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%.

翻译：计算流体动力学（CFD）模拟是许多工程设计中不可或缺的建模步骤，但其计算成本通常较高。目前已有一些基于图神经网络（GNN）的CFD方法被提出。然而，现有方法继承了传统数值模拟器的缺陷，同时忽略了有限体积法（一种实际CFD应用中常见的方法）所使用网格中的单元特征。具体而言，这些GNN方法中的输入节点对模拟域内浸没物体及其周围环境的信息掌握极为有限。此外，网格的单元特征（如单元体积、面表面积和面质心）并未被纳入GNN方法的消息传递操作中。为克服这些不足，本文提出了两种新颖的几何表示方法：最短向量（SV）和定向积分距离（DID）。从网格中提取的SV和DID为每个输入节点提供了全局几何视角，从而无需通过消息传递来收集这类信息。本文还引入了在图表卷积中使用有限体积特征（FVF）作为节点和边的属性，使其消息传递操作能够适应不同节点。最后，本文首次展示了在低分辨率数据可用条件下，如何采用残差训练来提高流场预测精度。在两个数据集上针对五种不同最先进的GNN CFD方法进行的实验结果表明，SV、DID、FVF和残差训练可有效将当前基于GNN的方法的预测误差降低高达41%。