Simple and efficient representations for the fundamental solutions of Stokes flow in a half-space
Fluid Dynamics
2023-07-19 v2
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.
Keywords
Cite
@article{arxiv.1504.00102,
title = {Simple and efficient representations for the fundamental solutions of Stokes flow in a half-space},
author = {Zydrunas Gimbutas and Leslie Greengard and Shravan Veerapaneni},
journal= {arXiv preprint arXiv:1504.00102},
year = {2023}
}