Permeable materials are a promising trailing edge noise reduction technique. The noise reduction is a result of the unsteady interaction between the two communicating boundary layers, in a process referred to as the pressure release mechanism. However, in practice the aeroacoustic performance of permeable trailing edges degrades under lifting conditions, i.e. with a pressure and velocity differential. This study aims at investigating such flow physics using the Lattice Boltzmann Method through 3DS Power FLOW. A numerical setup was created to explore the impact of velocity and pressure differentials between two communicating boundary layers and relate them to the aeroacoustic performance of porous media. The proposed numerical setup consists of two vertically stacked temporally developing channel flows separated by a porous medium (6δ × (4δ + t) × 2 δ), where δ and t are the half-channel height and the porous medium thickness respectively. The two channel flows communicate through fully resolved porous media, here, 75% porous triply periodic minimal surfaces. A large drag increase is observed for all geometries. An increase in anti-correlation between the pressure fluctuations between the channels is found to be related to a drag increase. It was concluded that the spanwise coherent turbulent structures drive the increase in drag. These structures are also affected by the geometry of the porous medium at the surface of the grazing flows. The presence of large coherent turbulent structures leads to a shift in turbulent energy scales. This is related to the modification of the wall pressure spectrum, where it was observed that less energy is present at low frequencies, whereas a peak was observed at a higher frequency. The crossover frequency is between 150Hz and 600Hz.

Numerical simulations and optimisation methods, such as mesh adaptation, rely on the accurate and inexpensive use of error estimation methods. Adjoint-based error estimation is the most accurate method, and generally the most costly. A strong contributor to this cost is the need to compute a higher resolution adjoint solution. Here, it is proposed to use super-resolution neural networks to super-resolve a fine adjoint solution from a lower-cost coarse adjoint solution: a superAdjoint. The method is compared to reference error estimators on an unsteady Burgers’ equation using the method of manufactured solutions. Two forms of the superAdjoint were implemented, a twice and a four times refining super-resolution neural network. These were used to demonstrate both the computational cost reduction and the potential for the reduction of the storage footprint of the primal problem. The first, referred to as 2×CNN, was able to reconstruct the spatially enriched adjoint solution, thus providing a robust and inexpensive local output error. The second, the 4×CNN, was able to demonstrate the reconstruction ability of super-resolution neural networks for higher upscaling factors. This was leveraged in order to subsample the primal solution in space, thus reducing substantially the storage footprint of the discrete primal solution. Both superAdjoints could achieve the desired level of accuracy when compared to the reconstruction of the refined adjoint-based error estimate. Moreover, superAdjoint was shown to be able to generalise to a new QoI that was untrained for. This gives great confidence in the use of super-resolution neural networks for the reduction of both computational cost and storage requirements of adjoint-based error estimation, and goal-oriented mesh adaptation.