Commun. Comput. Phys., 14 (2013), pp. 1207-1227.


Nearly Singular Integrals in 3D Stokes Flow

Svetlana Tlupova 1*, J. Thomas Beale 2

1 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA.
2 Department of Mathematics, Duke University, Durham, NC 27708-0320, USA.

Received 2 August 2012; Accepted (in revised version) 8 February 2013
Available online 13 June 2013
doi:10.4208/cicp.020812.080213a

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.

AMS subject classifications: 35J47, 65N80, 76D07

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Key words: Stokes equations, boundary integral equation method, nearly singular integrals.

*Corresponding author.
Email: stlupova@umich.edu (S. Tlupova), beale@math.duke.edu (J. T. Beale)
 

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