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A multigrid pseudospectral method for steady flow computation. (English) Zbl 1032.76648
Summary: 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.

##### MSC:
 76M22 Spectral methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids
##### Keywords:
multigrid; Picard iteration; pseudospectral; random perturbation
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