The boundary element method for the solution of Stokes equations in two-dimensional domains

Abstract A boundary element method for the solution of Stokes equations governing creeping flow or Stokes flow in the interior of an arbitrary two-dimensional domain is presented. A procedure for introducing pressure data on the boundary of the domain is also included and the integral coefficients of the resulting linear algebraic equations are evaluated analytically. Calculations are performed in a circular domain using a variety of different boundary conditions, including a combination of the fluid velocity and the pressure. Results are presented both on the boundary and inside the solution domain in order to illustrate that the boundary element method developed here provides an efficient technique, in terms of accuracy and convergence, to investigate Stokes flow numerically.