Navier-Stokes Equations in a Rectangular Domain - Lid Driven Cavity Simulation

This program solves the incompressible Navier-Stokes equations within a rectangular domain with prescribed velocity boundary conditions. The standard configuration implements a lid-driven cavity problem, where the top boundary moves tangentially while other walls remain stationary. The computational implementation typically employs staggered grid arrangements for pressure-velocity coupling, utilizing algorithms like the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) or projection methods to handle the incompressibility constraint. Building upon this foundation, users can explore various boundary condition modifications, such as analyzing scenarios with spatially varying velocities along specific boundaries. The code structure allows systematic investigation of different computational grid resolutions (from coarse to fine meshes) and solver parameters (tolerance settings, iteration methods) to assess their impact on solution accuracy and convergence rates. The computational framework can be extended to three-dimensional simulations, introducing additional challenges in handling larger equation systems and visualization complexities while yielding more physically comprehensive results. The program serves as an essential educational tool for understanding fundamental computational fluid dynamics (CFD) principles, providing hands-on experience with discretization techniques, stability analysis, and validation against benchmark solutions through vorticity and streamline visualization outputs.