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

X. Garnaud; L. Lesshafft; P. J. Schmid; J. M. Chomaz

doi:10.1016/j.jcp.2012.01.038

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

X. Garnaud, L. Lesshafft, P. J. Schmid, J. M. Chomaz

Laboratoire d'Hydrodynamique de l'Ecole Polytechnique

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	3912-3927
Number of pages	16
Journal	Journal of Computational Physics
Volume	231
Issue number	10
DOIs	https://doi.org/10.1016/j.jcp.2012.01.038
Publication status	Published - 20 May 2012

Keywords

Eigenvalue solver
Global modes
Krylov method
Matrix-free
Spectral transformation

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10.1016/j.jcp.2012.01.038

Cite this

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

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.",

keywords = "Eigenvalue solver, Global modes, Krylov method, Matrix-free, Spectral transformation",

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AU - Garnaud, X.

AU - Lesshafft, L.

AU - Schmid, P. J.

AU - Chomaz, J. M.

PY - 2012/5/20

Y1 - 2012/5/20

N2 - 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.

AB - 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.

KW - Eigenvalue solver

KW - Global modes

KW - Krylov method

KW - Matrix-free

KW - Spectral transformation

U2 - 10.1016/j.jcp.2012.01.038

DO - 10.1016/j.jcp.2012.01.038

M3 - Article

AN - SCOPUS:84858746563

SN - 0021-9991

VL - 231

SP - 3912

EP - 3927

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 10

ER -

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

Abstract

Keywords

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