Finite Volume Features, Global Geometry Representations, and Residual
  Training for Deep Learning-based CFD Simulation
Loh Sher En Jessica Naheed Anjum Arafat Wei Xian Lim Wai Lee Chan Adams Wai Kin Kong
Computational fluid dynamics (CFD) simulation is an irreplaceable modelling
step 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 finite
volume method, a common method in practical CFD applications. Specifically, the
input nodes in these GNN methods have very limited information about any object
immersed in the simulation domain and its surrounding environment. Also, the
cell characteristics of the mesh such as cell volume, face surface area, and
face centroid are not included in the message-passing operations in the GNN
methods. To address these weaknesses, this work proposes two novel geometric
representations: Shortest Vector (SV) and Directional Integrated Distance
(DID). Extracted from the mesh, the SV and DID provide global geometry
perspective to each input node, thus removing the need to collect this
information through message-passing. This work also introduces the use of
Finite Volume Features (FVF) in the graph convolutions as node and edge
attributes, enabling its message-passing operations to adjust to different
nodes. Finally, this work is the first to demonstrate how residual training,
with the availability of low-resolution data, can be adopted to improve the
flow field prediction accuracy. Experimental results on two datasets with five
different state-of-the-art GNN methods for CFD indicate that SV, DID, FVF and
residual training can effectively reduce the predictive error of current
GNN-based methods by as much as 41%.