Introduction to Computational Fluid Dynamics (CFD). Instructor: Prof. M. Ramakrishna, Department of Aerospace Engineering, IIT Madras.
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September 23, 2023
English
English [CC]
Description
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)
Course Curriculum
- Lecture 01 – Introduction, Why and How We Need Computers Unlimited
- Lecture 02 – Representing Arrays and Functions on Computers Unlimited
- Lecture 03 – Representing Functions – Box Functions Unlimited
- Lecture 04 – Representing Functions – Polynomials and Hat Functions Unlimited
- Lecture 05 – Hat Functions, Quadratic and Cubic Representations Unlimited
- Lecture 06 – Demo – Hat Functions, Aliasing Unlimited
- Lecture 07 – Representing Derivatives – Finite Differences Unlimited
- Lecture 08 – Finite Differences, Laplace Equation Unlimited
- Lecture 09 – Laplace Equation – Jacobi Iterations Unlimited
- Lecture 10 – Laplace Equation – Iteration Matrices Unlimited
- Lecture 11 – Laplace Equation – Convergence Rate Unlimited
- Lecture 12 – Laplace Equation – Convergence Rate (cont.) Unlimited
- Lecture 13 – Demo – Representation Error, Laplace Equation Unlimited
- Lecture 14 – Demo – Laplace Equation, SOR Unlimited
- Lecture 15 – Laplace Equation, Linear Wave Equation Unlimited
- Lecture 16 – Linear Wave Equation – Closed Form and Numerical Solution, Stability Analysis Unlimited
- Lecture 17 – Generating a Stable Scheme and Boundary Conditions Unlimited
- Lecture 18 – Modified Equation Unlimited
- Lecture 19 – Effect of Higher Derivative Terms on Wave Equation Unlimited
- Lecture 20 – Artificial Dissipation, Unwinding, Generating Schemes Unlimited
- Lecture 21 – Demo – Modified Equation, Wave Equation Unlimited
- Lecture 22 – Demo – Wave Equation, Heat Equation Unlimited
- Lecture 23 – Quasi-linear One-dimensional Wave Equation Unlimited
- Lecture 24 – Shock Speed, Stability Analysis, Derive Governing Equations Unlimited
- Lecture 25 – One-dimensional Euler Equations, Attempts to Decouple Unlimited
- Lecture 26 – Derive Eigenvectors, Writing Programs Unlimited
- Lecture 27 – Applying Boundary Conditions Unlimited
- Lecture 28 – Implicit Boundary Conditions Unlimited
- Lecture 29 – Flux Vector Splitting, Setup Roe’s Averaging Unlimited
- Lecture 30 – Roe’s Averaging Unlimited
- Lecture 31 – Demo – One Dimensional Flow Unlimited
- Lecture 32 – Accelerating Convergence – Preconditioning, Dual Time Stepping Unlimited
- Lecture 33 – Accelerating Convergence, Intro to Multigrid Method Unlimited
- Lecture 34 – Multigrid Method Unlimited
- Lecture 35 – Multigrid Method, Parallel Computing Unlimited
- Lecture 36 – Calculus of Variations – Three Lemmas and a Theorem Unlimited
- Lecture 37 – Calculus of Variations – Application to Laplace Equation Unlimited
- Lecture 38 – Calculus of Variations, Random Walks Unlimited
- Lecture 39 – Overview and Recap of the Course Unlimited
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