TY - JOUR
T1 - On the use of matrix-free shift-invert strategies for global flow instability analysis
AU - Gomez Carrasco, Francisco Jose
AU - Perez, Jose Miguel
AU - Blackburn, Hugh Maurice
AU - Theofilis, Vassilios
PY - 2015
Y1 - 2015
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.
AB - 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.
UR - http://www.sciencedirect.com/science/article/pii/S1270963814002284/pdfft?md5=0d6cd0344262d1849be2df314ff6a4bd&pid=1-s2.0-S1270963814002284-main.pdf
U2 - 10.1016/j.ast.2014.11.003
DO - 10.1016/j.ast.2014.11.003
M3 - Article
VL - 44
SP - 69
EP - 76
JO - Aerospace Science and Technology
JF - Aerospace Science and Technology
SN - 1270-9638
ER -