Development of a second order approximation for the NavierStokes equations
Abstract
The purpose of this paper is the development of a 2nd order finite difference approximation to the steady state NavierStokes equations governing flow of an incompressible fluid in a closed cavity. The approximation leads to a system of equations that has proved to be very stable. In fact, numerical convergence was obtained for Reynolds numbers up to 20,000. However, it is shown that extremely small mesh sizes are needed for excellent accuracy with a Reynolds number of this magnitude. The method uses a nine point finite difference approximation to the convection term of the vorticity equation. At the same time it is capable of avoiding values at corner nodes where discontinuities in the boundary conditions occur. Figures include level curves of the stream and vorticity functions for an assortment of grid sizes and Reynolds numbers.
 Publication:

Computers and Fluids
 Pub Date:
 September 1981
 Bibcode:
 1981CF......9..279S
 Keywords:

 Computational Fluid Dynamics;
 Finite Difference Theory;
 Incompressible Fluids;
 NavierStokes Equation;
 Reynolds Number;
 Vorticity Equations;
 Cavities;
 Difference Equations;
 Mesh;
 Nodes (Standing Waves);
 Series (Mathematics);
 Stream Functions (Fluids);
 Vortices;
 Fluid Mechanics and Heat Transfer