Numerical Solutions of Two-dimensional Stokes Flows by the Boundary Knot Method

Abstract

In this paper, the boundary knot method (BKM) is adopted for accurately analyzing two-dimensional Stokes flows, dominated by viscous force and pressure gradient force. The Stokes flows, which denoted the flow fields with extremely viscous fluid or with very small velocity, appear in various engineering applications, such that it is very important to develop an efficient and accurate numerical method to solve the Stokes equations. The BKM, which can avoid the controversial fictitious boundary for sources, is an integral-free boundary-type meshless method and its solutions are expressed as linear combinations of non-singular general solutions for Stokes equations. The weighting coefficients in the solution expressions can be acquired by enforcing the satisfactions. of boundary conditions at every boundary node, since the non-singular general solutions are derived in this paper and already satisfied the Stokes equations. Three examples of two-dimensional Stokes flows. were adopted to validate the accuracy and the simplicity of the BKM. Besides, the optimal shape parameter in the non-singular general solutions was determined by examining the minimum average residual of the linear system from the BKM.