A multigrid method for the NavierStokes and Boussinesq equations
Abstract
A nonlinear multigrid method is developed for the NavierStokes and Boussinesq equations using a discretization of finite volume type on Cartesian staggered grids and a nonlinear collective GaussSeidel method for smoothing. A simple multigrid algorithm incorporating the cycles V, F, W and an adaptive multigrid cycle (A cycle) is presented. Numerical experiments are described for a driven square cavity problem and a free convection problem in a rectangular cavity. Of the three cycles tested, namely V, W and A, the A cycle is found to be most efficient. The rate of convergence is shown to improve slightly when the mesh size is decreased. The multigrid method is found to be very much faster than single grid iteration with the smoother.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1989
 Bibcode:
 1989STIN...9012886S
 Keywords:

 Boussinesq Approximation;
 Computational Fluid Dynamics;
 Computational Grids;
 Gauss Equation;
 NavierStokes Equation;
 Algorithms;
 Convection;
 Problem Solving;
 Smoothing;
 Fluid Mechanics and Heat Transfer