Computation of evolution of Tollmein-Schlichten waves based on the global stability analysis

A computational methodology is presented for calculating spatial evolution of Tollmien-Schlichting waves and their amplitude growth-rate factor in substantially non-parallel compressible flows, based on a global stability analysis of stationary solutions of the full Navier-Stokes equations. Three stages of this methodology (obtaining a stationary solution, carrying out a global stability analysis and post-processing) are described, and results are presented of its validation based on the comparison of the results of calculating the characteristics of Tollmien-Schlichting waves on a flat plate with the corresponding results of the classical stability theory in the parallel approximation. An example of calculating the flow around a plate with a rectangular cavity is presented to illustrate the possibility of applying the proposed methodology to non-parallel flows.