Overview

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.

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.
mod12lec56.
mod12lec57.
mod12lec58.
mod12lec59.
mod12lec60.