An extensible Benchmarking Graph-Mesh dataset for studying Steady-State Incompressible Navier-Stokes Equations
This provides a standardized dataset and evaluation protocol for researchers in geometric deep learning and computational fluid dynamics, though it is incremental as it builds on existing efforts.
The paper tackles the lack of benchmarking datasets for studying steady-state incompressible Navier-Stokes equations by proposing a 2-D graph-mesh dataset for airflow over airfoils at high Reynolds numbers and introducing metrics for evaluating geometric deep learning models on physical quantities.
Recent progress in \emph{Geometric Deep Learning} (GDL) has shown its potential to provide powerful data-driven models. This gives momentum to explore new methods for learning physical systems governed by \emph{Partial Differential Equations} (PDEs) from Graph-Mesh data. However, despite the efforts and recent achievements, several research directions remain unexplored and progress is still far from satisfying the physical requirements of real-world phenomena. One of the major impediments is the absence of benchmarking datasets and common physics evaluation protocols. In this paper, we propose a 2-D graph-mesh dataset to study the airflow over airfoils at high Reynolds regime (from $10^6$ and beyond). We also introduce metrics on the stress forces over the airfoil in order to evaluate GDL models on important physical quantities. Moreover, we provide extensive GDL baselines.