BEM for low Reynolds number flow past a steady circular cylinder in an unbounded domain

Dang, Bwebum; Chadwick, Edmund

Abstract

Consider a two dimensional steady low Reynolds number flow past a circular cylinder. The theoretical treatment in Chadwick [1] is detailed and elaborated. A Boundary Integral representation that matches an outer Oseen flow and inner Stokes flow is given, and the matching error is shown to be smallest when the outer domain is as close as possible to the body. Also, it is shown that as the Green's function is approached, the oseenlet becomes the stokeslet to leading order, and has the same order of magnitude error as the matching error. This means a novel Boundary Integral representation in terms of oseenlets is possible. To test this, we have developed a corresponding Boundary Element code that used point collocation weighting functions, linear shape functions, two point Gaussian quadrature with analytic removal of the Green's function singularity for the integrations. We compare against various methods for the benchmark problem of flow past a circular cylinder. The other methods are: representations using stokeslets (that suffer from Stokes' paradox that gives unbounded velocity) ; Lambs [9] treatment; Yano and Kieda's Oseen flow treatment [17]; an the matched asymptotic formulation of Kaplun [7]. In particular we use the drag coefficient for comparison. The advantage of this method over existing ones is demonstrated and discussed.

Citation

Dang, B., & Chadwick, E. (2019). BEM for low Reynolds number flow past a steady circular cylinder in an unbounded domain. In C. Fresneda-Portillo (Ed.),

• Conference Name: 12th UK Conference on Boundary Integral Methods (UKBIM12)
• Conference Location: Oxford
• Start Date: Jul 8, 2019
• End Date: Jul 9, 2019
• Online Publication Date: Jul 1, 2019
• Publication Date: Jul 1, 2019
• Deposit Date: Jul 3, 2023
• Publicly Available Date: Jul 5, 2023
• Publisher: Oxford Brookes University
• Chapter Number: 8
• ISBN: 9781999741297
• Publisher URL: https://radar.brookes.ac.uk/radar/items/dd58e98a-6942-456f-98a5-0203f2a159e0/1/