Génie Chimique

This course provides a comprehensive introduction to the

Mathematical Modeling and numerical simulation of Transport Phenomena, focusing on the transition from physical laws to computational solutions. It begins by classifying Partial Differential Equations (PDEs) into elliptic, parabolic, and hyperbolic types to determine their physical behavior and appropriate solver strategies. The core of the curriculum focuses on Discretization Methods, comparing the Finite Difference, Finite Element, and Finite Volume methods, with a strong emphasis on the latter for its conservation properties. These techniques are applied specifically to Steady-State Conduction (Elliptic Equations), covering essential practical aspects such as mesh generation, interfacial conductivity, and boundary conditions. Finally, the course details efficient numerical algorithms for solving the resulting algebraic systems, including the TDMA method for one-dimensional problems and iterative techniques like Gauss-Seidel and Relaxation for multi-dimensional 2D and 3D simulations.