Neural operators offer an efficient data-driven approach to predicting complex automotive aerodynamic flows. However, spectral bias limits their ability to reconstruct fine-scale flow variations around geometric features such as side mirrors and wheel arches. Reliable assessment of local geometric changes therefore requires models that capture fine spatial detail together with global flow interactions. Inspired by iterative refinement and state evolution, we propose CIS-Transolver, a cross-layer incremental-state neural operator that integrates local multiscale information into global flow modeling. The method extracts local feature variations and encodes them as zeroth- to second-order geometric moments. These encodings are combined with information from earlier layers to form a cross-layer memory. Memory-derived corrections enter the value branch of Physics-Attention, allowing local details to inform global physical-state interactions throughout the network. We systematically evaluate CIS-Transolver on three public automotive aerodynamics benchmarks, ShapeNet-Car, AhmedML, and DrivAerNet++, covering surface pressure fields and volumetric pressure and velocity fields. CIS-Transolver achieves the lowest mean relative L2 error among the evaluated methods for all five prediction metrics across the three benchmarks. Relative error reductions average 8.72% compared with the best baseline for each metric. Also achieves the lowest high-frequency spectral errors across all five metrics, with an average relative reduction of 16.06% compared with the best baseline. These results support cross-layer reuse of local information for fine-scale automotive flow prediction.

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