Optimised flow control based on automatic differentiation in compressible turbulent channel flows

This study presents an automatic differentiation (AD)-based optimisation framework for flow control in compressible turbulent channel flows. Using a differentiable solver, JAX-Fluids, we designed fully differentiable boundary conditions that allow for the precise calculation of gradients with respect to boundary control variables. This facilitates the efficient optimisation of flow control methods. The framework’s adaptability and effectiveness are demonstrated using two boundary conditions: opposition control and tunable permeable walls. Various optimisation targets are evaluated, including wall friction and turbulent kinetic energy (TKE), across different time horizons. In each optimisation, there were around $4\times 10^4$ control variables and $3\times 10^{9}$ state variables in a single episode. Results indicate that TKE targeted opposition control achieves a more stable and significant reduction in drag, with effective suppression of turbulence throughout the channel. In contrast, strategies that focus directly on minimising wall friction were found to be less effective, exhibiting instability and increased turbulence in the outer region. The tunable permeable walls also show potential to achieve stable drag reduction through a ‘flux-inducing’ mechanism. This study demonstrates the advantages of AD-based optimisation in complex flow control scenarios and provides physical insight into the choice of the quantity of interest for improved optimisation performance.