Numerical solution of the NavierStokes equations by multigrid techniques
Abstract
Techniques for formulation of coupled equations for multigrid computational solution of the discretized steadystate NavierStokes equations are investigated. Different versions of the NavierStokes equations, distinguished by the total number of variables, are considered, together with various relaxation schemes. Emphasis is given to the efficiency of the numerical models for producing solutions, and governing equations are formulated in terms of the velocity vector and pressure, the stream function, and the stream function and vorticity. The efficiency of the methods is assessed as a function of the Re and the mesh size. A solution is found for a sample problem of a driven cavity flow with Re up to 200, using 12 x 12, 24 x 24, and 48 x 48 grid configurations. An asymptotic rate of convergence is defined which is not dependent on the initial approximation.
 Publication:

Numerical Methods in Laminar and Turbulent Flow
 Pub Date:
 1981
 Bibcode:
 1981nmlt.proc..141T
 Keywords:

 Computational Fluid Dynamics;
 Discrete Functions;
 Ducted Flow;
 NavierStokes Equation;
 Steady State;
 Cavity Flow;
 Relaxation Method (Mathematics);
 Reynolds Number;
 Stream Functions (Fluids);
 Vorticity;
 Fluid Mechanics and Heat Transfer