Mod-05 Lec-23 Direct methods for linear algebraic equations; Gaussian elimination method

Course Lectures

• Mod-01 Lec-01 Motivation for CFD and Introduction to the CFD approach

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• Mod-01 Lec-02 Illustration of the CFD approach through a worked out example

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• Mod-02 Lec-03 Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation

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• Mod-02 Lec-04 Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation

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• Mod-02 Lec-05 Forces acting on a control volume; Stress tensor;

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• Mod-02 Lec-06 Kinematics of deformation in fluid flow; Stress vs strain rate relation

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• Mod-02 Lec-07 Equations governing flow of incompressible flow;

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• Mod-03 Lec-08 Cut out the first 30s; Spatial discretization of a simple flow domain;

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• Mod-03 Lec-09 Finite difference approximation of pth order of accuracy for qth order derivative;

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• Mod-03 Lec-10 One-sided high order accurate approximations,Explicit and implicit formulations

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• Mod-03 Lec-11 Numerical solution of the unsteady advection equation using different finite.

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• Mod-03 Lec-12 Need for analysis of a discretization scheme; Concepts of consistency

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• Mod-03 Lec-13 Statement of the stability problem

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• Mod-03 Lec-14 Consistency and stability analysis of the unsteady diffusion equation

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• Mod-03 Lec-15 Interpretation of the stability condition,Stability analysis of the generic scalar equ

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• Mod-04 Lec-16 Template for the generic scalar transport equation and its extension to the solution

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• Mod-04 Lec-17 Illustration of application of the template using the MacCormack scheme

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• Mod-04 Lec-18 Stability limits of MacCormack scheme

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• Mod-04 Lec-19 Artificial compressibility method and the streamfunction-vorticity method

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• Mod-04 Lec-20 Pressur e equation method for the solution of NS equations

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• Mod-04 Lec-21 Pressure-correction approach to the solution of NS equations on a staggered grid

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• Mod-05 Lec-22 Need for effici ent solution of linear algebraic equations

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• Mod-05 Lec-23 Direct methods for linear algebraic equations; Gaussian elimination method

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• Mod-05 Lec-24 Gauss-Jordan method; LU decomposition method; TDMA and Thomas algorithm

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• Mod-05 Lec-25 Basic iterative methods for linear algebraic equations: Description of point -Jacobi

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• Mod-05 Lec-26 Convergence analysis of basic iterative schemes,Diagonal dominance condition

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• Mod-05 Lec-27 Application to the Laplace equation

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• Mod-05 Lec-28 Advanced iterative methods: Alternating Direction Implicit Method; Operator splitting

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• Mod-05 Lec-29 Advanced iterative methods,Strongly Implicit Procedure,Conjugate gradient method

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• Mod-05 Lec-30 Illustration of the Multigrid method for the Laplace equation

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• Mod-06 Lec-31 Overview of the approach of numerical solution of NS equations for simple domains

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• Mod-06 Lec-32 Derivation of the energy conservation equation

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• Mod-06 Lec-33 Derivation of the species conservation equation; dealing with chemical reactions

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• Mod-06 Lec-34 Turbulence,Characteri stics of turbulent flow,Dealing with fluctuations

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• Mod-06 Lec-35 Derivation of the Reynolds -averaged Navier -Stokes equations

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• Mod-06 Lec-36 Reynol ds stresses in turbulent flow,Time and length scales of turbulence

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• Mod-06 Lec-37 One-equation model for turbulent flow

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• Mod-06 Lec-38 Two -equation model for turbulent flow; Numerical calculation of turbulent

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• Mod-06 Lec-39 Calculation of near-wall region in turbulent flow; wall function approach

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• Mod-07 Lec-40 Need for special methods for dealing with irregular fl ow geometry

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• Mod-07 Lec-41 Transformation of the governing equations; Illustration for the Laplace equation

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• Mod-07 Lec-42 Finite volume method for complicated flow domain

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• Mod-07 Lec-43 Finite volume method for the general case

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• Mod-07 Lec-44 Generation of a structured grid for irregular flow domain; Algebraic methods

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• Mod-07 Lec-45 Unstructured grid generation,Domain nodalization

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• Mod-07 Lec-46 Delaunay triangulation method for unstructured grid generation

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• Mod-07 Lec-47 Co -located grid approach for irregular geometries; Pressure correction equations

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