Enhancing Wall-Bounded Turbulence Simulation through Differentiable Neural Wall Modeling*

Efficiently simulating complex turbulence at high Reynolds numbers is crucial for numerous engineering applications. Accurate reconstruction of near-wall flow features is of paramount importance to effectively simulate wall-bounded turbulence. Wall-Modeled Large Eddy Simulation (WMLES) offers an efficient alternative to Wall-Resolved Large Eddy Simulation (WRLES) and Direct Numerical Simulation (DNS), especially for high Reynolds numbers. However, the traditional equilibrium wall-stress model, based on the algebraic log law, lacks accuracy for non-equilibrium flows. Recent advances in Deep Neural Networks (DNNs) provide an opportunity for a more generalized wall model. In this study, we propose the development of a differentiable neural solver inspired by WMLES. By seamlessly integrating sequential neural networks with a differentiable Computational Fluid Dynamics (CFD) solver, we aim to effectively learn turbulent wall-bounded flows across various conditions. The proposed models will be trained using a posterior metric to ensure accurate a posteriori predictions. Through comparisons with purely data-driven models and conventional WMLES, our proposed method demonstrates advantages in terms of efficiency and generalizability.