APPSolver: Adaptive Patch Partitioning for Point-Wise Ship Flow Prediction on Unstructured Meshes

Predicting high-fidelity flow fields around ship hulls is central to hydrodynamic performance analysis, yet traditional CFD solvers remain computationally prohibitive for rapid design exploration across multiple vessel types and operating conditions. Existing deep-learning surrogates often interpolate unstructured CFD meshes onto regular grids, which can blur near-field resolution, while direct point-level global attention on large unstructured meshes can be computationally expensive. In this paper, we introduce APPSolver, a neural surrogate that learns next-step point-wise flow-field prediction directly on the unstructured free-surface ship CFD mesh without re-gridding. APPSolver is built around Adaptive Patch Partitioning (APP), a quadtree-based strategy that groups unstructured points into local spatial patches according to the non-uniform density inherent in ship CFD meshes: fine near the hull and wake, coarse in the far field. The resulting patch tokens are processed by a Transformer backbone together with optional condition token that encode ship geometry and condition parameters via a frozen large language model, forming a unified token-space model for one-step temporal advancement of velocity and pressure fields. On the ShipBench dataset, APP-Transformer achieves the lowest MAE and MSE. Ablation studies quantify the compression-fidelity trade-off of APP and demonstrate that condition token provide preliminary gains in some leave-one-hull-out settings. The code will be released upon acceptance.