Grid- and geometry-independent AI-CFD Acceleration for unsteady flow calculation

Abstract

Conventional computational fluid dynamics (CFD) requires substantial computational cost to resolve unsteady flows, and most AI-CFD models developed for acceleration re- main strongly grid dependent. In particular, image-based convolutional neural networks and the original Tier System (TS) are essentially restricted to structured grids and specific geometries, which limits their applicability to practical engineering meshes. To alleviate this limitation, this study proposes a Directional Tier System (DTS) that extends the TS concept to unstructured and mixed grids by incorporating local directional components and inter-cell distances into the data representation. DTS is combined with a residual- based multi-layer perceptron framework built on a finite-volume perspective, so that the network learns the nonlinear mapping between successive flow fields while being moni- tored by continuity and momentum residuals. First, the predictive capability of DTS is validated against the original TS under identical mean-squared-error (MSE) training conditions using a counterflow test case. The results show that DTS reproduces almost the same loss convergence and spatial error distributions as TS on both structured and unstructured grids, confirming that the proposed representation does not degrade the baseline accuracy. Next, the AI-CFD model is evaluated in terms of grid-, geometry-, and topology-invariant behavior. Through counterflow cases with varying resolutions and mixed (tri–quad) meshes, DTS is shown to preserve the main unsteady trends and residual growth characteristics irrespective of grid type. Obstacle flows with different shapes demonstrate that the model focuses on underlying physical relations rather than the external geometry, and multiple-obstacle cases reveal that complex topological changes can be handled while maintaining physically meaningful bulk flow structures. Finally, a “general unsteady flow model” is constructed using 100 two-dimensional cases with randomly varied grids, shapes, and obstacle topologies, of which 95 are used for training and five for testing. Even when the training data are intentionally subsampled to 50% and 20% of the available snapshots, the DTS-based AI-CFD maintains reason- able prediction quality up to approximately 10–20 autoregressive time steps, especially for large-scale flow patterns. These findings indicate that DTS can serve as a grid- and topology-agnostic input representation for CFD-oriented neural operators and provide a practical stepping stone toward general-purpose unsteady flow AI-CFD models. Re- maining limitations include the relatively short reliable prediction horizon and the lack of optimized data sampling, which are discussed as directions for future work.