A fundamental solution method for viscous flow problems with obstacles in a periodic array

Abstract

We present here a fundamental solution method for two-dimensional viscous flow problems with obstacles in a two-dimensional periodic array. Our problem is mathematically a boundary value problem of the Stokes equations with periodic boundary conditions, to which it is difficult to give a good approximation by the ordinary fundamental solution method. We propose a fundamental solution method for our problem based on the periodic fundamental solution obtained by Hasimoto (J. Fluid Mech. 5 (1959) 317). In our method, the solution is approximated by using a linear combination of the periodic fundamental solutions.