A new fast multipole boundary element method for solving 2-D Stokes flow problems based on a dual BIE formulation

Abstract

A fast multipole boundary element method (BEM) is presented in this paper for large-scale analysis of two-dimensional (2-D) Stokes flow problems based on a dual boundary integral equation (BIE) formulation. In this dual BIE formulation, a linear combination of the conventional BIE for velocity and the hypersingular BIE for traction is employed to achieve better conditioning for the BEM systems of equations. In both the velocity and traction BIEs, the direct formulations are used, that is, the boundary variables involved are the velocity and traction directly. The fast multipole formulations for both the velocity BIE and traction BIE for 2-D Stokes flow problems are presented in this paper based on the complex variable representations of the fundamental solutions. Several numerical examples are presented to study the accuracy and efficiency of the proposed approach. The numerical results clearly demonstrate the potentials of the developed fast multipole BEM for solving large-scale 2-D Stokes flow problems.