Learn · Finite Element Method in Thermal Engineering
Lecture 59 of 60Week 12
Lecture -59 : The Petrov-Galerkin stabilized Navier-Stokes equations Q1Q1 elements part II
Prof. Subhankar Sen · IIT-ISM Dhanbad
Credits and licence
- From
- Finite Element Method in Thermal Engineering, IIT-ISM Dhanbad (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. Coordinated by IIT Kharagpur.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Lecture -1 : Introduction
- Lecture -2 : Introduction to tensors
- Lecture -3 : Strong form of differential equations, primary and secondary variables
- Lecture -4 : Introduction to variational methods
- Lecture - 5 : Illustration of variational methods , variational methods of FEM
- Lecture -6 : BVP, IVP and IBVP, types of finite elements
- Lecture -7 : Weight and shape functions, weak form
- Lecture -8 : Domain decomposition
- Lecture -9: Types of boundary conditions, IEN, ID and LM arrays in one-dimension
- Lecture -10 : ID and LM arrays in two- dimensions, SDOF and multi-DOF
- Lecture -11 : Galerkin weak form of Poisson equation
- Lecture -12 : FDM, FVM and FEM
- Lecture -13 : FDM and FVM for one- dimensional Poisson equation
- Lecture -14: FEM for one-dimensional Poisson equation
- Lecture -15 : FEM using a single bar element
- Lecture -16 : Isoparametric elements
- Lecture -17 : Illustration for linear bar elements
- Lecture -18 : Quadratic bar elements, quadrilateral elements
- Lecture -19 : Gauss quadrature for bilinear quadrilateral elements
- Lecture -20 : Local coordinates in 2- D, numerical examples
- Lecture -21 : Implementation of boundary conditions
- Lecture -22 : Implementation of CBC and RBC in 1-D and 2-D
- Lecture -23 : Shape functions of linear triangular elements
- Lecture -24 : GFEM solution of 2-D Poisson equation of heat conduction
- Lecture -25 : GFEM solution of 2-D Poisson equation of heat conduction part 2
- Lecture - 26 : Calculation of element level entries of linear triangular elements
- Lecture 27 : Solving 2-D Poisson equation using linear triangular elements
- Lecture -28 : Classification of linear equation solvers, Gauss elimination
- Lecture -29 : Illustration of Thomas algorithm
- Lecture -30 : Stationary iterative methods, preconditioning, matrix-free methods
- Lecture -31 : Formation of element level matrices and vectors for Parabolic PDE
- Lecture -32 : Consistent mass matrix of bar and triangular elements
- Lecture -33 : GFEM explicit, implicit and Crank-Nicolson solutions of parabolic PDE in 1-D
- Lecture -34 : GFEM for hyperbolic PDEs; first order wave equation, skew- symmetric matrice
- Lecture -35 : Galerkin discretized semi- discrete form of the second order wave equation
- Lecture -36 : Weak form and fully discrete form of convection-diffusion equation
- Lecture -37 : Peclet number, convection and diffusion matrices for bar elements
- Lecture -38 : GFEM solution using 2-noded or linear bar elements
- Lecture-39 : GFEM solution using 3-noded or quadratic bar elements
- Lecture -40 : GFEM explicit solution of 1-D transient convection-diffusion equation
- Lecture -41 : Implicit GFEM solution of 1-D unsteady convection-diffusion equation
- Lecture -42 : Upwinding and artificial viscosity
- Lecture -43 : The Petrov-Galerkin stabilization
- Lecture -44 : Petrov-Galerkin weak form of steady convection-diffusion equation
- Lecture -45 : Petrov-Galerkin stabilization treatment numerical example
- Lecture -46 : Stable Pe limit for convection- diffusion, Navier-stokes equations of motion
- Lecture -47 : Coupled and segregated formulations, LBB condition for stable solutions
- Lecture - 48 : Saddle point problems, inf-sup or LBB compatibility condition, stable elements
- Lecture -49 : Connectivity and assembly using Q1Q0 elements for 2-D lid-driven cavity
- Lecture -50 : Coupled Galerkin weak form of 2-D, steady Navier-Stokes equations of motion
- Lecture -51 : Preprocessor arrays using Q1Q0 element for 2-D Navier-Stokes flow (GFEM)
- Lecture -52 : Generation of Q1Q0 element level matrix terms for 2-D Navier-Stokes flow (GFEM)
- Lecture -53 : Calculation of x-momentum GFEM matrix for Q1Q0 element
- Lecture - 54 : Calculation of y-momentum GFEM matrix for Q1Q0 element
- Lecture -55 : Calculation of GFEM Stokes flow matrix for Q1Q0 element
- Lecture -56 : Implementation of BCs using Q1Q0 elements for 2-D Stokes flow (GFEM)
- Lecture -57 : Illustration of assembly using Q1Q0 elements for 2-D Stokes flow (GFEM)
- Lecture -58 : The Petrov-Galerkin stabilized Navier-Stokes equations Q1Q1 elements part I
- Lecture -59 : The Petrov-Galerkin stabilized Navier-Stokes equations Q1Q1 elements part II
- Lecture -60 : The Petrov-Galerkin stabilized Navier-Stokes equations Q1Q1 elements part III