Method of Fundamental Solutions for Three-Dimensional Stokes Flow in Exterior Field

Abstract

The main purpose of the present paper is to provide practical and numerical implementations of the method of fundamental solutions for three-dimensional exterior Stokes problems with quiet far-field condition and discuss the issues therein. The solutions of the steady Stokes problems are obtained by utilizing the boundary collocation method as well as the expansion of Stokeslets, which are the fundamental solutions of the steady Stokes equations. To validate the proposed model, numerical results of a lid-driven cavity flow, uniform flow passing a sphere, and a rotating dumbbell-shaped body show good agreement with the numerical and analytical solutions available in the literature. Also, a hypothetical problem with both vorticity and velocity boundary conditions is solved and compared with the analytical solution. The proposed model is then properly exploited to obtain the flow results of uniform flow passing a pair of vertical spheres in tandem and uniform flow passing a pair of horizontal spheres in tandem. Furthermore, the accuracy of the present numerical scheme is addressed and the detail flow characteristics, such as pressure distribution, streamline contour, velocity field, and vorticity fields are sketched.