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Course11210590860 lectures

Finite Element Method in Thermal Engineering

Prof. Subhankar Sen · IIT-ISM Dhanbad

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Lecture -1 : Introduction Video
  2. Lecture -2 : Introduction to tensors Video
  3. Lecture -3 : Strong form of differential equations, primary and secondary variables Video
  4. Lecture -4 : Introduction to variational methods Video
  5. Lecture - 5 : Illustration of variational methods , variational methods of FEM Video

Week 2

  1. Lecture -6 : BVP, IVP and IBVP, types of finite elements Video
  2. Lecture -7 : Weight and shape functions, weak form Video
  3. Lecture -8 : Domain decomposition Video
  4. Lecture -9: Types of boundary conditions, IEN, ID and LM arrays in one-dimension Video
  5. Lecture -10 : ID and LM arrays in two- dimensions, SDOF and multi-DOF Video

Week 3

  1. Lecture -11 : Galerkin weak form of Poisson equation Video
  2. Lecture -12 : FDM, FVM and FEM Video
  3. Lecture -13 : FDM and FVM for one- dimensional Poisson equation Video
  4. Lecture -14: FEM for one-dimensional Poisson equation Video
  5. Lecture -15 : FEM using a single bar element Video

Week 4

  1. Lecture -16 : Isoparametric elements Video
  2. Lecture -17 : Illustration for linear bar elements Video
  3. Lecture -18 : Quadratic bar elements, quadrilateral elements Video
  4. Lecture -19 : Gauss quadrature for bilinear quadrilateral elements Video
  5. Lecture -20 : Local coordinates in 2- D, numerical examples Video

Week 5

  1. Lecture -21 : Implementation of boundary conditions Video
  2. Lecture -22 : Implementation of CBC and RBC in 1-D and 2-D Video
  3. Lecture -23 : Shape functions of linear triangular elements Video
  4. Lecture -24 : GFEM solution of 2-D Poisson equation of heat conduction Video
  5. Lecture -25 : GFEM solution of 2-D Poisson equation of heat conduction part 2 Video

Week 6

  1. Lecture - 26 : Calculation of element level entries of linear triangular elements Video
  2. Lecture 27 : Solving 2-D Poisson equation using linear triangular elements Video
  3. Lecture -28 : Classification of linear equation solvers, Gauss elimination Video
  4. Lecture -29 : Illustration of Thomas algorithm Video
  5. Lecture -30 : Stationary iterative methods, preconditioning, matrix-free methods Video

Week 7

  1. Lecture -31 : Formation of element level matrices and vectors for Parabolic PDE Video
  2. Lecture -32 : Consistent mass matrix of bar and triangular elements Video
  3. Lecture -33 : GFEM explicit, implicit and Crank-Nicolson solutions of parabolic PDE in 1-D Video
  4. Lecture -34 : GFEM for hyperbolic PDEs; first order wave equation, skew- symmetric matrice Video
  5. Lecture -35 : Galerkin discretized semi- discrete form of the second order wave equation Video

Week 8

  1. Lecture -36 : Weak form and fully discrete form of convection-diffusion equation Video
  2. Lecture -37 : Peclet number, convection and diffusion matrices for bar elements Video
  3. Lecture -38 : GFEM solution using 2-noded or linear bar elements Video
  4. Lecture-39 : GFEM solution using 3-noded or quadratic bar elements Video
  5. Lecture -40 : GFEM explicit solution of 1-D transient convection-diffusion equation Video

Week 9

  1. Lecture -41 : Implicit GFEM solution of 1-D unsteady convection-diffusion equation Video
  2. Lecture -42 : Upwinding and artificial viscosity Video
  3. Lecture -43 : The Petrov-Galerkin stabilization Video
  4. Lecture -44 : Petrov-Galerkin weak form of steady convection-diffusion equation Video
  5. Lecture -45 : Petrov-Galerkin stabilization treatment numerical example Video

Week 10

  1. Lecture -46 : Stable Pe limit for convection- diffusion, Navier-stokes equations of motion Video
  2. Lecture -47 : Coupled and segregated formulations, LBB condition for stable solutions Video
  3. Lecture - 48 : Saddle point problems, inf-sup or LBB compatibility condition, stable elements Video
  4. Lecture -49 : Connectivity and assembly using Q1Q0 elements for 2-D lid-driven cavity Video
  5. Lecture -50 : Coupled Galerkin weak form of 2-D, steady Navier-Stokes equations of motion Video

Week 11

  1. Lecture -51 : Preprocessor arrays using Q1Q0 element for 2-D Navier-Stokes flow (GFEM) Video
  2. Lecture -52 : Generation of Q1Q0 element level matrix terms for 2-D Navier-Stokes flow (GFEM) Video
  3. Lecture -53 : Calculation of x-momentum GFEM matrix for Q1Q0 element Video
  4. Lecture - 54 : Calculation of y-momentum GFEM matrix for Q1Q0 element Video
  5. Lecture -55 : Calculation of GFEM Stokes flow matrix for Q1Q0 element Video

Week 12

  1. Lecture -56 : Implementation of BCs using Q1Q0 elements for 2-D Stokes flow (GFEM) Video
  2. Lecture -57 : Illustration of assembly using Q1Q0 elements for 2-D Stokes flow (GFEM) Video
  3. Lecture -58 : The Petrov-Galerkin stabilized Navier-Stokes equations Q1Q1 elements part I Video
  4. Lecture -59 : The Petrov-Galerkin stabilized Navier-Stokes equations Q1Q1 elements part II Video
  5. Lecture -60 : The Petrov-Galerkin stabilized Navier-Stokes equations Q1Q1 elements part III Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT-ISM Dhanbad
Department
Mechanical Engineering
Teacher
Prof. Subhankar Sen
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. Coordinated by IIT Kharagpur.
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