Learn · Computational Fluid Dynamics

Lecture 22 of 65Module 3- Basics of CFD: Part 1- Finite Difference Methods

Lesson 22- Introduction to finite difference methods

Prof. Sreenivas Jayanti · IIT Madras

Credits and licence

From
Computational Fluid Dynamics, IIT Madras (at NPTEL)
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
Who can watch
Tweens profiles and older. How courses are placed

All the lectures

  1. Lesson 1- Motivation Video
  2. Lesson 2- Flow in a rectangular duct: Problem formulation Video
  3. Lesson 3- Flow in a rectangular duct: Discretiztion of flow domain Video
  4. Lesson 4- Tutorial 1: Converting PDE to algebraic equation using FD approximation Video
  5. Lesson 5- Tutorial 1 contd.: Solution for algebraic equations using Gauss- Seidel Method Video
  6. Lesson 6- Flow in a triangular duct: Problem formulation Video
  7. Lesson 7- Flow in a triangular duct: Discretiztion of flow domain Video
  8. Lesson 8- Tutorial 2: Converting PDE to algebraic equation using Finite Volume method Video
  9. Lesson 9- Tutorial 2 contd.: Description of FV method and solution using G-S Method Video
  10. Lesson 10- Effect of grid spacing & upcoming course outline Video
  11. Lesson 11- Mass conservation equations Video
  12. Lesson 12- Momentum conservation equations Video
  13. Lesson 13- Forces acting on control volume Video
  14. Lesson 14- Kinematics of deformation in fluid flow Video
  15. Lesson 15- Equations governing fluid flow in incompressible fluid Video
  16. Lesson 16- Navier-Stokes equation for simple cases of flow Video
  17. Lesson 17- Energy conservation equations Video
  18. Lesson 18- Practical cases of fluid flow with heat transfer in CFD point of view Video
  19. Lesson 19- Practical cases of fluid flow with mass transfer in CFD point of view Video
  20. Lesson 20- Equations governing fluid flow with chemical reactions Video
  21. Lesson 21- Concept of wellposedness of mathematical problems Video
  22. Lesson 22- Introduction to finite difference methods Video
  23. Lesson 23- Finite difference approximation on an uniform mesh Video
  24. Lesson 24- Higher order and mixed derivatives Video
  25. Lesson 25- Solution of Poisson equation in rectangular duct- Turorial Video
  26. Lesson 26- Discretization of time domain Video
  27. Lesson 27- FD approx. on a non-uniform mesh and need of analysis of obtained discretization Video
  28. Lesson 28- Need for the analysis of discretized equation Video
  29. Lesson 29- Properties of Numerical Schemes: Accuracy, Conservation property, Boundedness, Consistency, Stability and Convergence Video
  30. Lesson 30- Properties of Numerical Schemes: Stability analysis Video
  31. Lesson 31- Tutorial on Stability Analysis Video
  32. Lesson 32- Analysis of Generic 1-d scalar transport equation Video
  33. Introduction to the solution of coupled N-S equations Video
  34. N-S equation in compressible flow- Mac Cormack Scheme Video
  35. Stability limits of Mac-Cormack Scheme and the intro to Beam-Warming Scheme Video
  36. Implicit Beam-Warming Scheme Video
  37. Compressible flow to Incompressible flow Video
  38. Lesson 38 - Solution of coupled equations: Incompressible flow Video
  39. Lesson 39 - Artificial compressiblity method, Stream function-vorticity method Video
  40. Lesson 40 - Pressure equation method, Staggered grid system Video
  41. Lesson 41 - Pressure Correction Method Video
  42. Lesson 42 - Tutorial on Pressure Correction Method Video
  43. Lesson 43 - Tutorial on Pressure Correction Method contd. Video
  44. Lesson 44 - Introduction to the basic numerical methods Video
  45. Lesson 45 - Direct Methods: solution of the system of algebraic equations Video
  46. Lesson 46 - Tri-diagonal Matrix Algorithm: Derivation Video
  47. Lesson 47 - TDMA and other iterative methods Video
  48. Lesson 48 - Recap of basic iterative methods. Video
  49. Lesson 49 - Convergence analysis of basic iterative methods Video
  50. Lesson 50 - Successive Over Relaxation (SOR) method Video
  51. Lesson 51 - Alternating Direction Implicit (ADI) method Video
  52. Lesson 52 - Strongly Implicit Procedure (ILU) method Video
  53. Lesson 53 - Multigrid method Video
  54. Lesson 54 - Body Fitted Grid Approach Video
  55. Lesson 55 - Formulation Of Finite Volume Method Video
  56. Lesson 56 - Methods For Unstructured Grid Generation Video
  57. Lesson 57- Triangulation: The Advancing Front Method Video
  58. Lesson 58 - The Advancing Front Method continuation Video
  59. Lesson 59 -Time and length scale of turbulance Video
  60. Lesson 60 -The turbulent closure problem Video
  61. Lesson 61 -The generic formulation for turbulence Video
  62. Lesson 62 -More generic formulation and summary Video
  63. Live Session 12-02-2021 Video
  64. Live Session 12-03-2021 Video
  65. Live Session 09-04-2021 Video