用几何感知物理网络模拟多孔结构内外的流动,无需针对每种形状重新训练。
Geometry-Aware Physics-Informed PointNets for Modeling Flows Across Porous Structures
- 融合流体与多孔介质物理方程,统一损失函数中施加纳维-斯托克斯与达西-福煦赫方程
- 在2D和3D场景中对已见与未见几何均实现低误差流速与压力预测,准确复现尾流结构
- 适用于设计优化,支持不同边界条件与参数变化,显著减少重复建模成本
由于流体与多孔区域之间的耦合物理特性,以及需要在多样化几何与边界条件下泛化,预测穿过并绕过多孔体的流动极具挑战。本文采用两种物理信息学习方法:物理信息点网(PIPN)与物理信息几何感知神经算子(P-IGANO),在自由流区域强制满足不可压缩纳维-斯托克斯方程,在多孔区域采用达西-福煦赫扩展模型,并在统一损失函数中联合求解。数据集通过OpenFOAM生成,涵盖含多孔障碍物的2D管道与含树冠及建筑的3D防风场景。首先通过制造解法验证流程可靠性,随后评估对未见形状的泛化能力;对PI-GANO进一步测试变量边界条件与参数设置下的表现。结果表明,无论是否见过的几何,流速与压力误差均保持较低,尾流结构重现准确。性能主要在尖锐界面及大梯度区域下降。本研究首次系统评估了PIPN/PI-GANO在同时模拟穿流与绕流中的表现,展示了其在无需按几何重训的前提下加速设计研究的潜力。
原文摘要 · Abstract (English)
Predicting flows that occur both through and around porous bodies is challenging due to coupled physics across fluid and porous regions and the need to generalize across diverse geometries and boundary conditions. We address this problem using two Physics Informed learning approaches: Physics Informed PointNets (PIPN) and Physics Informed Geometry Aware Neural Operator (P-IGANO). We enforce the incompressible Navier Stokes equations in the free-flow region and a Darcy Forchheimer extension in the porous region within a unified loss and condition the networks on geometry and material parameters. Datasets are generated with OpenFOAM on 2D ducts containing porous obstacles and on 3D windbreak scenarios with tree canopies and buildings. We first verify the pipeline via the method of manufactured solutions, then assess generalization to unseen shapes, and for PI-GANO, to variable boundary conditions and parameter settings. The results show consistently low velocity and pressure errors in both seen and unseen cases, with accurate reproduction of the wake structures. Performance degrades primarily near sharp interfaces and in regions with large gradients. Overall, the study provides a first systematic evaluation of PIPN/PI-GANO for simultaneous through-and-around porous flows and shows their potential to accelerate design studies without retraining per geometry.
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