Method of fundamental solutions for multidimensional Stokes equations by the dual-potential formulation

Abstract

A simple and accurate boundary-type meshless method of fundamental solutions (MFS) is applied to solve both 2D and 3D Stokes flows based on the dual-potential formulation of velocity potential and stream function vector. Using the dual-potential concept, the solutions of both 2D and 3D Stokes flows are obtained by combining the much simpler fundamental solutions of Laplace (potential) and bi-harmonic equations without using the complicated singular fundamental solutions such as Stokeslets and their derivatives as well as source doublet hypersingularity. The developed algorithm is used to test five numerical experiments for 2D flows: (1) circular cavity, (2) wave-shaped bottom cavity and (3) circular cavity with eccentric rotating cylinder; and for 3D flows: (4) a uniform flow passing a sphere and (5) a uniform flow passing a pair of spheres. Good results are obtained as comparing with solutions of analytical and numerical methods such as FEM, BEM and other meshfree schemes.