Learn · Introduction to CFD

Lecture 10 of 39Introduction to CFD

Laplace equation - Iteration matrices

Prof. M. Ramakrishna · IIT Madras

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From
Introduction to CFD, IIT Madras (at NPTEL)
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CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures

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