This study investigates the application of Physics-Informed Neural Networks (PINNs) and a hybrid CFD–PINN framework for simulating steady laminar flow past a circular obstacle at \(Re=40\) . Comparative analysis reveals that while standalone PINNs can approximate the general flow field, it struggles to capture sharp velocity gradients, flow separation, and pressure variations with the same accuracy as traditional CFD solvers. The finite volume method (FVM) in OpenFOAM provides high-fidelity solutions in such regions but at a higher computational cost. The proposed CFD–PINN hybrid approach leverages the strengths of both methods, integrating physics-based solvers with data-driven learning. Results show that the CFD–PINN model closely matches the CFD predictions in both velocity and pressure fields, particularly near critical flow regions, while maintaining a computational cost only marginally higher than CFD alone. This hybrid framework offers improved generalization and robustness for flow simulations, particularly in cases with limited data or complex geometries. The study establishes a foundation for future research in machine learning enhanced CFD, highlighting the potential of CFD–PINN frameworks for efficient, accurate, and scalable simulations in engineering applications.
