A point cloud-based mesh-independent convolutional neural network frameworks for flow field prediction on variable geometries

Abstract

Despite advancements in high-performance computing and numerical algorithms, Computational Fluid Dynamics (CFD) remains challenging for practical real-time applications, particularly in analysis and design tasks such as digital twin implementations. While traditional Reduced-Order Methods offer efficient and accurate predictions of entire flow fields, autoencoder Convolutional Neural Networks (CNNs) have demonstrated success in reconstructing CFD solutions due to their exceptional local feature extraction capabilities and scalability. However, their applicability is constrained to simple geometries because of the reliance on Cartesian or pixel-like grid structures. In this study, we propose a novel Point-based U-Net (PointUNet) framework incorporating Local Point Encoding (LPE) as a mesh-independent autoencoder model. The key functionality of LPE lies in its ability to transform point cloud data into a standard input array for conventional CNNs using a Virtual Reference Grid. This approach avoids data loss typically associated with interpolation or extrapolation, enabling greater flexibility in mesh generation and complex geometry handling. Verification was conducted using airfoil flows at transonic speeds and cylinder flows at low Reynolds numbers with various cross-sectional shapes, achieving minimal verification errors. The results were compared directly with other point cloud methods, demonstrating superior accuracy and efficiency in predicting highly nonlinear flows involving separation and shock waves, showing better agreement with full-order CFD solutions.