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

Xavier Garnaud (1) , Lutz Lesshafft (1) , Peter Schmid (1) , Jean-Marc Chomaz (1)

1 LadHyX - Laboratoire d'hydrodynamique

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.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Xavier Garnaud, Lutz Lesshafft, Peter Schmid, Jean-Marc Chomaz. A relaxation method for large eigenvalue problems, with an application to flow stability analysis. Journal of Computational Physics, 2012, 231, pp.3912-3927. ⟨10.1016/j.jcp.2012.01.038⟩. ⟨hal-00716681⟩