Adaptive-Mesh Optimizations for Scale-Resolving Simulations using Dynamic Closures

We present a data-driven approach for computing adjoint-based sensitivities in scale-resolving turbulent simulations. Scale-resolving simulations such as direct numerical simulations (DNS) and large-eddy simulations (LES) are much more computationally expensive than steady models, such as Reynolds-averaged Navier-Stokes (RANS). Each scale-resolving evaluation of a quantity of interest, often a statistical time-average, requires orders of magnitude more computational time and resources than in steady-state. This cost limits the applicability of unsteady simulations to many-query studies, such as shape optimization and mesh adaptation for numerical error control. Furthermore, unsteady adjoints, already an expensive proposition, cannot be directly applied to scale-resolving problems due to their chaotic nature. Our sensitivity-calculation approach does not use unsteady adjoint equations but instead relies on unsteady data to train a corrected turbulence model, which then yields the required adjoint solutions. It is non-intrusive and inexpensive, requiring only a small number of unsteady forward simulations, but sufficiently powerful to capture unsteady effects in the sensitivities. Results for high-order discretizations of the unsteady Navier-Stokes equations, augmented by a corrected Spalart-Allmaras turbulence closure, demonstrate the ability of the approach in driving aerodynamic shape optimization in turbulent-flow conditions, and in adapting unsteady flowfields to target statistical outputs of interest.