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# Computational Fluid Dynamics

## Syllabus

Computational Fluid Dynamics by Prof. Suman Chakraborty.
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.
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 : Implementation 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 : FV Discretization of 2-D Unsteady State Diffusion.
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.
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### Taught by

IIT Kharagpur July 2018

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