Numerical simulation of three-dimensional viscous flows using the vector potential method

A method for solving three-dimensional viscous incompressible flows is presented. A complete set of the Navier-Stokes equation is transferred and expressed in terms of the vorticity, the scalar and the vector potential. In this formation, the velocity field satisfies the equation of continuity automatically. The vorticity transport equations discretized by the centred differences are solved by the rational Runge-Kutta (RRK) time integration scheme, and the Poisson equations are solved by the successive over-relaxatation (SOR) method. The numerical solutions of flows in a cubic cavity, in a square duct and in a rectangular duct with the aspect ratio of 2 are presented. Comparison of computed results with other calculations confirms the accuracy and reliability of the present approach.