Modules / Lectures

Sl.No Chapter Name English
1Motivation for CFD and Introduction to the CFD approachDownload
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2Illustration of the CFD approach through a worked out exampleDownload
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3Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation and Statement of the momentum conservation equationDownload
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4Forces acting on a control volume; Stress tensor; Derivation of the momentum conservation equation ; Closure problem; Deformation of a fluid element in fluid flowDownload
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5Kinematics of deformation in fluid flow; Stress vs strain rate relation; Derivation of the Navier-Stokes equations Download
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6Equations governing flow of incompressible flow; Initial and boundary conditions; Wellposedness of a fluid flow problem Download
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7Equations 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. Download
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8cut out the first 30s; Spatial discretization of a simple flow domain; Taylorís series expansion and the basis of finite difference approximation of a derivative; Central and one-sided difference approximations; Order of accuracy of finite difference apDownload
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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 Download
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10One -sided high order accurate approximations; Explicit and implicit formulations for the time derivatives Download
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11Numerical solution of the unsteady advection equation using different finite difference approximations Download
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12Need for analysis of a discretization scheme; Concepts of consistency, stability and convergence and the equivalence theorem of Lax ; Analysis for consistency Download
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13Statement of the stability problem; von Neumann stability analysis of the first order wave equationDownload
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14Consistency and stability analysis of the unsteady diffusion equation; Analysis for two- and three -dimensional cases; Stability of implicit schemes Download
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15Interpretation 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 Download
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16Template for the generic scalar transport equation and its extension to the solution of Navier-Stokes equa tions for a compressible flow. Download
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17Illustration of application of the template using the MacCormack scheme for a three-dimensional compressible flowDownload
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18Stability 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 Download
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19Artificial compressibility method and the streamfunction-vorticity method for the solution of NS equations and their limitations Download
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20Pressur e equation method for the solution of NS equations Download
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21Pressure-correction approach to the solution of NS equations on a staggered grid; SIMPLE and its family of methods Download
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22Need for effici ent solution of linear algebraic equations; Classification of approaches for the solution of linear algebraic equations. Download
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23Direct methods for linear algebraic equations; Gaussian elimination methodDownload
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24Gauss-Jordan method; LU decomposition method; TDMA and Thomas algorithm Download
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25Basic iterative methods for linear algebraic equations: Description of point -Jacobi, Gauss-Seidel and SOR methods Download
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26Convergence analysis of basic iterative schemes; Diagonal dominance condition for convergence; Influence of source terms on the diagonal dominance condition; Rate of convergence Download
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27Application to the Laplace equation Download
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28Advanced iterative methods: Alternating Direction Implicit Method; Operator splittingDownload
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29Advanced iterative methods; Strongly Implicit Proc edure; Conjugate gradient method; Multigrid method Download
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30Illustration of the Multigrid method for the Laplace equationDownload
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31Overview of the approach of numerical solution of NS equations for simple domains; Introduction to complexity arising from physics and geometry Download
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32 Derivation of the energy conservation equation Download
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33 Derivation of the species conservation equation; dealing with chemical reactionsDownload
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34Turbulence; Characteri stics of turbulent flow; Dealing with fluctuations and the concept of time-averaging Download
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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 Download
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36Reynol ds stresses in turbulent flow; Time and length scales of turbulence; Energy cascade; Mixing length model for eddy viscosity Download
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37One-equation model for turbulent flow Download
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38 Two -equation model for turbulent flow; Numerical calculation of turbulent reacting flows Download
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39Calculation of near-wall region in turbulent flow; wall function approach; near-wall turbulence models Download
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40Need for special methods for dealing with irregular fl ow geometry; Outline of the Body-fitted grid approach ; Coordinate transformation to a general, 3-D curvilinear systemDownload
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41Transformation of the governing equations; Illustration for the Laplace equation; Appearance and significance of cross -derivative terms; Concepts of structured and unstructured grids.Download
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42Finite vol ume method for complicated flow domain; Illustration for the case of flow through a duct of triangular cross -section. Download
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43Finite volume method for the general case Download
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44Generation of a structured grid for irregular flow domain; Algebraic methods; Elliptic grid generation method Download
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45 Unstructured grid generation; Domain nodalization; Advancing front method for triangulationDownload
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46Delaunay triangulation method for unstructured grid generation Download
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47Co -located grid approach for irregular geometries; Pressure correction equation for a co -located structured grid; Pressure correction equation for a co-located unstructured grid.Download
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