  Data-driven modeling approaches can produce fast surrogates to study
large-scale physics problems. Among them, graph neural networks (GNNs) that
operate on mesh-based data are desirable because they possess inductive biases
that promote physical faithfulness, but hardware limitations have precluded
their application to large computational domains. We show that it is
\textit{possible} to train a class of GNN surrogates on 3D meshes. We scale
MeshGraphNets (MGN), a subclass of GNNs for mesh-based physics modeling, via
our domain decomposition approach to facilitate training that is mathematically
equivalent to training on the whole domain under certain conditions. With this,
we were able to train MGN on meshes with \textit{millions} of nodes to generate
computational fluid dynamics (CFD) simulations. Furthermore, we show how to
enhance MGN via higher-order numerical integration, which can reduce MGN's
error and training time. We validated our methods on an accompanying dataset of
3D $\text{CO}_2$-capture CFD simulations on a 3.1M-node mesh. This work
presents a practical path to scaling MGN for real-world applications.
