European Journal of Mechanics B/Fluids 24 (2005) 703–716 The method of fundamental solutions for Stokes flow in a rectangular cavity with cylinders D.L. Young a,∗ , C.W. Chen a , C.M. Fan a , K. Murugesan a , C.C. Tsai b a Department of Civil Engineering & Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan b Department of Information Technology, Toko University, Chia-Yi County, Taiwan Received 26 August 2004; received in revised form 6 February 2005; accepted 17 March 2005 Available online 5 May 2005 Abstract Numerical solutions based on the method of fundamental solutions are discussed for Stokes flow inside a rectangular cavity in the presence of circular cylinders. The Stokeslets are used as the fundamental solutions to obtain the solution for the flow field by a linear combination of fundamental solutions. Flow results on the cellular structure of flow field resulting from the dynamics of cylinders and the horizontal walls of the cavity are reported for (i) one rotating cylinder in a rectangular cavity with two parallel horizontal sides moving in the same directions as well as in the opposite directions, (ii) two rotating cylinders kept apart in a rectangular cavity with two parallel horizontal sides moving in the same directions as well as in the opposite directions. The effect of aspect ratio of the rectangular cavity, direction of movement of the two parallel horizontal sides of the cavity and the diameter of the rotating cylinder on the flow structure are studied. The flow results obtained for the single cylinder case are in accordance with the results available in the literature. From the computational point of view, the present numerical procedure based on the method of fundamental solutions is efficient and simple to implement as compared to the mesh-dependent schemes, which needs complex mesh generation procedure for the multiply connected geometrical domains considered in this article.  2005 Elsevier SAS. All rights reserved. Keywords: Method of fundamental solutions; Stokeslet; Rectangular cavity; Rotating cylinders 1. Introduction Theoretical studies of Stokes flow in a rectangular cavity with rotating cylinders provide useful information on distributive mixing which has many industrial applications. Though the flow is dominated only by shear force, the presence of obstacles and the rotation of cylinders produce eddy zones and dead zones which affect the mixing process. For simple flow configurations involving only a moving wall with a stationary cylinder the Stokes equations could be solved directly by analytical method [1]. Sometimes, experimental methods have also been used to understand the complex flow structures created by chaotic mixing produced by discontinuous and sinusoidal flow [2] and shear flow past a circular cylinder with arbitrary rotational speeds [3]. Analytical solutions of Stokes equations for flow domains such as a rectangular cavity with rotating cylinders involve complex solution procedure [4]. Hence Hellou and Coutanceau [4] supported their analytical and numerical predictions with experimental * Corresponding author. Fax: +886 2 23626114. E-mail address: dlyoung@ntu.edu.tw (D.L. Young). 0997-7546/$ – see front matter  2005 Elsevier SAS. All rights reserved. doi:10.1016/j.euromechflu.2005.03.003