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Lecture 14 : Finite difference method (FDM) of discretization
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Computational Fluid Dynamics
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- 1 Computational Fluid Dynamics by Prof. Suman Chakraborty
- 2 Lecture 1 : Introduction to CFD
- 3 Lecture 2 : Classification of partial differential equations
- 4 Lecture 3 : Examples of partial differential equations
- 5 Lecture 4 : Examples of partial differential equations (contd.)
- 6 Lecture 5 : Nature of the charateristics of partial differential equation
- 7 Lecture 6 : Euler-Lagrangian equation
- 8 Lecture 7 : Approximate Solutions of Differential Equations
- 9 Lecture 8 : Variational formulation
- 10 Lecture 9 : Example of variational formulation and introduction to weighted residual method
- 11 Lecture 10 : Weighted Residual Method
- 12 Lecture 11 : Point Collocation method, the Galerkin's method & the 'M' form
- 13 Lecture 12 : Finite element method (FEM) of discretization
- 14 Lecture 13 : Finite element method of discretization (contd.)
- 15 Lecture 14 : Finite difference method (FDM) of discretization
- 16 Lecture 15 : Well posed boundary value problem
- 17 Lecture 16 : Finite volume method (FVM) of discretization
- 18 Lecture 17 : Illustrative examples of finite volume method
- 19 Lecture 18 : Illustrative examples of finite volume method (contd.)
- 20 Lecture 19 : Basic rules of finite volume discretization
- 21 Lecture 20 : Implementaion of boundary conditions in FVM
- 22 Lecture 21 : Implementation of boundary conditions in FVM (contd.)
- 23 Lecture 22 : 1-D Unsteady state diffusion problem
- 24 Lecture 23 : 1-D Unsteady state diffusion problem (contd.)
- 25 Lecture 24 : Consequences of Discretization of Unsteady State Problems
- 26 Lecture 25 : FTCS scheme
- 27 Lecture 26 : CTCS scheme (Leap frog scheme) & Dufort-Frankel scheme
- 28 Lecture 27 : FV Discretization of 2-D Unsteady State Diffusion
- 29 Lecture 28 : Solution to linear algebraic equations (contd.)
- 30 Lecture 29 : Elemination methods
- 31 Lecture 30 : Gaussian elemination and LU Decomposition methods
- 32 Lecture 31 : Illustrative example of elemination method
- 33 Lecture 32 : Tri-Diagonal Matrix Algorithm (TDMA)
- 34 Lecture 33 : Elimination Methods: Error Analysis
- 35 Lecture 34 : Elimination Methods: Error Analysis (Contd.)
- 36 Lecture 35 : Iteration methods
- 37 Lecture 36 : Generalized analysis of Iteration method
- 38 Lecture 37 : Further discussion on Iterative methods
- 39 Lecture 38 : Illustrative examples of Iterative methods
- 40 Lecture 39 : Gradient Search based methods
- 41 Lecture 40 : Steepest descent method (contd.)
- 42 Lecture 41 : Conjugate gradient method
- 43 Lecture 42 : Convection diffiusion equation
- 44 Lecture 43 : Central difference scheme applied to convection-diffusion equation
- 45 Lecture 44 : Upwind scheme
- 46 Lecture 45 : Illustrative examples
- 47 Lecture 46 : Exact solution of 1-D steady state convection diffusion equation (contd.)
- 48 Lecture 47 : Exponential scheme
- 49 Lecture 48 : Generalized convection diffusion formulation
- 50 Lecture 49 : 2-D convection diffusion problem
- 51 Lecture 50 : False (numerical) diffusion scheme and the QUICK scheme
- 52 Lecture 51 : Discretization of Navier Stokes Equation
- 53 Lecture 52 : Discretization of Navier Stokes Equation (Contd.)
- 54 Lecture 53 : Concept of Staggered Grid
- 55 Lecture 54 : SIMPLE Algorithm
- 56 Lecture 55 : Salient Features of SIMPLE Algorithm
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- 58 mod12lec57
- 59 mod12lec58
- 60 mod12lec59
- 61 mod12lec60
