Using LSTM to Replace Traditional Turbulence Models: A New Data-Driven RANS Correction Method

This project proposes a Reynolds shear stress prediction pipeline based on LSTM neural networks. Through physically inspired synthetic datasets and systematic ablation experiments, it verifies the superiority of sequence modeling in capturing the wall-normal structure of turbulence, opening up a new path for data-driven turbulence modeling.

The project reproduces and extends the research of Pasinato (2024), constructs a structured machine learning pipeline, and shows significant accuracy improvements compared to traditional RANS models.

Turbulence is an unsolved problem in classical physics. Reynolds-Averaged Navier-Stokes (RANS) equations are widely used in engineering, but due to the need for turbulence models to close the Reynolds stress term, traditional models such as k-ε and k-ω lack accuracy in complex flows like separated flows and rotating flows.

Machine learning (especially deep learning) provides new ideas to solve this problem. This project is based on the pioneering work of Pasinato (2024) to explore the application of LSTM in turbulence modeling.

The project aims to predict the wall-normal Reynolds shear stress profile. Input features include mean flow field distribution, turbulent kinetic energy (k), dissipation rate (ε), and spatial position coordinates, etc., with the output being the Reynolds shear stress distribution.

Three models are compared: linear baseline (traditional simplified approach), multi-layer perceptron (MLP, nonlinear but no sequence modeling), and LSTM (gated mechanism to capture spatiotemporal dependencies). Key findings: LSTM is significantly superior to non-sequential models, with higher accuracy near the wall and good generalization ability.

The dataset adopts a physically inspired synthetic strategy: using high-fidelity Direct Numerical Simulation (DNS) data as labels, covering various conditions through parameterized flows, and expanding samples via data augmentation to ensure physical consistency and diversity.

Ablation experiments evaluate the impact of features, architecture, and training strategies: wall-normal distance is the most critical feature, 2-3 layers of LSTM yield the best results, and adding physical constraints can improve generalization ability.

Quantitative indicators show that the prediction error of LSTM is significantly lower than traditional models such as k-ε and SST k-ω, with a correlation coefficient exceeding 0.95 and a 30-50% reduction in wall shear stress error.

In qualitative analysis, LSTM accurately predicts the logarithmic region of the velocity profile, performs better than traditional models in separated flow/reattachment regions, and better captures the statistical characteristics of turbulence intensity.

Current limitations: dependence on high-cost DNS data, unvalidated generalization to extreme conditions, potential violation of physical constraints, and need for improved computational efficiency.

Future directions: transfer learning to adapt to new working conditions, adding physical constraints via Physics-Informed Neural Networks (PINN), multi-scale modeling combined with Large Eddy Simulation (LES), uncertainty quantification, and geometric generalization.

This project represents the direction of data-driven turbulence modeling, integrating physics and machine learning. For the CFD community: in the short term, it provides a high-precision alternative model; in the medium term, it serves as a RANS correction term; in the long term, the goal is a general turbulence neural network.

For the ML community: it tests the ability to handle high-dimensional nonlinear problems. The physics-informed machine learning methodology is an important trend in the scientific computing field, promoting the integration of the two to solve complex system problems.