# Computational Fluid Dynamics

Indian Institute of Technology Kharagpur

Introduction to Computational Fluid Dynamics and Principles of Conservation: Continuity Equation, Navier Stokes Equation, Energy Equation and General Structure of Conservation Equations, Classification of Partial Differential Equations and Physical Behaviour, Approximate Solutions of Differential Equations: Error Minimization Principles, Variational Principles and Weighted Residual Approach, Fundamentals of Discretization: Finite Element Method, Finite Difference and Finite Volume Method, Finite Volume Method: Some Conceptual Basics and Illustrations through 1-D Steady State Diffusion Problems, Boundary Condition Implementation and Discretization of Unsteady State Problems, Important Consequences of Discretization of Time Dependent Diffusion Type Problems and Stability Analysis : Consistency, Stability and Convergence, LAX Equivalence theorem, Grid independent and time independent study, Stability analysis of parabolic equations (1-D unsteady state diffusion problems): FTCS (Forward time central space) scheme, Stability analysis of parabolic equations (1-D unsteady state diffusion problems): CTCS scheme (Leap frog scheme), Dufort-Frankel scheme, Stability analysis of hyperbolic equations: FTCS, FTFS, FTBS and CTCS Schemes, Finite Volume Discretization of 2-D unsteady State Diffusion type Problems, Solution of Systems of Linear Algebraic Equations: Elimination Methods, Iterative Methods, Gradient Search Methods, Discretization of Convection-Diffusion Equations: A Finite Volume Approach, Discretization of Navier Stokes Equations: Stream Function-Vorticity approach and Primitive variable approach, SIMPLE Algorithm, SIMPLER Algorithm, Unstructured Grid Formulation , Introduction to Turbulence Modeling.

• ##### Mod-01 Lec-01 Introduction to Computational Fluid Dynamics and Principles of Conservation
Prof. S. Chakraborty
• ##### Mod-01 Lec-02 Conservation of Mass and Momentum: Continuity and Navier Stokes Equation
Prof. S. Chakraborty
• ##### Mod01 Lec-03 Navier Stokes Equation (Contd.)
Prof. S. Chakraborty
• ##### Mod-01 Lec-04 Energy Equation and General Structure of Conservation Equations
Prof. S. Chakraborty
• ##### Mod-01 Lec-05 Classification of Partial Differential Equations and Physical Behaviour
Prof. S. Chakraborty
• ##### Mod-01 Lec-06 Classification of Partial Differential Equations and Physical Behaviour (Contd.)
Prof. S. Chakraborty
• ##### Mod-01 Lec-07 Approximate Solutions of Differential Equations: Error Minimization Principles
Prof. S. Chakraborty
• ##### Mod-01 Lec-08 Approximate Solutions of Differential Equations: Variational Principles
Prof. S. Chakraborty
• ##### Mod-01 Lec-09 Weighted Residual Approach and Introduction to Discretization
Prof. S. Chakraborty
• ##### Mod-01 Lec-10 Fundamentals of Discretization: Finite Element Method
Prof. S. Chakraborty
• ##### Mod-01 Lec-11 Fundamentals of Discretization: Finite Difference and Finite Volume Method
Prof. S. Chakraborty
• ##### Mod-01 Lec-12 Fundamentals of Discretization: Finite Volume Method (Contd.)
Prof. S. Chakraborty
• ##### Mod-01 Lec-13 Finite Volume Method:Some Concept Basics
Prof. S. Chakraborty
• ##### Mod-01 Lec-14 Finite Volume Method: Boundary Condition Implementation
Prof. S. Chakraborty
• ##### Mod-01 Lec-15 Finite Volume Method:Discretization of Unsteady State Problems
Prof. S. Chakraborty
• ##### Mod-01 Lec-16 Important Consequences of Discretization of Unsteady State Problems
Prof. S. Chakraborty
• ##### Mod-01 Lec-17 Important Consequences of Discretization of Time Dependent Diffusion
Prof. S. Chakraborty
• ##### Mod-01 Lec-18 Discretization of Hyperbolic Equations: Stability Analysis
Prof. S. Chakraborty
• ##### Mod-01 Lec-19 PART1:Stability of Second Order Hyperbolic Equations
Prof. S. Chakraborty
• ##### Mod-01 Lec-20 PART 1: Mid-Semester Assessment Review (Questions and Answers) (Contd.)
Prof. S. Chakraborty
• ##### Mod-01 Lec-21 Solution of Systems of Linear Algebraic Equations
Prof. S. Chakraborty
• ##### Mod-01 Lec-22 Solution of Systems of Linear Algebraic Equations: Elimination Methods
Prof. S. Chakraborty
• ##### Mod-01 Lec-23 Solution of Systems of Linear Algebraic Equations: Elimination Methods (Contd.)
Prof. S. Chakraborty
• ##### Mod-01 Lec-24 Elimination Methods: Error Analysis
Prof. S. Chakraborty
• ##### Mod-01 Lec-25 Iterative Methods for Numerical Solution of Systems of Linear Algebraic Equations
Prof. S. Chakraborty
• ##### Mod-01 Lec-26 Iterative Methods for Numerical Solution of Systems of Linear Algebraic Equations
Prof. S. Chakraborty
• ##### Mod-01 Lec-27 Iterative Methods: Further Examples
Prof. S. Chakraborty
• ##### Mod-01 Lec-28 PART1:Combination of Iteration & Elimination Techniques
Prof. S. Chakraborty
• ##### Mod-01 Lec-29 Gradient Search Methods (Contd.)
Prof. S. Chakraborty
• ##### Mod-01 Lec-30 Discretization of Convection-Diffusion Equations: A Finite Volume Approach
Prof. S. Chakraborty
• ##### Mod-01 Lec-31 Discretization of Convection-Diffusion Equations: A Finite Volume Approach (Contd.)
Prof. S. Chakraborty
• ##### Mod-01 Lec-32 Discretization of Convection- Diffusion Equations: A Finite Volume Approach (Contd.)
Prof. S. Chakraborty
• ##### Mod-01 Lec-33 Discretization of Convection -Diffusion Equations: A Finite Volume Approach (Contd.)
Prof. S. Chakraborty
• ##### Mod-01 Lec-34 Discretization of Convection-Diffusion Equations: A Finite Volume Approach ( Contd.)
Prof. S. Chakraborty
• ##### Mod-01 Lec-35 Discretization of Navier Stokes Equations
Prof. S. Chakraborty
• ##### Mod-01 Lec-36 Discretization of Navier Stokes Equations ( Contd.)
Prof. S. Chakraborty
• ##### Mod-01 Lec-37 Discretization of Navier Stokes Equations ( Contd. )
Prof. S. Chakraborty
• ##### Mod-01 Lec-39 Unstructured Grid Formulation (Contd.)
Prof. S. Chakraborty
• ##### Mod-01 Lec-40 What is there in implementing a CFD Code
Prof. S. Chakraborty
• ##### Mod-01 Lec-41 Introduction to Turbulence Modeling
Prof. S. Chakraborty
• ##### Mod-01 Lec-42 Introduction to Turbulence Modeling (Contd.)
Prof. S. Chakraborty
• ##### Mod-01 Lec-43 End Semester Questions Review
Prof. S. Chakraborty