Publication data accompanying the paper “Quantum-Inspired Tensor-Network Fractional-Step Method for Incompressible Flow in Curvilinear Coordinates”, published in Computer Physics Communications (DOI: 10.1016/j.cpc.2026.110169). The publication and this dataset are associated with the European Union’s Horizon Europe research and innovation programme (HORIZON-CL4-2021-DIGITAL-EMERGING-02-10) under grant agreement No. 101080085, QCFD (https://doi.org/10.3030/101080085). The dataset contains the simulation data used in the publication, including reference finite-difference results and matrix-product-state (MPS) results for curvilinear incompressible flow benchmarks, covering non-rotating and rotating cylinder cases in steady and transient regimes, as well as additional validation data.