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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.

76M22 Spectral methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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