TY  - JOUR
KW  - Global linear instability analysis
KW  -  Large-scale eigenvalue problems
KW  -  Krylov subspace
KW  -  Jacobian-free methods
Y1  - 2015/07//
VL  - 44
EP  - 76
SN  - 1270-9638
N2  - 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.
TI  - On the Use of Matrix-Free Shift-Invert Strategies For Global Flow Instability Analysis
ID  - upm36553
JF  - Aerospace Science and Technology
SP  - 69
A1  - Gómez Carrasco, Francisco
A1  - Pérez Pérez, José Miguel
A1  - Blackburn, Hugh M.
A1  - Theofilis, Vassilios
AV  - public
UR  - http://www.sciencedirect.com/science/article/pii/S1270963814002284
ER  -