Numerical solution of the Navier-Stokes equations by multi-grid techniques

Techniques for formulation of coupled equations for multigrid computational solution of the discretized steady-state Navier-Stokes equations are investigated. Different versions of the Navier-Stokes 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.