Physics-Informed Neural Network Surrogate Modeling Approach of Active/Passive Flow Control for Drag Reduction

This paper presents a novel surrogate modeling method with physics constraints that is specifically designed for optimal design in flow control systems. The governing partial differential equations describing these flows are presented, considering a simplified fluid confined within a channel bounded by two parallel walls. Boundary conditions and flow control are introduced through geometric grooves and transpiration effects. The discretization of the governing equations and boundary conditions is also discussed. For numerical simulations, a Galerkin-based PDE solver is employed, utilizing spectral methods. The separation of Fourier components results in a system of ordinary differential equations for the modal functions. The effectiveness of transpiration in inducing flow control is evaluated by comparing the computed values with the reference pressure gradient required to drive the flow in the channel without transpiration. Data for the physics-informed neural network optimization is sampled using the Latin hypercube sampling method. The dataset, generated by direct numerical simulation, is divided into training and validation datasets. A deep neural network, consisting of multiple hidden layers, is utilized for constructing the surrogate model. The optimization process involves the use of Genetic Algorithms to search for acceptable local optimal values. The integration of GAs with the surrogate model involves several steps. Numerical experiments are conducted to validate the effectiveness of the PINN-based surrogate model approach. The results demonstrate an average acceptable error when comparing the test dataset with the predictions of the PINN surrogate model. Furthermore, the effectiveness of the proposed approach is demonstrated through a comparison between the results obtained from direct numerical simulation (DNS) and the predictions generated by the surrogate model. This comparative analysis serves to validate the accuracy and reliability of the surrogate model in capturing the key characteristics and behaviors of the flow control system.