The application of boundary value techniques in the solution of the NavierStokes equation
Abstract
An investigation of the numerical boundary value techniques for a twodimensional steady state, viscous, incompressible flow in a rectangular cavity is presented. Solutions for the twodimensional NavierStokes equations are found in the case of a plate moving over the top of the fluidfilled cavity. Four boundary equations are defined and an elliptic parabolic partial differential equation system is obtained. Consideration is given to successive line overrelaxation models in the Re range 100500,000. An iterative solution procedure is demonstrated for the finite difference equations. The number of iterations necessary to reach an accuracy of 1/1000 for each Re is found to decrease with the boundary value technique.
 Publication:

Numerical Methods in Laminar and Turbulent Flow
 Pub Date:
 1981
 Bibcode:
 1981nmlt.proc...65D
 Keywords:

 Boundary Value Problems;
 Ducted Flow;
 Incompressible Flow;
 NavierStokes Equation;
 Two Dimensional Flow;
 Viscous Flow;
 Computational Fluid Dynamics;
 Convergence;
 Finite Difference Theory;
 Flow Geometry;
 Iterative Solution;
 Reynolds Number;
 Steady State;
 Vorticity Equations;
 Fluid Mechanics and Heat Transfer