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


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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