Turbulence Modeling supported by Statistical Machine Learning Models

Turbulence modeling is an important area of study within the fluid dynamics community. Recent advances in computational power, particularly with the development of GPUs and TPUs, have led to the emergence of Machine Learning and Deep Learning techniques as valuable tools for modeling turbulence at different stages: (i) enhancing RANS models, (ii) creating new wall models, (iii) contributing to flow control, and (iv) generating instantaneous turbulent flow fields, to cite a few. The presentation will tackle two of these challenges. The first is developing a data-driven wall model in the context of wall-modeled Large Eddy Simulations (wmLES) of turbulent separated flows. To address the instantaneous and non-equilibrium separation phenomenon, the Mixture Density Network (MDN), the neural network implementation of a Gaussian Mixture Model initially used for uncertainty prediction, is employed as the wall shear stress model. The second challenge focuses on enhancing turbulence injection methods. According to Dhamankar et al. (2015), the developed method should be memory-efficient, suitable for various flow problems, and incorporate known information about turbulence without introducing spurious low-frequency oscillations or unrealistic inflow characteristics. The generated turbulence should develop as quickly as possible after the inlet. To address this challenge, diffusion probabilistic models (DDPM) and score-based models, known to be powerful tools for generating high-quality samples while being straightforward to define and efficient to train, are selected to reproduce Decaying Homogeneous Turbulent Turbulence (DHIT) samples.