Numerical method for adjoint global stability analysis of compressible flows based on matrix-free approach

A numerical method for three-dimensional adjoint global linear stability analysis of compressible flows was developed. The compressible adjoint Navier-Stokes equations were derived. The developed method solves the adjoint stability problems using a time-stepping method which is a matrix-free approach. Because of the low memory requirement of the matrix-free approach, the developed method can analyze three-dimensional flows. The method was applied to a flow field around a two-dimensional cylinder and a three-dimensional cubic lid-driven cavity flow. Sensitivity regions of the flow fields were calculated using the direct and adjoint global modes. We confirmed that numerical and experimental results reported by the previous studies were precisely reproduced by the developed method.