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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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Description:

COURSE OUTLINE : CFD or computational fluid dynamics is a branch of continuum mechanics that deals with numerical simulation of fluid flow and heat transfer problems. The exact analytical solutions of various integral, differential or integro-differential equations, obtained from mathematical modeling of any continuum problem, are limited to only simple geometries. Thus for most situations of practical interest, analytical solutions cannot be obtained and a numerical approach should be applied. In the field of mechanics, the approach of obtaining approximate numerical solutions with the help of digital computers is known as Computational Mechanics whereas the same is termed as Computational Fluid Dynamics for thermo-fluidic problems. CFD, thus, deals with obtaining an approximate numerical solution of the governing equations based on the fundamental conservation laws of mass, momentum, and energy.

Computational Fluid Dynamics

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#Science #Physics #Fluid Mechanics #Fluid Dynamics #Computational Fluid Dynamics #Mathematics #Differential Equations #Partial Differential Equations #Engineering #Finite Element Analysis #Finite Element Method #Numerical Analysis #Finite Difference Method #Applied Mathematics #Numerical Methods #Finite Volume Method

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