Multigrid and defect correction for the steady Navier-Stokes equation

Theoretical and experimental convergence results are presented for multigrid and iterative defect correction applied to finite volume discretizations of the steady, 2D, compressible Navier-Stokes equations. Iterative defect correction is introduced for circumventing the difficulty in finding a solution of discretized equations with a second- or higher-order accurate convective part. As a smoothing technique, use is made of point Gauss-Seidel relaxation with, inside the latter, Newton iteration as a basic solution method. The multigrid technique appears to be very efficient for smooth as well as non-smooth problems. Iterative defect correction appears to be very efficient for smooth problems only, though still reasonably efficient for non-smooth problems.