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The rapid development of deep learning has significant implications for the advancement of computational fluid dynamics. 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 models for unstructured grid-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-message 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. [ABSTRACT FROM AUTHOR]

Understanding the aerodynamic hysteresis loop phenomenon is essential when assessing aerodynamic performance and designing aircraft control systems. This phenomenon is a result of time delay effects in unsteady flow. Traditional methods of predicting unsteady aerodynamic forces using computational fluid dynamics have drawbacks, such as long cycles and low efficiency. In this paper, we focus on predicting the aerodynamic hysteresis loop of the NACA (National Advisory Committee for Aeronautics) 0012 airfoil in transonic flow using a new model called LIDNN (Latin hypercube sample input deep neural network). This model integrates input signals and optimization methods to improve upon traditional neural network models. Based on the example validation, the LIDNN model is authenticated as an accurate and efficient method in predicting the unsteady aerodynamic hysteresis loop of the NACA 0012 airfoil in transonic flow, and another significant advantage of the proposed model is its ability to solve multivariable problems effectively, even under varying Mach numbers. [ABSTRACT FROM AUTHOR]