A shift-invert strategy for global flow instability analysis using matrix-free methods

J. M. Pérez, F. Gómez, H. M. Blackburn, Vassilis Theofilis

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearch

2 Citations (Scopus)

Abstract

A new time-stepping shift-invert algorithm for linear stability analysis of large-scale 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. Compared with the classical exponential method, the new approach has the advantage of converging to specific parts of the full global spectrum. Validations and comparisons to the exponential power method have been performed in three different cases: (i) the stenotic flow, (ii) the backward-facing step and (iii) the two-dimensional swirl flow. It is shown that, although the exponential method remains the method of choice if leading eigenvalues are sought, the present method can be competitive when access to specific parts of the full global spectrum is required. 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. 

Original languageEnglish
Title of host publication42nd AIAA Fluid Dynamics Conference and Exhibit 2012
Subtitle of host publication25-28 June, 2012, New Orleans, Louisiana [proceedings]
PublisherAmerican Institute of Aeronautics and Astronautics
Number of pages12
ISBN (Electronic)9781600869334
DOIs
Publication statusPublished - 2012
EventAIAA Fluid Dynamics Conference and Exhibit 2012 - New Orleans, United States of America
Duration: 25 Jun 201228 Jun 2012
Conference number: 42

Conference

ConferenceAIAA Fluid Dynamics Conference and Exhibit 2012
CountryUnited States of America
CityNew Orleans
Period25/06/1228/06/12

Cite this

Pérez, J. M., Gómez, F., Blackburn, H. M., & Theofilis, V. (2012). A shift-invert strategy for global flow instability analysis using matrix-free methods. In 42nd AIAA Fluid Dynamics Conference and Exhibit 2012: 25-28 June, 2012, New Orleans, Louisiana [proceedings] American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2012-3276