An application of boundary element method to incompressible laminar viscous flows

An attempt is made to apply direct boundary element method to the numerical solution of incompressible Navier-Stokes equations. The flow equations are modelled in terms of stream function and vorticity in two spatial dimensions. A new type of boundary condition on the vorticity is presented, which is particularly useful in the boundary element method. Boundary integral equations are derived by using fundamental solutions known as logarithmic potential and time-dependent heat potential. Boundary unknowns are discretized by constant and linear boundary elements. Triangular and eight-noded isoparametric cells are considered. Charged points are translated upstream in the evaluation of convective terms in order to increase the order of stability. Unknown stream function and vorticity are staggered in the computational scheme. Nonlinear flow equations are solved by simple iteration. Boundary element results for two-dimensional examples with low Reynolds numbers are compared favorably with exact or finite element solutions.