Efficient Temporal Prediction of Compressible Flows in Irregular Domains Using Fourier Neural Operators

This paper investigates the temporal evolution of high-speed compressible fluids governed by the two-dimensional Euler equations in irregular flow fields using the Fourier Neural Operator (FNO). We reconstruct the irregular flow field point set into sequential format compatible with FNO input requirements, and then embed temporal bundling technique within a recurrent neural network (RNN) for multi-step prediction. We further employ a composite loss function to balance errors across different physical quantities. Experiments are conducted on three different types of irregular flow fields, including orthogonal and non-orthogonal grid configurations. Then we comprehensively analyze the physical component loss curves, flow field visualizations, and physical profiles. On non-orthogonal grids, our method consistently achieves improvements in both computational efficiency and error compared to other baseline models. Results demonstrate that our approach achieves high accuracy, as evidenced by maximum relative L2 errors of (0.75%,0.56%,0.35%) for (p,T,∥u∥) respectively (where p, T, and ∥u∥ denote pressure, temperature, and velocity magnitude), and offers substantial improvements in computational efficiency over traditional numerical methods. Within this data-driven context, the method accurately and efficiently simulates the temporal evolution of high-speed compressible flows in irregular domains.