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Computational Fluid Dynamics

Computational Fluid Dynamics. 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 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. (from nptel.ac.in)

Lecture 11 - Finite Difference and Finite Volume Method

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Introduction to Computational Fluid Dynamics and Principles of Conservation

Lecture 01 - Introduction to Computational Fluid Dynamics and Principles of Conservation

Lecture 02 - Conservation of Mass and Momentum: Continuity and Navier-Stokes Equation

Lecture 03 - Navier-Stokes Equation (cont.)

Lecture 04 - Energy Equation and General Structure of Conservation Equations

Classification of Partial Differential Equations and Physical Behavior

Lecture 05 - Classification of Partial Differential Equations and Physical Behavior

Lecture 06 - Classification of Partial Differential Equations and Physical Behavior (cont.)

Approximate Solutions of Differential Equations

Lecture 07 - Error Minimization Principles

Lecture 08 - Variational Principles and Weighted Residual Approach

Lecture 09 - Weighted Residual Approach and Introduction to Discretization

Fundamentals of Discretization

Lecture 10 - Finite Element Method

Lecture 11 - Finite Difference and Finite Volume Method

Lecture 12 - Finite Volume Method (cont.)

Lecture 13 - Finite Volume Method: Some Conceptual Basics and Illustrations through 1-D Steady State Diffusion Problems

Lecture 14 - Finite Volume Method: Boundary Condition Implementation and Discretization of Unsteady State Problems

Lecture 15 - Finite Volume Method: Discretization of Unsteady State Problems

Discretization of Unsteady State Problems

Lecture 16 - Important Consequences of Discretization of Unsteady State Problems

Important Consequences of Discretization of Time Dependent Diffusion Type Problems

Lecture 17 - Important Consequences of Discretization of Time Dependent Diffusion Type Problems and Stability Analysis

Lecture 18 - Discretization of Hyperbolic Equations: Stability Analysis

Lecture 19 - Stability of Second Order Hyperbolic Equations, Mid-Semester Assessment Review

Lecture 20 - Finite Volume Discretization of 2-D Unsteady State Diffusion Type

Lecture 21 - Solution of Systems of Linear Algebraic Equations

Lecture 22 - Solution of Systems of Linear Algebraic Equations: Elimination Methods

Lecture 23 - Solution of Systems of Linear Algebraic Equations: Elimination Methods (cont.)

Lecture 24 - Elimination Methods: Error Analysis

Lecture 25 - Iterative Methods for Numerical Solution of Systems of Linear Algebraic Equations

Lecture 26 - Iterative Methods for Numerical Solution of Systems of Linear Algebraic Equations (cont.)

Lecture 27 - Iterative Methods: Further Examples

Lecture 28 - Combination of Iteration and Elimination Techniques, Introduction to Gradient Search Methods

Lecture 29 - Gradient Search Methods (cont.)

Discretization of Convection-Diffusion Equations: A Finite Volume Approach

Lecture 30 - Central Difference Scheme, The Physical Basis of the Upwind Scheme

Lecture 31 - Upwind Scheme, Exact Solution of a One Dimensional Problem

Lecture 32 - Exponential Scheme and Hybrid Scheme

Lecture 33 - Power Law Scheme, Generalized Convection-Diffusion Formulation

Lecture 34 - Finite Volume Discretization of Two-dimensional Convection-Diffusion Problem

Discretization of Navier-Stokes Equations

Lecture 35 - Discretization of the Momentum Equation: Stream Function-Vorticity Approach and Primitive Variable Approach

Lecture 36 - Staggered Grid and Collocated Grid, SIMPLE Algorithm

Lecture 37 - SIMPLE Algorithm

Lecture 38 - SIMPLER Algorithm, Fundamentals of Unstructured Grid Formulation

Unstructured Grid Formulation

Lecture 39 - Unstructured Grid Formulation (cont.)

What is There in Implementing a CFD Code?

Lecture 40 - What is There in Implementing a CFD Code?

Introduction to Turbulence Modeling

Lecture 41 - Introduction to Turbulence Modeling

Lecture 42 - Introduction to Turbulence Modeling (cont.)

Lecture 43 - Course Review