Meshless boundary node methods for Stokes problems

Abstract

In this study, we present the first meshless boundary node method (BNM) for two-dimensional and three-dimensional Stokes problems. The BNM exploits the advantages of the reduced dimensionality of boundary integral equations (BIEs) and the meshless attribute of moving least squares (MLS) approximations. However, because MLS shape functions lack the property of a delta function, the direct collocation scheme used in the BNM to impose boundary conditions doubles the numbers of unknowns and system equations. To overcome this drawback, we propose a dual boundary node method (DBNM), which uses the velocity BIE on the velocity boundary and the traction BIE on the traction boundary. In the DBNM, the boundary conditions are incorporated directly into the BIEs and they can be imposed easily, while the numbers of unknowns and system equations are only half of those in the BNM, thereby leading to higher computational precision and speed. Selected numerical tests illustrate the efficiency of the BNM and the DBNM.