Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

LBM-GNN: Graph Neural Network Enhanced Lattice Boltzmann Method

Yue Li

TL;DR

This work addresses the limited stability and accuracy of the Lattice Boltzmann Method (LBM) at high Reynolds numbers and on coarse grids. It introduces LBM-GNN, a hybrid approach that uses a Graph Neural Network to learn local adjustments to the relaxation time $\tau$ and to directly correct post-collision distributions $\Delta f_i$, integrated into the LBM collision step. Across Poiseuille flow and Taylor-Green vortex benchmarks, LBM-GNN demonstrates improved stability and better conservation (notably momentum) while maintaining or slightly improving accuracy, extending stable operation up to roughly $Re\approx3200$ on moderate grids with about a 7% computational overhead. This hybrid physics-ML method offers a practical route to more robust CFD simulations and sets the stage for 3D, multiphase, and control-aware extensions.

Abstract

In this paper, we present LBM-GNN, a novel approach that enhances the traditional Lattice Boltzmann Method (LBM) with Graph Neural Networks (GNNs). We apply this method to fluid dynamics simulations, demonstrating improved stability and accuracy compared to standard LBM implementations. The method is validated using benchmark problems such as the Taylor-Green vortex, focusing on accuracy, conservation properties, and performance across different Reynolds numbers and grid resolutions. Our results indicate that GNN-enhanced LBM can maintain better conservation properties while improving numerical stability at higher Reynolds numbers.

LBM-GNN: Graph Neural Network Enhanced Lattice Boltzmann Method

TL;DR

This work addresses the limited stability and accuracy of the Lattice Boltzmann Method (LBM) at high Reynolds numbers and on coarse grids. It introduces LBM-GNN, a hybrid approach that uses a Graph Neural Network to learn local adjustments to the relaxation time and to directly correct post-collision distributions , integrated into the LBM collision step. Across Poiseuille flow and Taylor-Green vortex benchmarks, LBM-GNN demonstrates improved stability and better conservation (notably momentum) while maintaining or slightly improving accuracy, extending stable operation up to roughly on moderate grids with about a 7% computational overhead. This hybrid physics-ML method offers a practical route to more robust CFD simulations and sets the stage for 3D, multiphase, and control-aware extensions.

Abstract

In this paper, we present LBM-GNN, a novel approach that enhances the traditional Lattice Boltzmann Method (LBM) with Graph Neural Networks (GNNs). We apply this method to fluid dynamics simulations, demonstrating improved stability and accuracy compared to standard LBM implementations. The method is validated using benchmark problems such as the Taylor-Green vortex, focusing on accuracy, conservation properties, and performance across different Reynolds numbers and grid resolutions. Our results indicate that GNN-enhanced LBM can maintain better conservation properties while improving numerical stability at higher Reynolds numbers.

Paper Structure

This paper contains 17 sections, 6 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Lattice Boltzmann Method
  4. Graph Neural Network Enhancement
  5. Integration of GNN with LBM
  6. GNN Architecture Details
  7. Training Methodology
  8. Implementation Details
  9. Validation
  10. Poiseuille Flow
  11. Analytical Solution
  12. Validation Results
  13. Taylor-Green Vortex Validation
  14. Resolution Study
  15. Reynolds Number Study
  16. ...and 2 more sections

Figures (10)

  • Figure 1: Integration of GNN with LBM. The GNN enhances the collision step by predicting optimized distribution functions based on pre-collision states and macroscopic variables.
  • Figure 2: Architecture of the SimpleLBMGNN model. The network processes distribution functions, density, and velocity through MLP layers to output relaxation parameter adjustments and direct corrections.
  • Figure 3: Poiseuille flow validation at Re=100. Both methods achieve good agreement with the analytical solution, with velocity error below 1%.
  • Figure 4: Error variation with Reynolds number for Poiseuille flow. The GNN-enhanced method shows slightly better performance at higher Reynolds numbers.
  • Figure 5: Error convergence with grid refinement for Poiseuille flow.
  • ...and 5 more figures