This study proposes a neural network (NN)-assisted, physics-informed framework for global flow-based upscaling to accelerate reservoir simulation. While traditional global upscaling methods can accurately capture fine-scale flow characteristics, their high computational cost hinders practical application in ensemble-based uncertainty quantification and optimization workflows. Existing NN-assisted upscaling approaches predominantly rely on numerical simulation data, which remains computationally expensive and often lacks physical interpretability. Furthermore, no current method enables physics-informed training for corner-point grid (CPG) models without simulation data, limiting the application of deep learning in practical geological model upscaling. To address these limitations, we develop a finite-volume physics-informed Fourier neural operator (FV-PIFNO) as a pressure-solution surrogate model for CPG models. This physics-driven approach eliminates the need for simulation data and inherently enforces inter-grid flux continuity during inference. A flow-based numerical post-processing procedure is designed to compute coarse-grid transmissibility and well index that are strictly equivalent to fine-scale fluxes, naturally extending to non-orthogonal CPG systems. Comparisons are designed between different mapping and driving methods. Validation on synthetic models demonstrates that the fully physics-constrained approach achieves high accuracy in both single-phase and two-phase flow simulations, along with strong generalization to heterogeneous scenarios. Application to a standard SAIGUP model confirms that the framework achieves accuracy comparable to numerical upscaling while significantly improving computational efficiency, demonstrating its potential for practical, high-fidelity reservoir upscaling.