Direct method for solution of three-dimensional unsteady incompressible Navier-Stokes equations

Abstract

A three-dimensional, unsteady analysis for the velocity-vorticity formulation of the Navier-Stokes (NS) equations is described. This formulation highlights the natural separation of the spin dynamics of a fluid particle from its translational kinematics. This separation is exploited to produce a single pass direct inversion of the full unsteady NS operator without the need to iterate either the future wall vorticity or the nonlinear vorticity convection terms. The method has uniform second-order accuracy in time and space. As an example, it is applied to the problem of the three-dimensional flow within a shear-driven cubical box. Results are obtained for Re = 100, 400, and 1000 using a preliminary (25, 25, 25) mesh.