  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.
