Sensitivity Analysis of Turbulent Flows Using Adjoint Stabilized March

Adjoint-based sensitivity analysis is of interest in computational science due to its ability to compute sensitivities at a lower cost with respect to several design parameters. However, conventional sensitivity analysis methods fail in the presence of chaotic flows. Popular approaches to chaotic sensitivity analysis involve solving a least-squares minimization problem to compute the shadowing direction, yielding a space-time linear system of equations. The stabilized march approach for adjoint-based chaotic sensitivity analysis involves solving a boundary value problem instead of the minimization problem. It has been proven in the past work that the sensitivities from the stabilized march approach converge to the true sensitivity for large integration times. However, the approach requires converged Lyapunov subspaces before running the algorithm. In this work, we propose a hybrid of the stabilized march and the non-intrusive least-squares shadowing. This approach uses the stabilized march for the subspaces that converge fast and least-squares shadowing for the slower converging modes.