Geometry-Aware Physics-Informed PointNets for Modeling Flows Across Porous Structures
This work addresses the problem of modeling complex porous flows for design studies in engineering, offering a method that generalizes across geometries without retraining, though it is incremental as it builds on existing physics-informed neural network approaches.
The paper tackled predicting flows through and around porous structures by developing Physics Informed PointNets (PIPN) and Physics Informed Geometry Aware Neural Operator (PI-GANO), which enforce fluid dynamics equations in a unified loss and condition on geometry and material parameters, resulting in consistently low velocity and pressure errors in both seen and unseen cases with accurate wake structure reproduction.
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.