Predictions of Fluid Flow and Heat Transfer Problems by the VorticityVelocity Formulation of the NavierStokes Equations
Abstract
A relatively novel formulation of the NavierStokes equations is evaluated for obtaining solutions of 2dimensional incompressible fluid flow and convective heat transfer problems. A vorticity transport equation along with two Poisson equations for the velocity components and the energy equation are solved by a finite difference scheme. A direct solution procedure is used for solving simultaneously the dependent variables along a grid line, using a block tridiagonal matrix algorithm. As test problems, laminar flow motion and heat transfer in a square cavity and in a horizontal concentric annulus induced by various strength of buoyancy and external shear forces are investigated. The formulation is found to be stable for high Reynolds and Grashof numbers and has features that may be desirable for solving a wide variety of flow and heat transfer problems.
 Publication:

Journal of Computational Physics
 Pub Date:
 July 1986
 DOI:
 10.1016/00219991(86)900136
 Bibcode:
 1986JCoPh..65..227F
 Keywords:

 Annular Flow;
 Computational Fluid Dynamics;
 Convective Heat Transfer;
 Flow Velocity;
 NavierStokes Equation;
 Vorticity Equations;
 Buoyancy;
 Finite Difference Theory;
 High Reynolds Number;
 Incompressible Flow;
 Laminar Flow;
 Poisson Equation;
 Shear Flow;
 Fluid Mechanics and Heat Transfer