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 co-ordinates 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.