, New York, NY 10010, USA Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1110, USA
S. Veerapaneni*
Affiliation:
Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Low-Reynolds-number flows: Boundary integral methods Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Stokesian dynamics
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 776 , 10 August 2015 , R1
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Copyright
© 2015 Cambridge University Press 

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