用神经网络提升流体模拟中界面清晰度，避免模糊失真。
Physics-Informed Neural Networks for Enhanced Interface Preservation in Lattice Boltzmann Multiphase Simulations
- 将物理约束神经网络嵌入格子玻尔兹曼方法，动态修正界面扩散。
- 界面宽度缩小47%，梯度峰值提升32%，相分离误差降低60%。
- 适合需要精确界面追踪的多相流模拟，如液滴变形、喷雾过程。
本文提出一种基于物理信息神经网络（PINNs）的改进方法，用于在多相格子玻尔兹曼方法（LBM）模拟中保持界面清晰度。界面扩散是多相LBM中的常见挑战，严重影响界面动力学关键现象的模拟精度。我们构建了耦合的PINN-LBM框架，在保持物理一致性的同时有效抑制数值扩散。通过液滴模拟验证，采用定量指标评估界面宽度、最大梯度、相分离程度、有效界面宽度及界面能。结果表明，该方法显著优于传统LBM：界面宽度平均缩小47%，最大梯度提升32%，相分离误差降低60%。可视化分析进一步凸显其在长时间模拟中维持清晰界面的能力。综合分析显示，神经网络成功补偿了数值扩散，同时与底层流体动力学保持一致。
原文摘要 · Abstract (English)
This paper presents an improved approach for preserving sharp interfaces in multiphase Lattice Boltzmann Method (LBM) simulations using Physics-Informed Neural Networks (PINNs). Interface diffusion is a common challenge in multiphase LBM, leading to reduced accuracy in simulating phenomena where interfacial dynamics are critical. We propose a coupled PINN-LBM framework that maintains interface sharpness while preserving the physical accuracy of the simulation. Our approach is validated through droplet simulations, with quantitative metrics measuring interface width, maximum gradient, phase separation, effective interface width, and interface energy. The enhanced visualization techniques employed in this work clearly demonstrate the superior performance of PINN-LBM over standard LBM for multiphase simulations, particularly in maintaining well-defined interfaces throughout the simulation. We provide a comprehensive analysis of the results, showcasing how the neural network integration effectively counteracts numerical diffusion, while maintaining physical consistency with the underlying fluid dynamics.
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