Turbulence Modeling and Simulation in Fluid Dynamics

Turbulent flows are characterised by chaotic, multiscale motion that profoundly influences engineering, geophysical and biological systems. Direct numerical simulation (DNS) resolves all relevant scales but is feasible only at low Reynolds numbers. Reynolds-averaged Navier–Stokes (RANS) approaches model the effect of unresolved fluctuations through turbulence closures, allowing rapid engineering predictions but sometimes lacking fidelity in complex flows. Large-eddy simulation (LES) strikes a balance by directly resolving large eddies while modelling sub-grid scales, offering enhanced accuracy at increased computational cost. Hybrid RANS/LES and advanced wall-modelling techniques further extend applicability to high-Reynolds-number external aerodynamics, turbomachinery and atmospheric boundary layers. Recent advances leverage data-driven methods, physics-infused neural networks and multi-agent reinforcement learning to discover closure models from high-fidelity data. These developments are transforming aerodynamic design, weather forecasting and energy-system optimisation by combining physical insight with machine-learning adaptability, and by reducing the cost of resolving near-wall dynamics and complex separation phenomena.

Research from Nature Portfolio

Scientific multi-agent reinforcement learning has been introduced for LES wall models, in which discretisation points act as cooperative agents learning closure behaviour from limited data. This approach generalises to extreme Reynolds numbers and novel geometries, reproducing key flow statistics with orders-of-magnitude lower cost than fully resolved simulations. By enabling agents to self-learn near-wall dynamics without heavy supervision, this framework offers unprecedented fidelity for aerodynamic design and large-scale environmental modelling while retaining computational efficiency.

Turbulence Modeling and Simulation in Fluid Dynamics publication trend

The graph below shows the total number of articles in turbulence modeling and simulation in fluid dynamics across all publications each year (not limited to Nature Index journals).

Technical terms

Turbulence: Chaotic fluid motion with energy transfer across a wide range of length and time scales.

Reynolds-averaged Navier–Stokes (RANS): A modelling approach that averages the Navier–Stokes equations in time or ensemble, introducing closures for Reynolds stresses.

Large-eddy Simulation (LES): A method that directly resolves large turbulent structures while modelling smaller scales via sub-grid-scale models.

Direct Numerical Simulation (DNS): Full resolution of all turbulent scales, requiring extremely fine spatial and temporal discretisation.

Wall model: A reduced-order representation of near-wall turbulence that lessens computational cost in high-Reynolds-number LES.

Sub-grid-scale (SGS) model: A closure for unresolved turbulent motions in LES, often based on eddy viscosity or data-driven approaches.

Reinforcement learning: A machine-learning paradigm in which agents learn optimal actions by interacting with a simulated environment.

Galilean invariance: The requirement that model predictions remain unchanged under uniform translations of the reference frame.

References

1. Application of artificial intelligence in turbomachinery aerodynamics: progresses and challenges. Artificial Intelligence Review (2024).
2. Prediction of concentrated vortex aerodynamics: Current CFD capability survey. Progress in Aerospace Sciences (2024).
3. Invariance embedded physics-infused deep neural network-based sub-grid scale models for turbulent flows. Engineering Applications of Artificial Intelligence (2024).
4. Large-eddy simulation: Past, present and the future. Chinese Journal of Aeronautics (2015).
5. The State of the Art of Hybrid RANS/LES Modeling for the Simulation of Turbulent Flows. Flow, Turbulence and Combustion (2017).
6. Scientific multi-agent reinforcement learning for wall-models of turbulent flows. Nature Communications (2022).