用图神经网络增强格子玻尔兹曼方法，提升流体模拟的稳定性与精度。
LBM-GNN: Graph Neural Network Enhanced Lattice Boltzmann Method
- 将GNN嵌入格子玻尔兹曼方法，通过图结构建模流体粒子交互
- 在不同雷诺数和网格下，数值稳定性显著提升，守恒性更好
- 适合需要高精度流体仿真的工程与科学计算场景
本文提出LBM-GNN，一种将图神经网络（GNN）融入传统格子玻尔兹曼方法（LBM）的新方法。该方法应用于流体动力学模拟，在泰勒-格林涡等基准问题上验证了其优越性。实验表明，相比标准LBM，该方法在不同雷诺数和网格分辨率下均表现出更优的数值稳定性和守恒性。尤其在高雷诺数条件下，仍能保持良好的计算稳定性，且能量与动量守恒性能更佳。结果证明，GNN的引入有效提升了LBM在复杂流动模拟中的鲁棒性与精度。
原文摘要 · Abstract (English)
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.
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