نبذة مختصرة : This thesis presents the development, implementation, and verification of a numerical frame- work for solving the governing equations of mass, momentum, and energy in two-dimensional incompressible flows. The study adopts the Finite Volume Method and focuses on structured meshes, with attention to the discretization of convective and diffusive terms, temporal integra- tion strategies, and pressure–velocity coupling. Starting from the mathematical formulation of the Navier–Stokes and energy equations, the work investigates how different numerical schemes, solvers, and conditions affect accuracy, sta- bility, and physical consistency of the solution. The proposed C++ solver is verified through a series of canonical benchmark problems: steady and transient heat conduction in multi-material domains, scalar transport in the Smith–Hutton flow field, forced convection in the lid-driven cavity, and natural convection in a differentially heated cavity (DHC). The last part explores the quasi-turbulent regime of DHC at high Rayleigh numbers via Direct Numerical Simulation (DNS). Time-averaged quantities, turbulent kinetic energy, and Reynolds stresses are computed to provide a deeper understanding of unsteady convection and its tran- sition. Results have been systematically validated against reference solutions and literature data, con- firming the accuracy and robustness of the numerical approach. The numerical framework developed in this thesis is general, modular, and adaptable to other thermal engineering ap- plications. It enables parametric studies and the analysis of energy transfer mechanisms under varying boundary and flow conditions, offering a valuable tool for research and design in the field of heat and mass transfer.
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