Volume 14, Issue 5
Nearly Singular Integrals in 3D Stokes Flow

Svetlana Tlupova & J. Thomas Beale

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

Published online: 2013-11

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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.

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@Article{CiCP-14-1207, author = {}, title = {Nearly Singular Integrals in 3D Stokes Flow}, journal = {Communications in Computational Physics}, year = {2013}, volume = {14}, number = {5}, pages = {1207--1227}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.020812.080213a}, url = {http://global-sci.org/intro/article_detail/cicp/7199.html} }
TY - JOUR T1 - Nearly Singular Integrals in 3D Stokes Flow JO - Communications in Computational Physics VL - 5 SP - 1207 EP - 1227 PY - 2013 DA - 2013/11 SN - 14 DO - http://dor.org/10.4208/cicp.020812.080213a UR - https://global-sci.org/intro/article_detail/cicp/7199.html KW - AB -

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.

Svetlana Tlupova & J. Thomas Beale. (2020). Nearly Singular Integrals in 3D Stokes Flow. Communications in Computational Physics. 14 (5). 1207-1227. doi:10.4208/cicp.020812.080213a
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