Example: 1D steady diffusion

This lecture covers the general conservation equation for steady/unsteady diffusion, including convection, diffusion, and source terms. It delves into the numerical flow simulation of steady convection-diffusion problems, such as heat conduction. The lecture also explains the process of discretizing the domain into control volumes and nodes, integrating over control volumes, and applying the divergence theorem. Boundary conditions, linear algebraic equations, and different types of boundary conditions like Dirichlet, Neumann, and Robin are discussed. The lecture concludes with assembling the algebraic system using a tri-diagonal matrix and solving for the unknowns using numerical methods.