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Computational fluid dynamics (CFD) simulation is an irreplaceable modellingstep in many engineering designs, but it is often computationally expensive.Some graph neural network (GNN)-based CFD methods have been proposed. However,the current methods inherit the weakness of traditional numerical simulators,as well as ignore the cell characteristics in the mesh used in the finitevolume method, a common method in practical CFD applications. Specifically, theinput nodes in these GNN methods have very limited information about any objectimmersed in the simulation domain and its surrounding environment. Also, thecell characteristics of the mesh such as cell volume, face surface area, andface centroid are not included in the message-passing operations in the GNNmethods. To address these weaknesses, this work proposes two novel geometricrepresentations: Shortest Vector (SV) and Directional Integrated Distance(DID). Extracted from the mesh, the SV and DID provide global geometryperspective to each input node, thus removing the need to collect thisinformation through message-passing. This work also introduces the use ofFinite Volume Features (FVF) in the graph convolutions as node and edgeattributes, enabling its message-passing operations to adjust to differentnodes. Finally, this work is the first to demonstrate how residual training,with the availability of low-resolution data, can be adopted to improve theflow field prediction accuracy. Experimental results on two datasets with fivedifferent state-of-the-art GNN methods for CFD indicate that SV, DID, FVF andresidual training can effectively reduce the predictive error of currentGNN-based methods by as much as 41%.

Finite Volume Features, Global Geometry Representations, and Residual Training for Deep Learning-based CFD Simulation