Solving the linear system - Nonlinearity

This lecture covers the concepts of solving linear systems and dealing with nonlinearity in numerical flow simulations. It starts with point-iterative methods like Jacobi and Gauss-Seidel, leading to the introduction of multigrid methods to improve convergence rates. The lecture explains how multigrid methods work by combining iterations on meshes of different sizes to reduce both short and long-wavelength errors efficiently. It also discusses linearization methods such as Picard's and Newton's methods to handle nonlinearity in equations. Possible convergence issues and remedies are explored, including under-relaxation techniques. The lecture concludes with practical examples and the implementation of these methods in MATLAB for academic use.