Internal three-dimensional viscous flow solutions using the vorticity-potential method

A numerical solution procedure for internal three-dimensional viscous flow is proposed in this paper. The formulation is based on the non-primitive variables, the vorticity and potentials, on a curvilinear grid. A new upwind difference scheme is introduced to overcome the convective instabilities arising in the central difference scheme for the vorticity transport equations, while keeping false diffusion to a minimum level. Developing flows in both straight and curved square ducts are simulated to validate the procedure. The results are compared with both experimental measurements and analytical solutions.