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Nearly Singular Integrals in 3D Stokes Flow

Published online by Cambridge University Press:  03 June 2015

Svetlana Tlupova  and
J. Thomas Beale
Svetlana Tlupova*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA
J. Thomas Beale*
Affiliation:
Department of Mathematics, Duke University, Durham, NC 27708-0320, USA
*
Corresponding author.Email:stlupova@umich.edu
Email:beale@math.duke.edu
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Abstract

A straightforward method is presented for computing three-dimensional Stokes flow, due to forces on a surface, with high accuracy at points near the surface. The flow quantities are written as boundary integrals using the free-space Green’s function. To evaluate the integrals near the boundary, the singular kernels are regularized and a simple quadrature is applied in coordinate charts. High order accuracy is obtained by adding special corrections for the regularization and discretization errors, derived here using local asymptotic analysis. Numerical tests demonstrate the uniform convergence rates of the method.

Keywords

35J4765N8076D07Stokes equationsboundary integral equation methodnearly singular integrals
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 5 , November 2013 , pp. 1207 - 1227
Copyright
Copyright © Global Science Press Limited 2013

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