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

A method for solving three-dimensional incompressible viscous flows is presented. A complete set of Navier-Stokes equations is transformed and expressed in terms of vorticity, scalar and vector potential. In this formulation, the velocity field satisfies the equation of continuity automatically. The vorticity transport equations discretized by the central finite difference are solved by the rational Runge-Kutta (RRK) time integration scheme, and the Poisson equations are solved by the successive-over-relaxation (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 the computed results with other calculations confirms the acurracy and reliability of the present approach.