Pseudospectral numerical code for investigation of linear stability of plane supersonic jet

A numerical code for investigation of the linear stability of compressible jet flows based on the Fourier pseudospectral approximation of spatial derivatives is described. The algebraic eigenvalue problem resulting from the pseudospectral approximation coupled with a coordinate transform clustering grid points near the jet mixing layers is solved with the ZGEEV routine from the LAPACK library. Such a numerical approach allows us to determine multiple instability modes whose existence is characteristic of high-speed jet flows. The results are compared and verified with those are obtained with the local shooting method that calculates each eigenvalue separately starting from some initial guess and iteratively refining the value with Newton's method. The results of linear stability analysis are presented for the supersonic plane jet flow with a parallel coflow.