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Computational Fluid Dynamics

Computational Fluid Dynamics. Instructor: Dr. Krishna M. Singh, Department of Mechanical and Industrial Engineering, IIT Roorkee. This course looks at all the aspects theoretical, numerical, and application aspects of computational fluid dynamics. Computational fluid dynamics (CFD) has become an essential tool in analysis and design of thermal and fluid flow systems in wide range of industries. Few prominent areas of applications of CFD include meteorology, transport systems (aerospace, automobile, high speed trains), energy systems, environment, electronics, biomedical (design of life support and drug delivery systems), etc.

The correct use of CFD as a design analysis or diagnostic tool requires a thorough understanding of underlying physics, mathematical modeling and numerical techniques. The user must be fully aware of the properties and limitations of the numerical techniques incorporated in CFD software. This course aims to provide precisely these insights of CFD. (from nptel.ac.in)

Lecture 06 - Momentum Equation: Navier-Stokes Equations


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Introduction to Computational Fluid Dynamics
Lecture 01 - General Introduction: Historical Background and Spectrum of Applications
Lecture 02 - CFD: Simulation Process and Course Outline
Mechanical Modeling
Lecture 03 - Conservation Laws and Mathematical Preliminaries
Lecture 04 - Mass Conservation: Continuity Equation
Lecture 05 - Momentum Equation: Newton's 2nd Law
Lecture 06 - Momentum Equation: Navier-Stokes Equations
Lecture 07 - Navier-Stokes Equation and its Simplified Forms
Lecture 08 - Energy and Scalar Transport Equations
Lecture 09 - Scalar Transport, Mathematical Classification and Boundary Conditions
Finite Difference Method
Lecture 10 - Finite Difference Method: Methodology and Grid Notation
Lecture 11 - Finite Difference Approximation of First Order Derivatives
Lecture 12 - Finite Difference Approximation of Second Order Derivatives
Lecture 13 - Finite Difference Approximation of Second Order Derivatives (cont.)
Lecture 14 - Approximation of Mixed Derivatives and Multi-Dimensional F.D. Formulae
Lecture 15 - Implementation of Boundary Conditions and Finite Difference Algebraic System
Lecture 16 - Applications of FDM to Scalar Transport Problems
Lecture 17 - Applications of FDM to Scalar Transport Problems (cont.)
Lecture 18 - Application of FDM to Advection-Diffusion and Computer Implementation Aspects
Lecture 19 - Computer Implementation of FDM for Steady State Heat Diffusion Problems
Lecture 20 - Computer Implementation of FDM for Steady State Heat Diffusion Problems (cont.)
Lecture 21 - Computer Implementation of FDM for Steady State Heat Diffusion Problems (cont.)
Solution of Algebraic Systems
Lecture 22 - Solution of Discrete Algebraic Systems
Lecture 23 - Direct and Basic Iterative Methods for Linear Systems
Lecture 24 - Accelerated Iterative Methods for Linear Systems
Time Integration Techniques
Lecture 25 - Two-Level and Multi-Level Methods for First Order Initial Value Problems
Lecture 26 - Two-Level and Multi-Level Methods for First Order IVPs (cont.)
Lecture 27 - Application to Unsteady Transport Problems
Finite Volume Method
Lecture 28 - Introduction to Finite Volume Method
Lecture 29 - Finite Volume Interpolation Schemes
Lecture 30 - Application to FVM to Scalar Transport
Finite Element Method
Lecture 31 - Introduction to Finite Element Method
Lecture 32 - Finite Element Shape Functions and Numerical Integration
Lecture 33 - Finite Element Shape Functions and Numerical Integration (cont.)
Lecture 34 - Application of FEM to Scalar Transport
Numerical Solution of Navier-Stokes Equations
Lecture 35 - Special Features of Navier-Stokes Equations
Lecture 36 - Time Integration Techniques for Navier-Stokes Equations
Lecture 37 - Implicit Pressure Correction Methods
Lecture 38 - SIMPLEC, SIMPLER and Fractional Step Methods
Numerical Simulation of Turbulent Flows
Lecture 39 - Turbulent Flows: Features and Simulation Strategies
Lecture 40 - Reynolds Averaging and RANS Simulation Models
Lecture 41 - RANS Turbulence Models and Large Eddy Simulation
Grid Generation and Aspects of Real Life CFD Analysis
Lecture 42 - Introduction to Grid Generation
Lecture 43 - Aspects of Practical CFD Analysis