Learn · Computational Fluid Dynamics
Lecture 3 of 60Week 1
Lecture 3 : Examples of partial differential equations
Prof. Suman Chakraborty · IIT Kharagpur
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All the lectures
- Lecture 1 : Introduction to CFD
- Lecture 2 : Classification of partial differential equations
- Lecture 3 : Examples of partial differential equations
- Lecture 4 : Examples of partial differential equations (contd.)
- Lecture 5 : Nature of the charateristics of partial differential equation
- Lecture 6 : Euler-Lagrangian equation
- Lecture 7 : Approximate Solutions of Differential Equations
- Lecture 8 : Variational formulation
- Lecture 9 : Example of variational formulation and introduction to weighted residual method
- Lecture 10 : Weighted residual method (contd.)
- Lecture 11 : Point Collocation method, the Galerkin's method & the 'M' form
- Lecture 12 : Finite element method (FEM) of discretization
- Lecture 13 : Finite element method of discretization (contd.)
- Lecture 14 : Finite difference method (FDM) of discretization
- Lecture 15 : Well posed boundary value problem
- Lecture 16 : Finite volume method (FVM) of discretization
- Lecture 17 : Illustrative examples of finite volume method
- Lecture 18 : Illustrative examples of finite volume method (contd.)
- Lecture 19 : Basic rules of finite volume discretization
- Lecture 20 : Implementaion of boundary conditions in FVM
- Lecture 21 : Implementaion of boundary conditions in FVM (contd.)
- Lecture 22 : 1-D Unsteady state diffusion problem
- Lecture 23 : 1-D Unsteady state diffusion problem (contd.)
- Lecture 24 : Consequences of Discretization of Unsteady State Problems
- Lecture 25 : FTCS scheme
- Lecture 26 : CTCS scheme (Leap frog scheme) & Dufort-Frankel scheme
- Lecture 27 : Part 1: FV Discretization of 2-D Unsteady State Diffusion Type problems; Part 2: Solution to linear algebraic equations
- Lecture 28 : Solution to linear algebraic equations (contd.)
- Lecture 29 : Elemination methods
- Lecture 30 : Gaussian elemination and LU Decomposition methods
- Lecture 31: Illustrative example of elemination method
- Lecture 32 : Tri-Diagonal Matrix Algorithm (TDMA)
- Lecture 33 : Elimination Methods: Error Analysis
- Lecture 34 : Elimination Methods: Error Analysis (Contd.)
- Lecture 35 : Iteration methods
- Lecture 36 : Generalized analysis of Iteration method
- Lecture 37 : Further discussion on Iterative methods
- Lecture 38 : Illustrative examples of Iterative methods
- Lecture 39 : Gradient Search based methods
- Lecture 40 : Steepest descent method (contd.)
- Lecture 41 : Conjugate gradient method
- Lecture 42 : Convection diffiusion equation
- Lecture 43 : Central difference scheme applied to convection-diffusion equation
- Lecture 44 : Upwind scheme
- Lecture 45 : Illustrative examples
- Lecture 46 : Exact solution of 1-D steady state convection diffusion equation (contd.)
- Lecture 47 : Exponential scheme
- Lecture 48 : Generalized convection diffusion formulation
- Lecture 49 : 2-D convection diffusion problem
- Lecture 50 : False (numerical) diffusion scheme and the QUICK scheme
- Lecture 51 : "Discretization of Navier Stokes equation "
- Lecture 52 : "Discretization of Navier Stokes equation (contd.) "
- Lecture 53 : "Concept of staggered grid "
- Lecture 54 : "SIMPLE algorithm "
- Lecture 55 : "Salient features of SIMPLE algorithm "
- Lecture 56 : Illustrative examples on the use of SIMPLE algorithm
- Lecture 57 : SIMPLER algorithm
- Lecture 58 : Illustrative examples of SIMPLER algorithm
- Lecture 59 : What is there in implementing a CFD Code
- Lecture 60 : Some representative case studies