Analysis of the 2D Stokes flows by the non-singular boundary integral equation method

Abstract

The non-singular boundary integral equation for the Laplace (Poisson) equation, the Biot-Savart law and the velocity-vorticity formulation are used to solve some typical flow field problems, such as the 2D Stokes flows in a square cavity and a circular cavity. The conventional treatment of singularity for the boundary element method is circumvented by the introduction of the Gauss flux theorem and other iterative analytic schemes, which are elaborated in detail in this paper. We have computed the 2D Stokes flows in a circular cavity and a square cavity, which are compared with the solutions with those of both analytic and some other numerical results, such as finite difference, finite element, and conventional boundary element methods available in the literature. The present study demonstrates that the nonsingular boundary element method gives very good results as compared with analytic or other numerical solutions, even in a very coarse grid.