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A relaxation method for large eigenvalue problems, with an application to flow stability analysis. (English) Zbl 1379.76016

Summary: 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.

MSC:

76M22 Spectral methods applied to problems in fluid mechanics
76E99 Hydrodynamic stability
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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