Solution of stokes flow problem using dual reciprocity boundary element method

Abstract

This paper describes a dual reciprocity boundary element model for the solution of incompressible viscous flows in slow motion, using velocity‐vorticity variables. The method involves the solution of advection‐diffusion type vorticity equations for vorticity whose so‐lenoidal vorticity components are obtained by solving Poisson type equations involving the velocity and vorticity components. Both the Poisson type equations and the vorticity advection‐diffusion type equations are solved using the dual reciprocity boundary element method (DRBEM). In DRBEM, all source terms, advective terms and time dependent terms are converted into boundary integrals and hence the computational domain of the problem reduces by one. Here the results of Stokes flow problems with very low Reynolds numbers in a typical square cavity are presented and compared with other model results. The DRBEM model has been found to be feasible and satisfactory.