Introduction to CFD


Lecture 1 - Introduction, Why and how we need computers


Lecture 2 - Representing Arrays and functions on computers


Lecture 3 - Representing functions - Box functions


Lecture 4 - Representing functions - Polynomials and Hat functions


Lecture 5 - Hat functions, Quadratic and Cubic representations


Lecture 6 - Demo - Hat functions, Aliasing


Lecture 7 - Representing Derivatives - finite differences


Lecture 8 - Finite differences, Laplace equation


Lecture 9 - Laplace equation - Jacobi iterations


Lecture 10 - Laplace equation - Iteration matrices


Lecture 11 - Laplace equation - convergence rate


Lecture 12 - Laplace equation - convergence rate Continued


Lecture 13 - Demo - representation error, Laplace equation


Lecture 14 - Demo - Laplace equation, SOR


Lecture 15 - Laplace equation - final, Linear Wave equation


Lecture 16 - Linear wave equation - Closed form and numerical solution, stability analysis


Lecture 17 - Generating a stable scheme and Boundary conditions


Lecture 18 - Modified equation


Lecture 19 - Effect of higher derivative terms on Wave equation


Lecture 20 - Artificial dissipation, upwinding, generating schemes


Lecture 21 - Demo - Modified equation, Wave equation


Lecture 22 - Demo - Wave equation / Heat Equation


Lecture 23 - Quasi-linear One-Dimensional. wave equation


Lecture 24 - Shock speed, stability analysis, Derive Governing equations


Lecture 25 - One-Dimensional Euler equations - Attempts to decouple


Lecture 26 - Derive Eigenvectors, Writing Programs


Lecture 27 - Applying Boundary conditions


Lecture 28 - Implicit Boundary conditions


Lecture 29 - Flux Vector Splitting, setup froms averaging


Lecture 30 - Roes averaging


Lecture 31 - Demo - One Dimensional flow


Lecture 32 - Accelerating convergence - Preconditioning, dual time stepping


Lecture 33 - Accelerating convergence - Intro to Multigrid method


Lecture 34 - Multigrid method


Lecture 35 - Multigrid method - final, Parallel Computing


Lecture 36 - Calculus of Variations - Three Lemmas and a Theorem


Lecture 37 - Calculus of Variations - Application to Laplace Equation


Lecture 38 - Calculus of Variations - Final and Random Walk


Lecture 39 - Overview and Recap of the course