Fundamental solution method for two-dimensional Stokes flow problems with one-dimensional periodicity

In this paper, we propose a fundamental solution method for two-dimensional Stokes flow problems with a one-dimensional infinite periodic array of obstacles. In the proposed method, we approximate the solution by a linear combination of periodic fundamental solutions of the Stokes flow equation. In terms of physics, this approximation illustrates Stokes flows due to forces acting on one-dimensional infinite periodic points. Numerical examples are included to demonstrate the effectiveness of the proposed method.