# Computational Fluid Dynamics

- Institution: IIT Madras
- Department: Chemical Engineering
- Teacher: Prof. Sreenivas Jayanti
- Level: Undergraduate
- Language: English
- Subjects: Chemistry, Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/103106073)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/103106073)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Motivation for CFD and Introduction to the CFD approach](https://invisiblenetwork.ai/learn/nptel/103106073/26491fb02a19) (Video)
2. [Illustration of the CFD approach through a worked out example](https://invisiblenetwork.ai/learn/nptel/103106073/d19e8115d5cb) (Video)
3. [Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation and Statement of the momentum conservation equation](https://invisiblenetwork.ai/learn/nptel/103106073/0cca8c57570d) (Video)
4. [Forces acting on a control volume; Stress tensor; Derivation of the momentum conservation equation ; Closure problem; Deformation of a fluid element in fluid flow](https://invisiblenetwork.ai/learn/nptel/103106073/6b720a1a1f7f) (Video)
5. [Kinematics of deformation in fluid flow; Stress vs strain rate relation; Derivation of the Navier-Stokes equations](https://invisiblenetwork.ai/learn/nptel/103106073/f3a4aa692192) (Video)
6. [Equations governing flow of incompressible flow; Initial and boundary conditions; Wellposedness of a fluid flow problem](https://invisiblenetwork.ai/learn/nptel/103106073/dc76a7c5f650) (Video)
7. [Equations for some simple cases; Generic scalar transport equation form of the governing equations; Outline of the approach to the solution of the N -S equations.](https://invisiblenetwork.ai/learn/nptel/103106073/932ffdd5f5b7) (Video)
8. [cut out the first 30s; Spatial discretization of a simple flow domain; Taylor’s series expansion and the basis of finite difference approximation of a derivative; Central and one-sided difference approximations; Order of accuracy of…](https://invisiblenetwork.ai/learn/nptel/103106073/e1be417680c7) (Video)
9. [Finite difference approximation of pth order of accuracy for qth order derivative; cross -derivatives; Examples of high order accurate formulae for several derivatives](https://invisiblenetwork.ai/learn/nptel/103106073/cb908226e9a5) (Video)
10. [One -sided high order accurate approximations; Explicit and implicit formulations for the time derivatives](https://invisiblenetwork.ai/learn/nptel/103106073/28155553796c) (Video)
11. [Numerical solution of the unsteady advection equation using different finite difference approximations](https://invisiblenetwork.ai/learn/nptel/103106073/8d3893c2409b) (Video)
12. [Need for analysis of a discretization scheme; Concepts of consistency, stability and convergence and the equivalence theorem of Lax ; Analysis for consistency](https://invisiblenetwork.ai/learn/nptel/103106073/22a0059962b2) (Video)
13. [Statement of the stability problem; von Neumann stability analysis of the first order wave equation](https://invisiblenetwork.ai/learn/nptel/103106073/6c4c088fef3e) (Video)
14. [Consistency and stability analysis of the unsteady diffusion equation; Analysis for two- and three -dimensional cases; Stability of implicit schemes](https://invisiblenetwork.ai/learn/nptel/103106073/8b9ba7cdb0c1) (Video)
15. [Interpretation of the stability condition; Stability analysis of the generic scalar equation and the concept of upwinding ; Diffusive and dissipative errors in numerical solution; Introduction to the concept of TVD schemes](https://invisiblenetwork.ai/learn/nptel/103106073/8ac85ac35267) (Video)
16. [Template for the generic scalar transport equation and its extension to the solution of Navier-Stokes equa tions for a compressible flow.](https://invisiblenetwork.ai/learn/nptel/103106073/04b4e54fcee9) (Video)
17. [Illustration of application of the template using the MacCormack scheme for a three-dimensional compressible flow](https://invisiblenetwork.ai/learn/nptel/103106073/a28e32d21526) (Video)
18. [Stability limits of MacCormack scheme; Limitations in extending compressible flow schemes to incompre ssible flows ; Difficulty of evaluation of pressure in incompressible flows and listing of various approaches](https://invisiblenetwork.ai/learn/nptel/103106073/c14a0b2c16a6) (Video)
19. [Artificial compressibility method and the streamfunction-vorticity method for the solution of NS equations and their limitations](https://invisiblenetwork.ai/learn/nptel/103106073/d1b4504b0319) (Video)
20. [Pressur e equation method for the solution of NS equations](https://invisiblenetwork.ai/learn/nptel/103106073/c57d52cbb18d) (Video)
21. [Pressure-correction approach to the solution of NS equations on a staggered grid; SIMPLE and its family of methods](https://invisiblenetwork.ai/learn/nptel/103106073/b1da56ae60cb) (Video)
22. [Need for effici ent solution of linear algebraic equations; Classification of approaches for the solution of linear algebraic equations.](https://invisiblenetwork.ai/learn/nptel/103106073/2e06ba6301d9) (Video)
23. [Direct methods for linear algebraic equations; Gaussian elimination method](https://invisiblenetwork.ai/learn/nptel/103106073/36f329ae5dbd) (Video)
24. [Gauss-Jordan method; LU decomposition method; TDMA and Thomas algorithm](https://invisiblenetwork.ai/learn/nptel/103106073/6be406b609b8) (Video)
25. [Basic iterative methods for linear algebraic equations: Description of point -Jacobi, Gauss-Seidel and SOR methods](https://invisiblenetwork.ai/learn/nptel/103106073/fdcc1ef275d8) (Video)
26. [Convergence analysis of basic iterative schemes; Diagonal dominance condition for convergence; Influence of source terms on the diagonal dominance condition; Rate of convergence](https://invisiblenetwork.ai/learn/nptel/103106073/a9cd8f8834f1) (Video)
27. [Application to the Laplace equation](https://invisiblenetwork.ai/learn/nptel/103106073/b73c0e19feee) (Video)
28. [Advanced iterative methods: Alternating Direction Implicit Method; Operator splitting](https://invisiblenetwork.ai/learn/nptel/103106073/322bed5d4c3f) (Video)
29. [Advanced iterative methods; Strongly Implicit Proc edure; Conjugate gradient method; Multigrid method](https://invisiblenetwork.ai/learn/nptel/103106073/a0b942246732) (Video)
30. [Illustration of the Multigrid method for the Laplace equation](https://invisiblenetwork.ai/learn/nptel/103106073/cea8551e811d) (Video)
31. [Overview of the approach of numerical solution of NS equations for simple domains; Introduction to complexity arising from physics and geometry](https://invisiblenetwork.ai/learn/nptel/103106073/d86ca675aa2e) (Video)
32. [Derivation of the energy conservation equation](https://invisiblenetwork.ai/learn/nptel/103106073/b3aabb967bab) (Video)
33. [Derivation of the species conservation equation; dealing with chemical reactions](https://invisiblenetwork.ai/learn/nptel/103106073/e6caf7805366) (Video)
34. [Turbulence; Characteri stics of turbulent flow; Dealing with fluctuations and the concept of time-averaging](https://invisiblenetwork.ai/learn/nptel/103106073/ee03c177e7d2) (Video)
35. [Derivation of the Reynolds -averaged Navier -Stokes equations; identification of the closure problem of turbulence; Boussinesq hypothesis and eddy viscosity](https://invisiblenetwork.ai/learn/nptel/103106073/0296aba14e17) (Video)
36. [Reynol ds stresses in turbulent flow; Time and length scales of turbulence; Energy cascade; Mixing length model for eddy viscosity](https://invisiblenetwork.ai/learn/nptel/103106073/231252b369e6) (Video)
37. [One-equation model for turbulent flow](https://invisiblenetwork.ai/learn/nptel/103106073/86d85c15e16d) (Video)
38. [Two -equation model for turbulent flow; Numerical calculation of turbulent reacting flows](https://invisiblenetwork.ai/learn/nptel/103106073/b48c1ba82c62) (Video)
39. [Calculation of near-wall region in turbulent flow; wall function approach; near-wall turbulence models](https://invisiblenetwork.ai/learn/nptel/103106073/173f7bfb44a8) (Video)
40. [Need for special methods for dealing with irregular fl ow geometry; Outline of the Body-fitted grid approach ; Coordinate transformation to a general, 3-D curvilinear system](https://invisiblenetwork.ai/learn/nptel/103106073/8f2609c64cd1) (Video)
41. [Transformation of the governing equations; Illustration for the Laplace equation; Appearance and significance of cross -derivative terms; Concepts of structured and unstructured grids.](https://invisiblenetwork.ai/learn/nptel/103106073/52bc08e34e2c) (Video)
42. [Finite vol ume method for complicated flow domain; Illustration for the case of flow through a duct of triangular cross -section.](https://invisiblenetwork.ai/learn/nptel/103106073/24822cac1719) (Video)
43. [Finite volume method for the general case](https://invisiblenetwork.ai/learn/nptel/103106073/e89c6f6188f4) (Video)
44. [Generation of a structured grid for irregular flow domain; Algebraic methods; Elliptic grid generation method](https://invisiblenetwork.ai/learn/nptel/103106073/a01cc5ef9089) (Video)
45. [Unstructured grid generation; Domain nodalization; Advancing front method for triangulation](https://invisiblenetwork.ai/learn/nptel/103106073/2a1b60ddbecf) (Video)
46. [Delaunay triangulation method for unstructured grid generation](https://invisiblenetwork.ai/learn/nptel/103106073/d2d97ca8c527) (Video)
47. [Co -located grid approach for irregular geometries; Pressure correction equation for a co -located structured grid; Pressure correction equation for a co-located unstructured grid.](https://invisiblenetwork.ai/learn/nptel/103106073/e3c0c50632fb) (Video)