Introduction to Computational Fluid Dynamics (CFD)
Introduction to Computational Fluid Dynamics (CFD). Instructor: Prof. M. Ramakrishna, Department of Aerospace Engineering, IIT Madras. Representation of mathematical ideas on the computer: numbers, functions, derivative, differential equations. Simple Problems: Solution to Laplace equation, one-dimensional first order wave equation, heat equation, finite difference schemes - stability and consistency, dissipation dispersion, finite volume method. One-dimensional Euler equations: Discretisation, Delta form, application of boundary conditions. Advanced topics: Roe's averaging, Multigrid Methods, SOR and variational techniques.
(from nptel.ac.in)
| Lecture 01 - Introduction, Why and How We Need Computers |
| Lecture 02 - Representing Arrays and Functions on Computers |
| Lecture 03 - Representing Functions - Box Functions |
| Lecture 04 - Representing Functions - Polynomials and Hat Functions |
| Lecture 05 - Hat Functions, Quadratic and Cubic Representations |
| Lecture 06 - Demo - Hat Functions, Aliasing |
| Lecture 07 - Representing Derivatives - Finite Differences |
| Lecture 08 - Finite Differences, Laplace Equation |
| Lecture 09 - Laplace Equation - Jacobi Iterations |
| Lecture 10 - Laplace Equation - Iteration Matrices |
| Lecture 11 - Laplace Equation - Convergence Rate |
| Lecture 12 - Laplace Equation - Convergence Rate (cont.) |
| Lecture 13 - Demo - Representation Error, Laplace Equation |
| Lecture 14 - Demo - Laplace Equation, SOR |
| Lecture 15 - Laplace Equation, 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, Unwinding, 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 Roe's Averaging |
| Lecture 30 - Roe's 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, 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, Random Walks |
| Lecture 39 - Overview and Recap of the Course |