Solution of stokes flow using an iterative DRBEM based on compactly-supported, positive-definite radial basis function

Abstract

This paper describes an iterative dual reciprocity boundary element method (DRBEM) based on the compactly-supported, positive definite radial basis function for the solution of Stokes flow problems. The method involves the solution of Laplace equations for vorticity, and Poisson equations for velocity with the solenoidal components of vorticity as right-hand sides. These equations are solved using iterative BEM and DRBEM. For the DRBEM, the compactly supported, positive definite radial basis function is used to approximate the body force term to convert it to boundary integrals. A relaxation method is devised such that the resulting algebraic equations are solved without the need of assembling a matrix. Hence, large systems of equations such as the fine discretization needed for Stokes flow problems can be handled easily. The results of Stokes flow in a square cavity and a circular cavity are presented and compared with other numerical model results. The iterative DRBEM solution is found to be satisfactory.