Integral transform solution of boundary layer equations in stream function-only formulation

Abstract

The boundary layer equations for steady incompressible laminar channel flow are solved through the integral transform method, by adopting the stream function-only formulation of the governing equations, instead of the more commonly used primitive variables formulation. This hybrid numerical–analytical approach provides benchmark results under user-prescribed accuracy targets and is recognized in the validation of purely numerical schemes. The relative merits of the stream function formulation are illustrated through numerical results for the convergence behavior in the case of a plane Poiseuille flow.