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A novel adjoint-based framework oriented to optimal flow control incompressible direct numerical simulations is presented. Also, a new formulationof the adjoint characteristic boundary conditions is introduced, which enhancesthe stability of the adjoint simulations. The flow configuration chosen as acase study consists of a two dimensional open cavity flow with aspect ratio$L/H=3$ and Reynolds number $Re=5000$. This flow configuration is of particularinterest, as the turbulent and chaotic nature of separated flows pushes theadjoint approach to its limit. The target of the flow actuation, defined ascost, is the reduction of the pressure fluctuations at the sensor location. Toexploit the advantages of the adjoint method, a large number of controlparameters is used. The control consists of an actuating sub-domain where atwo-dimensional body force is applied at every point within the sub-volume.This results in a total of $2.256 \cdot 10^6$ control parameters. The finalactuation achieved a successful reduction of the cost of $79.6\%$, by alteringthe directivity of the sound radiated by the trailing edge of the cavity andbreaking up the large shear layer instabilities into smaller structures.

Adjoint-based Optimal Flow Control for Compressible DNS