Overview

Instructor: Prof. Suman Chakraborty, Department of Mechanical Engineering, IIT Kharagpur.

This course provides an introduction to Computational Fluid Dynamics (CFD) with an emphasis on the fundamental principles that govern the implementation of CFD in practical applications. 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 integrodifferential 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

Mod-01 Lec-01 Introduction to Computational Fluid Dynamics and Principles of Conservation.
Mod-01 Lec-02 Conservation of Mass and Momentum: Continuity and Navier Stokes Equation.
Navier Stokes Equation (Contd.).
Mod-01 Lec-04 Energy Equation and General Structure of Conservation Equations.
Mod-01 Lec-05 Classification of Partial Differential Equations and Physical Behaviour.
Mod-01 Lec-06 Classification of Partial Differential Equations and Physical Behaviour (Contd.).
Mod-01 Lec-07 Approximate Solutions of Differential Equations: Error Minimization Principles.
Mod-01 Lec-08 Approximate Solutions of Differential Equations: Variational Principles.
Mod-01 Lec-09 Weighted Residual Approach and Introduction to Discretization.
Mod-01 Lec-10 Fundamentals of Discretization: Finite Element Method.
Mod-01 Lec-11 Fundamentals of Discretization: Finite Difference and Finite Volume Method.
Mod-01 Lec-12 Fundamentals of Discretization: Finite Volume Method (Contd.).
Mod-01 Lec-13 Finite Volume Method:Some Concept Basics.
Mod-01 Lec-14 Finite Volume Method: Boundary Condition Implementation.
Mod-01 Lec-15 Finite Volume Method:Discretization of Unsteady State Problems.
Mod-01 Lec-16 Important Consequences of Discretization of Unsteady State Problems.
Mod-01 Lec-17 Important Consequences of Discretization of Time Dependent Diffusion.
Mod-01 Lec-18 Discretization of Hyperbolic Equations: Stability Analysis.
Mod-01 Lec-19 PART1:Stability of Second Order Hyperbolic Equations.
Mod-01 Lec-20 PART 1: Mid-Semester Assessment Review (Questions and Answers) (Contd.).
Mod-01 Lec-21 Solution of Systems of Linear Algebraic Equations.
Mod-01 Lec-22 Solution of Systems of Linear Algebraic Equations: Elimination Methods.
Mod-01 Lec-23 Solution of Systems of Linear Algebraic Equations: Elimination Methods (Contd.).
Mod-01 Lec-24 Elimination Methods: Error Analysis.
Mod-01 Lec-25 Iterative Methods for Numerical Solution of Systems of Linear Algebraic Equations.
Mod-01 Lec-26 Iterative Methods for Numerical Solution of Systems of Linear Algebraic Equations.
Mod-01 Lec-27 Iterative Methods: Further Examples.
Mod-01 Lec-28 PART1:Combination of Iteration & Elimination Techniques.
Mod-01 Lec-29 Gradient Search Methods (Contd.).
Mod-01 Lec-30 Discretization of Convection-Diffusion Equations: A Finite Volume Approach.
Mod-01 Lec-31 Discretization of Convection-Diffusion Equations: A Finite Volume Approach (Contd.).
Mod-01 Lec-32 Discretization of Convection- Diffusion Equations: A Finite Volume Approach (Contd.).
Mod-01 Lec-33 Discretization of Convection -Diffusion Equations: A Finite Volume Approach (Contd.).
Mod-01 Lec-34 Discretization of Convection-Diffusion Equations: A Finite Volume Approach ( Contd.).
Mod-01 Lec-35 Discretization of Navier Stokes Equations.
Mod-01 Lec-36 Discretization of Navier Stokes Equations ( Contd.).
Mod-01 Lec-37 Discretization of Navier Stokes Equations ( Contd. ).
Mod-01 Lec-38 PART 1 : Discretization of Navier Stokes Equations (Contd.) PART 2 : Fundamentals.
Mod-01 Lec-39 Unstructured Grid Formulation (Contd.).
Mod-01 Lec-40 What is there in implementing a CFD Code.
Mod-01 Lec-41 Introduction to Turbulence Modeling.
Mod-01 Lec-42 Introduction to Turbulence Modeling (Contd.).
Mod-01 Lec-43 End Semester Questions Review.