Numerical methods for 3D viscous incompressible flows using velocity/vorticity formulation
Abstract
Incompressible NavierStokes equations formulated in terms of velocity and vorticity are solved, using finite differences on regular, staggered grids. Both sequential (or segregated) as well as block implicit techniques are used to simulate threedimensional viscous flows. In the first techniqaue, Poisson's equations for the velocity components are solved separately using a direct inversion procedure while the vorticity transport equations are solved iteratively using a zebra line relaxation. The method is applied to a threedimensional cavity flow and the solution is in good agreement with results available in literature. The second technique is a generalization of the Alternating Direction Implicit (ADI) method. Approximate factorization of the equations, written in a delta form, requires solutions of twodimensional like problems in alternating planes. It is shown that this technique is most suitable, particularly if the vorticity equations are written in conservation form. This method can be applied to time dependent problems with secondorder accuracy in time and space. No intermediate boundary conditions for the present formulation are required. Preliminary results of a test problem of a threedimensional flow over a backward facing step are presented.
 Publication:

AIAA, Aerospace Sciences Meeting
 Pub Date:
 January 1990
 Bibcode:
 1990aiaa.meetQW...D
 Keywords:

 Computational Fluid Dynamics;
 Incompressible Flow;
 Three Dimensional Flow;
 Viscous Flow;
 Backward Facing Steps;
 Cavity Flow;
 Iterative Solution;
 NavierStokes Equation;
 Poisson Equation;
 Reynolds Number;
 Fluid Mechanics and Heat Transfer