Efficient computation of global resolvent modes

Resolvent analysis of the linearized Navier-Stokes equations provides useful insight into dynamics transitional and turbulent flows can provide a model for dominant coherent structures within flow, particularly with large gain separation. Direct computation force response modes using singular value decomposition full resolvent matrix is feasible only simple problems; despite recent progress, cost complex remains considerable. In this paper, we propose new matrix-free method computing based on integration corresponding adjoint system in time domain. Our approach achieves an order magnitude speedup when compared to previous stepping methods by enabling all frequencies interest be computed simultaneously. Two different are presented: one transient response, providing leading fine frequency discretization; another steady-state periodic forcing, optimal suboptimal discrete set frequencies. The validated Ginzburg-Landau equation applied three dimensional flow around parabolic body.