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Course10110400145 lectures

Computational Fluid Dynamics using the Finite Element Method

Prof. Sanjay Mittal · IIT Kanpur

Start with lecture 1 At NPTEL

About

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

Week 1

  1. Lecture 1 : Introduction to CFD & HPC YouTube
  2. Lecture 2 : Overview of the course: Finite Element Methods for Fluid Dynamics YouTube

Week 2

  1. Lecture 3 : Simple Finite Difference Methods to solve ODEs YouTube
  2. Lecture 4 : Simple Finite Difference Methods to solve PDEs (Part - A) YouTube
  3. Lecture 5 : Simple Finite Difference Methods to solve PDEs (Part -B) YouTube

Week 3

  1. Lecture 6 : Vector Spaces, basis, completeness (Part -A) YouTube
  2. Lecture 7 : Vector Spaces, basis, completeness (Part- B) YouTube
  3. Lecture 8 : Continuity, Differentiability and Smoothness (Part - A) YouTube
  4. Lecture 9 : Continuity, Differentiability and Smoothness (Part - B) YouTube

Week 4

  1. Lecture 10 : Method of Weighted Residual YouTube
  2. Lecture 11 : Weak form of a Steady, 1D problem (Part - A) YouTube
  3. Lecture 12 : Weak form of a Steady, 1D problem (Part - B) YouTube

Week 5

  1. Lecture 13 : Galerkin's Approximation and Matrix form (Part - A) YouTube
  2. Lecture 14 : Galerkin's Approximation and Matrix form (Part - B) YouTube
  3. Lecture 15 : Example to illustrate Galerkin's approximation (Part - A) YouTube
  4. Lecture 16 : Example to illustrate Galerkin's approximation (Part - B) YouTube

Week 6

  1. Lecture 17: Piecewise Linear Finite Element Space: Element Level Matrices and Vectors (Part -A) YouTube
  2. Lecture 18: Piecewise Linear Finite Element Space: Element Level Matrices and Vectors (Part - B) YouTube
  3. Lecture 19: Assembly of Element Level Matrices and Vectors ( Part - A) YouTube
  4. Lecture 20: Assembly of Element Level Matrices and Vectors ( Part - B) YouTube

Week 7

  1. Lecture 21: Strong, Weak, and Galerkin forms of Two- and Three-Dimensional problems (Part - A) YouTube
  2. Lecture 22: Strong, Weak, and Galerkin forms of Two- and Three-Dimensional problems (Part - B) YouTube
  3. Lecture 23: Matrix form of Two- and Three-Dimensional Problems (Part - A) YouTube
  4. Lecture 24: Matrix form of Two- and Three-Dimensional Problems (Part - B) YouTube

Week 8

  1. Lecture 25: Assembly of element-level matrices and vectors for Two- and Three-Dimensional problems (Part - A) YouTube
  2. Lecture 26: Assembly of element-level matrices and vectors for Two- and Three-Dimensional problems (Part - B) YouTube
  3. Lecture 27: Classical Linear Electrostatics: vector unknown (Part - A) YouTube
  4. Lecture 28: Classical Linear Electrostatics: vector unknown (Part - B) YouTube

Week 9

  1. Lecture 29: Finite Element Interpolation/ Basis Functions (Part - A) YouTube
  2. Lecture 30: Finite Element Interpolation/ Basis Functions (Part - B) YouTube
  3. Lecture 31: Numerical Integration, Derivatives of shape function (Part - A) YouTube
  4. Lecture 32: Numerical Integration, Derivatives of shape function (Part - B) YouTube

Week 10

  1. Lecture 33: Introduction to time-dependent problems (Part - A) YouTube
  2. Lecture 34: Introduction to time-dependent problems (Part - B) YouTube
  3. Lecture 35: 1D Unsteady Linear Heat Conduction; Generalized Trapezoidal Method (Part - A) YouTube
  4. Lecture 36: 1D Unsteady Linear Heat Conduction; Generalized Trapezoidal Method (Part - B) YouTube

Week 11

  1. Lecture 37: Stability Analysis of Time Integration Methods YouTube
  2. Lecture 38: Convergence of Generalized Trapezoidal Method YouTube
  3. Lecture 39: Methods for non-linear problems YouTube

Week 12

  1. Lecture 40 : Numerical instability in the Galerkin Formulation for Advection Dominated Flows (Part - A) YouTube
  2. Lecture 41 : Numerical instability in the Galerkin Formulation for Advection Dominated Flows (Part - B) YouTube
  3. Lecture 42 : SUPG (Streamline-Upwind/Petrov-Galerkin) Method for Advection dominated flows (Part - A) YouTube
  4. Lecture 43 : SUPG (Streamline-Upwind/Petrov-Galerkin) Method for Advection dominated flows (Part - B) YouTube
  5. Lecture 44 : Stabilized Finite Element Formulations for Flows (Part - A) YouTube
  6. Lecture 45 : Stabilized Finite Element Formulations for Flows (Part - B) YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Aerospace Engineering
Teacher
Prof. Sanjay Mittal
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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