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

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.