A novel boundary element method for low Reynolds number external flow of biological fluid dynamics

Dang, BC

Abstract

Consider two dimensional low Reynolds number flow past a body. In this thesis, the problems of steady flow past a circular cylinder, steady flow past an elliptical cylinder, and the motion of a generic tail-like body are investigated. The theoretical treatment by Chadwick (Chadwick, 2013) is detailed and elaborated upon. 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 origin of 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 that a novel boundary integral representation in terms of oseenlets is possible. To test this, we have developed a corresponding boundary element code that uses point collocation
weighting functions, linear shape functions, and two-point Gaussian quadrature with analytic removal of the Green's function singularity for the integrations.

First, we compare against various methods for the benchmark problems of flow past a circular cylinder and also a cylinder with an elliptical cross-section. The other methods are: representations using stokeslets (that suffer from Stokes' paradox giving an unbounded velocity); Lamb's (Lamb, 1932) treatment; Yano and Kieda's Oseen flow treatment (Yano & Kieda, 1980); and the matched asymptotic formulations of Kaplun (Kaplun & Lagerstrom, 1957) and Proudman and Pearson (Proudman & Pearson, 1957) which Lee and Leal (Lee & Leal, 1986) later used. In particular
we use the drag force coefficient for the comparison. The advantage of this method over existing ones is that it is accurate, uncomplicated to use, and this is demonstrated and discussed. Finally, we consider the steady forward motion of a generic tail-like body and how the frequency varies against body thickness, amplitude, wavelength and Reynolds number, and then discuss the results.

Citation

Dang, B. A novel boundary element method for low Reynolds number external flow of biological fluid dynamics. (Thesis). University of Salford

• Thesis Type: Thesis
• Deposit Date: Jun 15, 2020
• Publicly Available Date: Jun 15, 2020
• Additional Information: Funders : Nigerian Government, University of Jos, Nigeria.
• Award Date: Jan 1, 2020