# Computational Fluid Dynamics using the Finite Element Method

- Institution: IIT Kanpur
- Department: Aerospace Engineering
- Teacher: Prof. Sanjay Mittal
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/101104001)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/101104001)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This course introduces the Finite Element Method as one of the methods to solve partial differential equations. The course aims at providing fundamental as well as working concepts for designing finite element formulations for solving equations of fluid flow. The traditional Galerkin Finite Element Method does not work for solving fluid dynamics equations. The stabilized finite element method is introduced to solve incompressible as well as compressible flows.

Intended audience: Undergraduate/Graduate Students pursuing Aerospace Engineering/Mechanical Engineering

Prerequisites: First year Math Courses and any one course in Fluid Mechanics

## Lectures

1. [Lecture 1 : Introduction to CFD & HPC](https://invisiblenetwork.ai/learn/nptel/101104001/1949ac5b5fa1) (YouTube)
2. [Lecture 2 : Overview of the course: Finite Element Methods for Fluid Dynamics](https://invisiblenetwork.ai/learn/nptel/101104001/09e04d96dcac) (YouTube)
3. [Lecture 3 : Simple Finite Difference Methods to solve ODEs](https://invisiblenetwork.ai/learn/nptel/101104001/44acacaef5ae) (YouTube)
4. [Lecture 4 : Simple Finite Difference Methods to solve PDEs (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/d46170e5312a) (YouTube)
5. [Lecture 5 : Simple Finite Difference Methods to solve PDEs (Part -B)](https://invisiblenetwork.ai/learn/nptel/101104001/519074491f22) (YouTube)
6. [Lecture 6 : Vector Spaces, basis, completeness (Part -A)](https://invisiblenetwork.ai/learn/nptel/101104001/5f2a32695776) (YouTube)
7. [Lecture 7 : Vector Spaces, basis, completeness (Part- B)](https://invisiblenetwork.ai/learn/nptel/101104001/a2ec40a770e8) (YouTube)
8. [Lecture 8 : Continuity, Differentiability and Smoothness (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/72bfcd79f139) (YouTube)
9. [Lecture 9 : Continuity, Differentiability and Smoothness (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/cb4f1a990d8b) (YouTube)
10. [Lecture 10 : Method of Weighted Residual](https://invisiblenetwork.ai/learn/nptel/101104001/961c35f31e1e) (YouTube)
11. [Lecture 11 : Weak form of a Steady, 1D problem (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/c97e6e5ee4e9) (YouTube)
12. [Lecture 12 : Weak form of a Steady, 1D problem (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/26d117258270) (YouTube)
13. [Lecture 13 : Galerkin's Approximation and Matrix form (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/2087a3ea4bc0) (YouTube)
14. [Lecture 14 : Galerkin's Approximation and Matrix form (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/8b8a20afc403) (YouTube)
15. [Lecture 15 : Example to illustrate Galerkin's approximation (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/bb8c3e9e4418) (YouTube)
16. [Lecture 16 : Example to illustrate Galerkin's approximation (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/356199f355c4) (YouTube)
17. [Lecture 17: Piecewise Linear Finite Element Space: Element Level Matrices and Vectors (Part -A)](https://invisiblenetwork.ai/learn/nptel/101104001/413d0d372229) (YouTube)
18. [Lecture 18: Piecewise Linear Finite Element Space: Element Level Matrices and Vectors (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/42d81584c0c5) (YouTube)
19. [Lecture 19: Assembly of Element Level Matrices and Vectors ( Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/77497840f9ac) (YouTube)
20. [Lecture 20: Assembly of Element Level Matrices and Vectors ( Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/021580d7c6f9) (YouTube)
21. [Lecture 21: Strong, Weak, and Galerkin forms of Two- and Three-Dimensional problems (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/a5cd912922c3) (YouTube)
22. [Lecture 22: Strong, Weak, and Galerkin forms of Two- and Three-Dimensional problems (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/8c58dc3ae03c) (YouTube)
23. [Lecture 23: Matrix form of Two- and Three-Dimensional Problems (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/9f94790db9f8) (YouTube)
24. [Lecture 24: Matrix form of Two- and Three-Dimensional Problems (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/b075356eab8d) (YouTube)
25. [Lecture 25: Assembly of element-level matrices and vectors for Two- and Three-Dimensional problems (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/d01811177ae9) (YouTube)
26. [Lecture 26: Assembly of element-level matrices and vectors for Two- and Three-Dimensional problems (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/39d51ca2d8d5) (YouTube)
27. [Lecture 27: Classical Linear Electrostatics: vector unknown (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/8e1bf1d9252f) (YouTube)
28. [Lecture 28: Classical Linear Electrostatics: vector unknown (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/47fab0b83a9a) (YouTube)
29. [Lecture 29: Finite Element Interpolation/ Basis Functions (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/96bc0b31723d) (YouTube)
30. [Lecture 30: Finite Element Interpolation/ Basis Functions (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/4ceb86818872) (YouTube)
31. [Lecture 31: Numerical Integration, Derivatives of shape function (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/a621154ad2ed) (YouTube)
32. [Lecture 32: Numerical Integration, Derivatives of shape function (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/f79fe1df1627) (YouTube)
33. [Lecture 33: Introduction to time-dependent problems (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/8b4f1f265f98) (YouTube)
34. [Lecture 34: Introduction to time-dependent problems (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/9d0bdddc3c81) (YouTube)
35. [Lecture 35: 1D Unsteady Linear Heat Conduction; Generalized Trapezoidal Method (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/9473ac8f9bce) (YouTube)
36. [Lecture 36: 1D Unsteady Linear Heat Conduction; Generalized Trapezoidal Method (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/c4a7fd5d54eb) (YouTube)
37. [Lecture 37: Stability Analysis of Time Integration Methods](https://invisiblenetwork.ai/learn/nptel/101104001/09e54c8c9b14) (YouTube)
38. [Lecture 38: Convergence of Generalized Trapezoidal Method](https://invisiblenetwork.ai/learn/nptel/101104001/b2a3accd9187) (YouTube)
39. [Lecture 39: Methods for non-linear problems](https://invisiblenetwork.ai/learn/nptel/101104001/93a49e5a859f) (YouTube)
40. [Lecture 40 : Numerical instability in the Galerkin Formulation for Advection Dominated Flows (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/65050d3e7ec7) (YouTube)
41. [Lecture 41 : Numerical instability in the Galerkin Formulation for Advection Dominated Flows (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/01a2aef5617e) (YouTube)
42. [Lecture 42 : SUPG (Streamline-Upwind/Petrov-Galerkin) Method for Advection dominated flows (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/75bb4342357a) (YouTube)
43. [Lecture 43 : SUPG (Streamline-Upwind/Petrov-Galerkin) Method for Advection dominated flows (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/6e7ec08c4805) (YouTube)
44. [Lecture 44 : Stabilized Finite Element Formulations for Flows (Part - A)](https://invisiblenetwork.ai/learn/nptel/101104001/90c854b01706) (YouTube)
45. [Lecture 45 : Stabilized Finite Element Formulations for Flows (Part - B)](https://invisiblenetwork.ai/learn/nptel/101104001/996ebd7f24b5) (YouTube)