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A highly accurate boundary treatment for confined Stokes flow
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-8998-985X
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
2012 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 66, 215-230 p.Article in journal (Refereed) Published
Abstract [en]

Fluid flow phenomena in the Stokesian regime abounds in nature as well as in microfluidic applications. Discretizations based on boundary integral formulations for such flow problems allow for a reduction in dimensionality but have to deal with dense matrices and the numerical evaluation of integrals with singular kernels. The focus of this paper is the discretization of wall confinements, and specifically the numerical treatment of flat solid boundaries (walls), for which a set of high-order quadrature rules that accurately integrate the singular kernel of the Stokes equations are developed. Discretizing by Nystrom's method, the accuracy of the numerical integration determines the accuracy of the solution of the boundary integral equations, and a higher order quadrature method yields a large gain in accuracy at negligible cost. The structure of the resulting submatrix associated with each wall is exploited in order to substantially reduce the memory usage. The expected convergence of the quadrature rules is validated through numerical tests, and this boundary treatment is further applied to the classical problem of a sedimenting sphere in the vicinity of solid walls.

Place, publisher, year, edition, pages
2012. Vol. 66, 215-230 p.
Keyword [en]
Stokes flow, Boundary integral method, Stokeslet, Quadrature, Singular integrals, Nystrom's method, Toeplitz matrix
National Category
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-104253DOI: 10.1016/j.compfluid.2012.06.008ISI: 000309146300019Scopus ID: 2-s2.0-84864803971OAI: oai:DiVA.org:kth-104253DiVA: diva2:565160
Funder
Swedish e‐Science Research Center
Note

QC 20121106

Available from: 2012-11-06 Created: 2012-10-31 Last updated: 2017-12-07Bibliographically approved

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Gustavsson, Katarina

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Numerical Analysis, NA (closed 2012-06-30)Linné Flow Center, FLOW
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