A multigrid method for solution of vorticity—velocity form of 3‐D navier—stokes equations

A multigrid method has been developed and applied to the simulation of unsteady three‐dimensional incompressible flow, using the Navier—Stokes equations in terms of vorticity and velocity variables. A system of equations for the velocity problem, consisting of the continuity equation and three curl equations, is first formulated as a uniquely determined, non‐singular system. An efficient and robust technique, namely the multigrid distributive Gauss—Seidel scheme, is developed for solution of this system of algebraic equations. The method is applied to study 3‐D flow in a shear‐driven cavity.