eprintid: 36553 rev_number: 14 eprint_status: archive userid: 1903 dir: disk0/00/03/65/53 datestamp: 2015-07-27 17:14:19 lastmod: 2019-05-31 16:44:40 status_changed: 2015-07-27 17:14:19 type: article metadata_visibility: show creators_name: Gómez Carrasco, Francisco creators_name: Pérez Pérez, José Miguel creators_name: Blackburn, Hugh M. creators_name: Theofilis, Vassilios title: On the Use of Matrix-Free Shift-Invert Strategies For Global Flow Instability Analysis rights: by-nc-nd ispublished: pub subjects: aeronautica full_text_status: public keywords: Global linear instability analysis, Large-scale eigenvalue problems, Krylov subspace, Jacobian-free methods abstract: A novel time-stepping shift-invert algorithm for linear stability analysis of laminar flows in complex geometries is presented. This method, based on a Krylov subspace iteration, enables the solution of complex non-symmetric eigenvalue problems in a matrix-free framework. Validations and comparisons to the classical exponential method have been performed in three different cases: (i) stenotic flow, (ii) backward-facing step and (iii) lid-driven swirling flow. Results show that this new approach speeds up the required Krylov subspace iterations and has the capability of converging to specific parts of the global spectrum. It is shown that, although the exponential method remains the method of choice if leading eigenvalues are sought, the performance of the present method could be dramatically improved with the use of a preconditioner. In addition, as opposed to other methods, this strategy can be directly applied to any time-stepper, regardless of the temporal or spatial discretization of the latter. date_type: published date: 2015-07 publication: Aerospace Science and Technology volume: 44 pagerange: 69-76 id_number: 10.1016/j.ast.2014.11.003 institution: Aeronauticos department: Motopropulsion refereed: TRUE issn: 1270-9638 official_url: http://www.sciencedirect.com/science/article/pii/S1270963814002284 referencetext: [1]D. Barkley, M. Grabiela, M. Gomes, R.D. Henderson, Three-dimensional instabil-ity in flow over a backward-facing step, J. Fluid Mech. 473 (2002) 167–190. [2]D. Barkley, H.M. Blackburn, S.J. Sherwin, Direct optimal growth analysis for timesteppers, Int. J.Num. Methods in Fluids 57 (2008) 1435–1458. [3]R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, V.E.J. Dongarra, R. Pozo, C. 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"Aerospace Science and Technology", v. 44 ; pp. 69-76. ISSN 1270-9638. https://doi.org/10.1016/j.ast.2014.11.003 . document_url: https://oa.upm.es/36553/1/INVE_MEM_2015_201017.pdf