Direct optimal growth analysis for timesteppers

TLDR

Transient growth analysis of flows with arbitrary geometric complexity is presented, allowing for streamwise‑varying flows and emphasizing global effects from localized convective stability. The method modifies a nonlinear Navier–Stokes solver to generate forward and adjoint linearized evolution operators, detailing the primitive‑variable formulation and the inner code changes and outer eigenvalue/SVD algorithms. Illustrative examples demonstrate the technique and offer practical guidance for large‑scale stability analysis. © 2008 John Wiley & Sons, Ltd.

Abstract

Abstract Methods are described for transient growth analysis of flows with arbitrary geometric complexity, where in particular the flow is not required to vary slowly in the streamwise direction. Emphasis is on capturing the global effects arising from localized convective stability in streamwise‐varying flows. The methods employ the ‘timestepper's approach’ in which a nonlinear Navier–Stokes code is modified to provide evolution operators for both the forward and adjoint linearized equations. First, the underlying mathematical treatment in primitive flow variables is presented. Then, details are given for the inner level code modifications and outer level eigenvalue and SVD algorithms in the timestepper's approach. Finally, some examples are shown and guidance provided on practical aspects of this type of large‐scale stability analysis. Copyright © 2008 John Wiley & Sons, Ltd.