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Introduction to Computational Fluid Dynamics

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 26 - Derive Eigenvectors, Writing Programs

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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