A relaxation method for large eigenvalue problems, with an application to flow stability analysis

Authors:
X. Garnaud;L. Lesshafft;P. J. Schmid;J. -M. Chomaz
Affiliations:
Laboratoire d'Hydrodynamique, Ecole Polytechnique - CNRS, Palaiseau, France;Laboratoire d'Hydrodynamique, Ecole Polytechnique - CNRS, Palaiseau, France;Laboratoire d'Hydrodynamique, Ecole Polytechnique - CNRS, Palaiseau, France;Laboratoire d'Hydrodynamique, Ecole Polytechnique - CNRS, Palaiseau, France
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

Linear stability analysis of fluid flows usually involves the numerical solution of large eigenvalue problems. We present a spectral transformation allowing the computation of the least stable eigenmodes in a prescribed frequency range, based on the filtering of the linearized equations of motion. This ''shift-relax'' method has the advantage of low memory requirements and is therefore suitable for large two- or three-dimensional problems. For demonstration purposes, this new method is applied to compute eigenmodes of a compressible jet.