<![CDATA[This paper presents a comprehensive comparative analysis of the Fi-nite Difference Method (FDM) and the Finite Volume Method (FVM)for solving the two-dimensional, unsteady, incompressible Navier-Stokesequations. The classical lid-driven cavity problem is utilized as the pri-mary benchmark to evaluate the inherent stability, convergence behav-ior, and physical fidelity of both numerical paradigms. Python-basedsolvers were developed utilizing a staggered Cartesian grid topology toeffectively eliminate the pressure-velocity decoupling artifact. The FDMsolver implements the explicit Fractional Step (Projection) method,providing rapid execution that is strictly constrained by the Courant-Friedrichs-Lewy (CFL) stability criterion. In contrast, the FVM solveremploys the implicit Semi-Implicit Method for Pressure-Linked Equa-tions (SIMPLE) algorithm, enhanced by Patankar’s Power-Law differ-encing scheme, to ensure robust grid-scale mass conservation withoutexcessive numerical diffusion. The numerical results for Reynolds num-bers of 100 and 400 demonstrate excellent quantitative agreement withthe canonical Ghia (1982) benchmarking data. The comparative evalu-ation underscores the operational trade-offs between the two methodolo-gies, confirming that while FDM offers mathematical elegance and speedfor orthogonal domains, FVM delivers superior conservative propertiesand stability that are essential for resolving highly convective, non-linearfluid phenomena.]]>
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