Geometry-Aware Physics-Informed PointNets for Modeling Flows Across Porous Structures

TL;DR

This paper introduces geometry-aware physics-informed neural networks for modeling complex flows through porous structures, demonstrating accurate predictions across diverse geometries and boundary conditions with potential for accelerating design processes.

Contribution

The paper presents novel physics-informed neural network architectures, PIPN and P-IGANO, that unify fluid and porous flow physics and generalize across geometries and parameters.

Findings

Low velocity and pressure errors in seen and unseen cases

Accurate wake structure reproduction

Performance degradation near sharp interfaces

Abstract

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.