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A nonstandard multigrid method with flexible multiple semicoarsening for the numerical solution of the pressure equation in a Navier-Stokes solver

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Abstract

Numerical methods for the incompressible Reynolds-averaged Navier-Stokes equations discretized by finite difference techniques on collocated cell-centered structured grids are considered in this paper. A widespread solution method to solve the pressure-velocity coupling problem is to use a segregated approach, in which the computational work is deeply controlled by the solution of the pressure problem. This pressure equation is an elliptic partial differential equation with possibly discontinuous or anisotropic coeffficients. The resulting singular linear system needs efficient solution strategies especially for 3-dimensional applications. A robust method (close to MG-S [22,34]) combining multiple cell-centered semicoarsening strategies, matrix-independent transfer operators, Galerkin coarse grid approximation is therefore designed. This strategy is both evaluated as a solver or as a preconditioner for Krylov subspace methods on various 2- or 3-dimensional fluid flow problems. The robustness of this method is shown.

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Authors and Affiliations

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

    Jean Piquet

  2. Laboratoire d'Informatique et de Mécanique pour les Sciences de l'Ingénieur UPR 3251, B.P. 133, F-91403, Orsay Cedex, France

    Xavier Vasseur

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  1. Jean Piquet
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Piquet, J., Vasseur, X. A nonstandard multigrid method with flexible multiple semicoarsening for the numerical solution of the pressure equation in a Navier-Stokes solver. Numerical Algorithms 24, 333–355 (2000). https://doi.org/10.1023/A:1019113814803

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