1  Motivation for CFD and Introduction to the CFD approach 
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2  Illustration of the CFD approach through a worked out example 
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3  Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation and Statement of the momentum conservation equation 
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4  Forces acting on a control volume; Stress tensor; Derivation of the momentum conservation equation ; Closure problem; Deformation of a fluid element in fluid flow 
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5  Kinematics of deformation in fluid flow; Stress vs strain rate relation; Derivation of the NavierStokes equations 
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6  Equations governing flow of incompressible flow; Initial and boundary conditions; Wellposedness of a fluid flow problem 
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7  Equations for some simple cases; Generic scalar transport equation form of the governing equations; Outline of the approach to the solution of the N S equations. 
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8  cut out the first 30s; Spatial discretization of a simple flow domain; Taylor’s series expansion and the basis of finite difference approximation of a derivative; Central and onesided difference approximations; Order of accuracy of finite difference ap 
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9  Finite difference approximation of pth order of accuracy for qth order derivative; cross derivatives; Examples of high order accurate formulae for several derivatives 
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10  One sided high order accurate approximations; Explicit and implicit formulations for the time derivatives 
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11  Numerical solution of the unsteady advection equation using different finite difference approximations 
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12  Need for analysis of a discretization scheme; Concepts of consistency, stability and convergence and the equivalence theorem of Lax ; Analysis for consistency 
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13  Statement of the stability problem; von Neumann stability analysis of the first order wave equation 
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14  Consistency and stability analysis of the unsteady diffusion equation; Analysis for two and three dimensional cases; Stability of implicit schemes 
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15  Interpretation of the stability condition; Stability analysis of the generic scalar equation and the concept of upwinding ; Diffusive and dissipative errors in numerical solution; Introduction to the concept of TVD schemes 
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16  Template for the generic scalar transport equation and its extension to the solution of NavierStokes equa tions for a compressible flow. 
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17  Illustration of application of the template using the MacCormack scheme for a threedimensional compressible flow 
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18  Stability limits of MacCormack scheme; Limitations in extending compressible flow schemes to incompre ssible flows ; Difficulty of evaluation of pressure in incompressible flows and listing of various approaches 
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19  Artificial compressibility method and the streamfunctionvorticity method for the solution of NS equations and their limitations 
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20  Pressur e equation method for the solution of NS equations 
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21  Pressurecorrection approach to the solution of NS equations on a staggered grid; SIMPLE and its family of methods 
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22  Need for effici ent solution of linear algebraic equations; Classification of approaches for the solution of linear algebraic equations. 
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23  Direct methods for linear algebraic equations; Gaussian elimination method 
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24  GaussJordan method; LU decomposition method; TDMA and Thomas algorithm 
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25  Basic iterative methods for linear algebraic equations: Description of point Jacobi, GaussSeidel and SOR methods 
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26  Convergence analysis of basic iterative schemes; Diagonal dominance condition for convergence; Influence of source terms on the diagonal dominance condition; Rate of convergence 
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27  Application to the Laplace equation 
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28  Advanced iterative methods: Alternating Direction Implicit Method; Operator splitting 
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29  Advanced iterative methods; Strongly Implicit Proc edure; Conjugate gradient method; Multigrid method 
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30  Illustration of the Multigrid method for the Laplace equation 
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31  Overview of the approach of numerical solution of NS equations for simple domains; Introduction to complexity arising from physics and geometry 
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32  Derivation of the energy conservation equation 
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33  Derivation of the species conservation equation; dealing with chemical reactions 
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34  Turbulence; Characteri stics of turbulent flow; Dealing with fluctuations and the concept of timeaveraging 
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35  Derivation of the Reynolds averaged Navier Stokes equations; identification of the closure problem of turbulence; Boussinesq hypothesis and eddy viscosity 
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36  Reynol ds stresses in turbulent flow; Time and length scales of turbulence; Energy cascade; Mixing length model for eddy viscosity 
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37  Oneequation model for turbulent flow 
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38  Two equation model for turbulent flow; Numerical calculation of turbulent reacting flows 
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39  Calculation of nearwall region in turbulent flow; wall function approach; nearwall turbulence models 
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40  Need for special methods for dealing with irregular fl ow geometry; Outline of the Bodyfitted grid approach ; Coordinate transformation to a general, 3D curvilinear system 
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41  Transformation of the governing equations; Illustration for the Laplace equation; Appearance and significance of cross derivative terms; Concepts of structured and unstructured grids. 
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42  Finite vol ume method for complicated flow domain; Illustration for the case of flow through a duct of triangular cross section. 
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43  Finite volume method for the general case 
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44  Generation of a structured grid for irregular flow domain; Algebraic methods; Elliptic grid generation method 
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45  Unstructured grid generation; Domain nodalization; Advancing front method for triangulation 
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46  Delaunay triangulation method for unstructured grid generation 
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47  Co located grid approach for irregular geometries; Pressure correction equation for a co located structured grid; Pressure correction equation for a colocated unstructured grid. 
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