Numerical solutions of lid-driven cavity flow problems for different boundary conditions

In this thesis, the two-dimensional, viscous, and incompressible flow within a lid-driven square cavity is investigated using numerical methods. The primary aim is to examine the effects of different Reynolds numbers on the flow structure and to analyze streamlines, vorticity distributions, and velocity components in detail. The mathematical model is based on the incompressible Navier-Stokes equations, which are reformulated using the vorticity-stream function formulation to eliminate the pressure term and simplify numerical computation. The governing equations are discretized using the Finite Difference Method (FDM), and the stream function equation is solved iteratively using the Gauss-Seidel method. The entire numerical algorithm is implemented in MATLAB. Numerical simulations performed for different Reynolds numbers 100≤ Re ≤5000 reveal that the flow structure is significantly influenced by the Reynolds number. While the flow remains laminar and symmetric at low Reynolds numbers, secondary vortices emerge and the flow becomes more complex as the Reynolds number increases. The results confirm that the lid-driven cavity problem is an effective benchmark for evaluating the accuracy and stability of numerical methods in fluid dynamics.