Direct sensitivity analysis for smooth unsteady compressible flows using complex differentiation

A method for the direct computation of the instantaneous sensitivities of unsteady compressible flows is proposed. It is based on the complex differentiation of the full compressible Navier-Stokes equations and does not require the storage of the unsteady flow solution to be differentiated. The method does not rely on any assumption on the basic Navier-Stokes solver, and can therefore be implemented in a straightforward way. The method is assessed on several cases, including a two-dimensional subsonic mixing layer. It is observed that the sensitivity patterns can be interpreted thanks to Kovasznay's decomposition for perturbations in a compressible flow.

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