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Last updated:

September 23, 2023

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FREE

This course includes:

Unlimited Duration

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Description

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)

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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