A multigrid pseudospectral method for steady flow computation

In this work two-dimensional steady flow problems are cast into a fixed-point formulation, Q = F(Q). The non-linear operator, F, is an approximate pseudospectral solver to the Navier-Stokes equations. To search the solution we employ Picard iteration together with a one-dimensional error minimization and a random perturbation in case of getting stuck. A monotone convergence is brought out, and is greatly improved by using a multigrid strategy. The efficacy of this approach is demonstrated by computing flow between eccentric rotating cylinders, and the regularized lid-driven cavity flow with Reynolds number up to 1000.