A block preconditioning technique for the streamfunction-vorticity formulation of the Navier-Stokes equations

Iterative methods of Krylov‐subspace type can be very effective solvers for matrix systems resulting from partial differential equations if appropriate preconditioning is employed. We describe and test block preconditioners based on a Schur complement approximation which uses a multigrid method for...

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Bibliographic Details
Published in:Numerical methods for partial differential equations 2012-05, Vol.28 (3), p.888-898
Main Authors: Fairag, Faisal A., Wathen, Andrew J.
Format: Article
Language:English
Subjects:
Navier-Stokes
Oseen
preconditioner
Schur complement
streamfunction vorticity
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Summary:Iterative methods of Krylov‐subspace type can be very effective solvers for matrix systems resulting from partial differential equations if appropriate preconditioning is employed. We describe and test block preconditioners based on a Schur complement approximation which uses a multigrid method for finite element approximations of the linearized incompressible Navier‐Stokes equations in streamfunction and vorticity formulation. By using a Picard iteration, we use this technology to solve fully nonlinear Navier‐Stokes problems. The solvers which result scale very well with problem parameters. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011
ISSN:0749-159X
1098-2426
DOI:10.1002/num.20661