Lagrangian large eddy simulations via physics-informed machine learning.

Area of Science:

• Computational Fluid Dynamics
• Turbulence Modeling
• Machine Learning Applications

Background:

• High-Reynolds number homogeneous isotropic turbulence (HIT) is governed by the Navier-Stokes (NS) equations, which are computationally challenging to solve.
• Traditional Large Eddy Simulation (LES) relies on Eulerian velocity fields and assumptions about subgrid-scale effects.
• A need exists for alternative turbulence modeling approaches that capture both Eulerian and Lagrangian flow characteristics.

Purpose of the Study:

• To develop a novel Lagrangian Large Eddy Simulation (L-LES) framework for modeling turbulence.
• To utilize Machine Learning (ML) for training and resolving L-LES equations based on direct numerical simulation (DNS) data.
• To incorporate physics-informed parameterization and neural networks for accurate turbulence evolution modeling.

Main Methods:

• Developed L-LES heuristics based on Lagrangian particle dynamics, generalizing smoothed particle hydrodynamics.
• Employed Machine Learning (ML) for training L-LES models using Lagrangian data from NS-DNS.
• Integrated physics-informed parameterization and neural networks within a differentiable programming framework.
• Utilized various loss functions, including physics-informed options, for efficient model training.

Main Results:

• The L-LES model successfully reproduced Eulerian and unique Lagrangian turbulence structures and statistics.
• The model demonstrated capability across a range of turbulent Mach numbers.
• Physics-informed ML training facilitated efficient and accurate turbulence evolution prediction.

Conclusions:

• L-LES offers a viable and accurate alternative to traditional Eulerian LES for turbulence simulation.
• The integration of Lagrangian methods with ML provides a powerful new tool for computational fluid dynamics.
• This physics-informed ML approach advances the modeling of subgrid-scale effects in turbulent flows.