A difference procedure for the Navier-Stokes equations in multiply-connected domains

The present study is concerned with the development of a difference scheme which makes it possible to solve the Navier-Stokes equations for plane, steady incompressible flows, taking into account a formulation involving a pure stream function equation. The basic equations are examined and the stream function formulation of the Navier-Stokes equations is obtained. The numerical solution of the problem for simply connected domains is described, giving attention to aspects of linearization, discretization, the solution of the linear system, and the complexity of the procedure. The developed procedure is extended to cases involving multiply-connected domains, and a description is provided of the additional algebraic equations required and the solution algorithm. Numerical experiments are also discussed, taking into consideration a test equation, plane flow problems, axisymmetric flows, and a multiply-connected plane problem.