Finite Volume Graph Network(FVGN): Predicting unsteady incompressible fluid dynamics with finite volume informed neural network

TL;DR

This paper introduces a finite volume informed graph neural network that improves unsteady incompressible fluid flow predictions, especially near boundaries, by integrating physical constraints and a novel aggregation mechanism, achieving better accuracy with less training.

Contribution

It presents a novel GNN model incorporating finite volume methods and a twice-massage aggregation mechanism for improved accuracy and efficiency in unsteady flow prediction.

Findings

Enhanced boundary layer flow prediction accuracy.

Reduced training time compared to fully data-driven models.

Improved geometric shape generalization ability.

Abstract

The rapid development of deep learning has significant implications for the advancement of Computational Fluid Dynamics (CFD). Currently, most pixel-grid-based deep learning methods for flow field prediction exhibit significantly reduced accuracy in predicting boundary layer flows and poor adaptability to geometric shapes. Although Graph Neural Network (GNN) models for unstructured grids based unsteady flow prediction have better geometric adaptability, these models suffer from error accumulation in long-term predictions of unsteady flows. More importantly, fully data-driven models often require extensive training time, greatly limiting the rapid update and iteration speed of deep learning models when facing more complex unsteady flows. Therefore, this paper aims to balance the demands for training overhead and prediction accuracy by integrating physical constraints based on the finite volume method into the loss function of the graph neural network. Additionally, it incorporates a twice-massage aggregation mechanism inspired by the extended stencil method to enhance the unsteady flow prediction accuracy and geometric shape generalization ability of the graph neural network model on unstructured grids. We focus particularly on the model's predictive accuracy within the boundary layer. Compared to fully data-driven methods, our model achieves better predictive accuracy and geometric shape generalization ability in a shorter training time.