Print Email Facebook Twitter Combining the Augmented Lagrangian Preconditioner withe the SIMPLE Schur Complement Approximation Title Combining the Augmented Lagrangian Preconditioner withe the SIMPLE Schur Complement Approximation Author He, X. (Chinese Academy of Sciences) Vuik, Cornelis (TU Delft Numerical Analysis) Klaij, Christiaan M. (Maritime Research Institute Netherlands (MARIN)) Date 2018 Abstract The augmented Lagrangian (AL) preconditioner and its variant have been successfully applied to solve saddle point systems arising from the incompressible Navier-Stokes equations discretized by the finite element method. Attractive features are the purely algebraic construction and robustness with respect to the Reynolds number and mesh renement. In this report, we reconsider the application of the AL preconditioner in the context of the stabilized finite volume methods and present the extension to the Reynolds-Averaged Navier-Stokes (RANS) equations, which are used to model turbulent flows in industrial applications. Furthermore, we propose a new variant of the AL preconditioner, obtained by substituting the approximation of the Schur complement from the SIMPLE preconditioner into the inverse of the Schur complement for the AL preconditioner. This new variant is applied to both Navier-Stokes and RANS equations to compute laminar and turbulent boundary-layer flows on grids with large aspect ratios. Spectral analysis shows that the new variant yields a more clustered spectrum of eigenvalues away from zero, which explains why it outperforms the existing variants in terms of the number of the Krylov subspace iterations. Subject Reynolds-Averaged Navier-Stokes equationsfinite volume methodblock structured preconditioneraugmented Lagrangian preconditionerSIMPLE precondition To reference this document use: http://resolver.tudelft.nl/uuid:c030d13e-6efb-47a7-bdb9-6a84522bcc44 DOI https://doi.org/10.1137/17M1144775 ISSN 1064-8275 Source SIAM Journal on Scientific Computing, 40 (3), 1362-1385 Bibliographical note Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. Part of collection Institutional Repository Document type journal article Rights © 2018 X. He, Cornelis Vuik, Christiaan M. Klaij Files PDF 17m1144775.pdf 1.18 MB Close viewer /islandora/object/uuid:c030d13e-6efb-47a7-bdb9-6a84522bcc44/datastream/OBJ/view