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NPTEL

Introduction to CFD

NPTEL via YouTube

Overview

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This course on Introduction to Computational Fluid Dynamics (CFD) aims to teach students the fundamentals of representing arrays and functions on computers, numerical solutions to Laplace and wave equations, stability analysis, boundary conditions, and accelerating convergence techniques like preconditioning and multigrid methods. The course covers topics such as finite differences, Jacobi iterations, artificial dissipation, upwinding, flux vector splitting, and parallel computing. The teaching method includes lectures, demonstrations, and programming exercises. This course is intended for students and professionals interested in learning the basics of CFD and its applications in engineering and scientific simulations.

Syllabus

Mod-01 Lec-01 Introduction, Why and how we need computers.
Mod-01 Lec-02 Representing Arrays and functions on computers.
Mod-01 Lec-03 Representing functions - Box functions.
Mod-01 Lec-04 Representing functions - Polynomials & Hat functions.
Mod-01 Lec-05 Hat functions, Quadratic & Cubic representations.
Mod-01 Lec-06 Demo - Hat functions, Aliasing.
Mod-01 Lec-07 Representing Derivatives - finite differences.
Mod-01 Lec-08 Finite differences, Laplace equation.
Mod-01 Lec-09 Laplace equation - Jacobi iterations.
Mod-01 Lec-10 Laplace equation - Iteration matrices.
Mod-01 Lec-11 Laplace equation - convergence rate.
Mod-01 Lec-12 Laplace equation - convergence rate Continued.
Mod-01 Lec-13 Demo - representation error, Laplace equation.
Mod-01 Lec-14 Demo - Laplace equation, SOR.
Mod-01 Lec-15 Laplace equation - final, Linear Wave equation.
Mod-01 Lec-16 Linear wave equation - Closed form & numerical solution, stability analysis.
Mod-01 Lec-17 Generating a stable scheme & Boundary conditions.
Mod-01 Lec-18 Modified equation.
Mod-01 Lec-19 Effect of higher derivative terms on Wave equation.
Mod-01 Lec-20 Artificial dissipation, upwinding, generating schemes.
Mod-01 Lec-21 Demo - Modified equation, Wave equation.
Mod-01 Lec-22 Demo - Wave equation / Heat Equation.
Mod-01 Lec-23 Quasi-linear One-Dimensional. wave equation.
Mod-01 Lec-24 Shock speed, stability analysis, Derive Governing equations.
Mod-01 Lec-25 One-Dimensional Euler equations - Attempts to decouple.
Mod-01 Lec-26 Derive Eigenvectors, Writing Programs.
Mod-01 Lec-27 Applying Boundary conditions.
Mod-01 Lec-28 Implicit Boundary conditions.
Mod-01 Lec-29 Flux Vector Splitting, setup Roe’s averaging.
Mod-01 Lec-30 Roe’s averaging.
Mod-01 Lec-31 Demo - One Dimensional flow.
Mod-01 Lec-32 Accelerating convergence - Preconditioning, dual time stepping.
Mod-01 Lec-33 Accelerating convergence, Intro to Multigrid method.
Mod-01 Lec-34 Multigrid method.
Mod-01 Lec-35 Multigrid method - final, Parallel Computing.
Mod-01 Lec-36 Calculus of Variations - Three Lemmas and a Theorem.
Mod-01 Lec-37 Calculus of Variations - Application to Laplace Equation.
Mod-01 Lec-38 Calculus of Variations -final & Random Walk.
Mod-01 Lec-39 Overview and Recap of the course.

Taught by

aerospace engineering

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