The integration of the two-dimensional laminar boundary-layer equations past the point of vanishing skin friction

A method is proposed for obtaining regular solutions of the boundary-layer equations near a point of vanishing skin friction for steady incompressible laminar two-dimensional flow. The boundary-layer equations are integrated numerically in the usual way until the separation point is approached; then the displacement thickness is prescribed as a regular function of the distance along the surface, leaving the pressure gradient to be calculated from the consequent solution. Numerical solutions are obtained with reversed flow and shallow separation bubbles inside the boundary layer without the occurrence of a singularity at the separation point.