<![CDATA[This study investigates the fundamental fluid dynamics of steady-state laminar flow past a circular cylinder using the Lattice Boltzmann Method (LBM) with a D2Q9 lattice arrangement. Developed using a vectorized Pythonic approach, the numerical solver employs the Bhatnagar-Gross-Krook (BGK) collision operator to resolve the mesoscopic particle distribution functions. The research focuses on the flow characteristics at low Reynolds numbers (Re) ranging from 20 to 70 to ensure stable convergence toward steady-state conditions. Results demonstrate that the LBM effectively captures critical hydrodynamic phenomena, including stagnation points, flow acceleration due to blockage effects, and the development of symmetric wake regions. Analysis reveals a linear correlation between increasing Reynolds numbers and the longitudinal elongation of the recirculation zone, confirming the solver's ability to maintain numerical stability and momentum conservation without the computational expense of conventional pressure-velocity coupling. These findings validate the use of open-source computational tools for rigorous fluid flow analysis and provide a robust dataset for future integration with multi-scale modeling and machine learning frameworks, such as Physics-Informed Neural Networks (PINNs).]]>
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