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Multigrid preconditioned Krylov subspace methods for three-dimensional numerical solutions of the incompressible Navier–Stokes equations

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Abstract

We consider numerical methods for the incompressible Reynolds averaged Navier–Stokes equations discretized by finite difference techniques on non-staggered grids in body-fitted coordinates. A segregated approach is used to solve the pressure–velocity coupling problem. Several iterative pressure linear solvers including Krylov subspace and multigrid methods and their combination have been developed to compare the efficiency of each method and to design a robust solver. Three-dimensional numerical experiments carried out on scalar and vector machines and performed on different fluid flow problems show that a combination of multigrid and Krylov subspace methods is a robust and efficient pressure solver.

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  1. Ecole Centrale de Nantes, Laboratoire de Mécanique des Fluides UMR 6598, CFD Group 1, rue de la Noë, B.P. 92101, F-44321, Nantes Cedex 3, France

    Jean Piquet & Xavier Vasseur

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  1. Jean Piquet
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  2. Xavier Vasseur
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Piquet, J., Vasseur, X. Multigrid preconditioned Krylov subspace methods for three-dimensional numerical solutions of the incompressible Navier–Stokes equations. Numerical Algorithms 17, 1–32 (1998). https://doi.org/10.1023/A:1011689512871

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