A new method for the numerical solution of time dependent viscous flow

A new method of solving numerically the Navier-Stokes equations for time dependent flow is presented. The velocity components and pressure are used as the main variables, but in order to ensure continuity on a global scale, the Stokes stream function is also employed. The solution process is formulated in cylindrical polar coordinates and both implicit and explicit versions are discussed. Time dependent development in the entrance region of a cylindrical pipe is investigated using the method and several interesting flow features are predicted.