In recent years, the development of deep learning is noticeably influencing
the progress of computational fluid dynamics. Numerous researchers have
undertaken flow field predictions on a variety of grids, such as MAC grids,
structured grids, unstructured meshes, and pixel-based grids which have been
many works focused on. However, predicting unsteady flow fields on unstructured
meshes remains challenging. When employing graph neural networks (GNNs) for
these predictions, the message-passing mechanism can become inefficient,
especially with denser unstructured meshes. Furthermore, unsteady flow field
predictions often rely on autoregressive neural networks, which are susceptible
to error accumulation during extended predictions. In this study, we integrate
the traditional finite volume method to devise a spatial integration strategy
that enables the formulation of a physically constrained loss function. This
aims to counter the error accumulation that emerged in autoregressive neural
networks during long-term predictions. Concurrently, we merge vertex-center and
cell-center grids from the finite volume method, introducing a dual
message-passing mechanism within a single GNN layer to enhance the
message-passing efficiency. We benchmark our approach against MeshGraphnets for
unsteady flow field predictions on unstructured meshes. Our findings indicate
that the methodologies combined in this study significantly enhance the
precision of flow field predictions while substantially minimizing the training
time cost. We offer a comparative analysis of flow field predictions, focusing
on cylindrical, airfoil, and square column obstacles in two-dimensional
incompressible fluid dynamics scenarios. This analysis encompasses lift
coefficient, drag coefficient, and pressure coefficient distribution comparison
on the boundary layers