Modules / Lectures

Sl.No | Chapter Name | English |
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1 | Motivation for CFD and Introduction to the CFD approach | PDF unavailable |

2 | Illustration of the CFD approach through a worked out example | PDF unavailable |

3 | Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation and Statement of the momentum conservation equation | PDF unavailable |

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 | PDF unavailable |

5 | Kinematics of deformation in fluid flow; Stress vs strain rate relation; Derivation of the Navier-Stokes equations | PDF unavailable |

6 | Equations governing flow of incompressible flow; Initial and boundary conditions; Wellposedness of a fluid flow problem | PDF unavailable |

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. | PDF unavailable |

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 one-sided difference approximations; Order of accuracy of finite difference ap | PDF unavailable |

9 | Finite difference approximation of pth order of accuracy for qth order derivative; cross -derivatives; Examples of high order accurate formulae for several derivatives | PDF unavailable |

10 | One -sided high order accurate approximations; Explicit and implicit formulations for the time derivatives | PDF unavailable |

11 | Numerical solution of the unsteady advection equation using different finite difference approximations | PDF unavailable |

12 | Need for analysis of a discretization scheme; Concepts of consistency, stability and convergence and the equivalence theorem of Lax ; Analysis for consistency | PDF unavailable |

13 | Statement of the stability problem; von Neumann stability analysis of the first order wave equation | PDF unavailable |

14 | Consistency and stability analysis of the unsteady diffusion equation; Analysis for two- and three -dimensional cases; Stability of implicit schemes | PDF unavailable |

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 | PDF unavailable |

16 | Template for the generic scalar transport equation and its extension to the solution of Navier-Stokes equa tions for a compressible flow. | PDF unavailable |

17 | Illustration of application of the template using the MacCormack scheme for a three-dimensional compressible flow | PDF unavailable |

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 | PDF unavailable |

19 | Artificial compressibility method and the streamfunction-vorticity method for the solution of NS equations and their limitations | PDF unavailable |

20 | Pressur e equation method for the solution of NS equations | PDF unavailable |

21 | Pressure-correction approach to the solution of NS equations on a staggered grid; SIMPLE and its family of methods | PDF unavailable |

22 | Need for effici ent solution of linear algebraic equations; Classification of approaches for the solution of linear algebraic equations. | PDF unavailable |

23 | Direct methods for linear algebraic equations; Gaussian elimination method | PDF unavailable |

24 | Gauss-Jordan method; LU decomposition method; TDMA and Thomas algorithm | PDF unavailable |

25 | Basic iterative methods for linear algebraic equations: Description of point -Jacobi, Gauss-Seidel and SOR methods | PDF unavailable |

26 | Convergence analysis of basic iterative schemes; Diagonal dominance condition for convergence; Influence of source terms on the diagonal dominance condition; Rate of convergence | PDF unavailable |

27 | Application to the Laplace equation | PDF unavailable |

28 | Advanced iterative methods: Alternating Direction Implicit Method; Operator splitting | PDF unavailable |

29 | Advanced iterative methods; Strongly Implicit Proc edure; Conjugate gradient method; Multigrid method | PDF unavailable |

30 | Illustration of the Multigrid method for the Laplace equation | PDF unavailable |

31 | Overview of the approach of numerical solution of NS equations for simple domains; Introduction to complexity arising from physics and geometry | PDF unavailable |

32 | Derivation of the energy conservation equation | PDF unavailable |

33 | Derivation of the species conservation equation; dealing with chemical reactions | PDF unavailable |

34 | Turbulence; Characteri stics of turbulent flow; Dealing with fluctuations and the concept of time-averaging | PDF unavailable |

35 | Derivation of the Reynolds -averaged Navier -Stokes equations; identification of the closure problem of turbulence; Boussinesq hypothesis and eddy viscosity | PDF unavailable |

36 | Reynol ds stresses in turbulent flow; Time and length scales of turbulence; Energy cascade; Mixing length model for eddy viscosity | PDF unavailable |

37 | One-equation model for turbulent flow | PDF unavailable |

38 | Two -equation model for turbulent flow; Numerical calculation of turbulent reacting flows | PDF unavailable |

39 | Calculation of near-wall region in turbulent flow; wall function approach; near-wall turbulence models | PDF unavailable |

40 | Need 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 system | PDF unavailable |

41 | Transformation of the governing equations; Illustration for the Laplace equation; Appearance and significance of cross -derivative terms; Concepts of structured and unstructured grids. | PDF unavailable |

42 | Finite vol ume method for complicated flow domain; Illustration for the case of flow through a duct of triangular cross -section. | PDF unavailable |

43 | Finite volume method for the general case | PDF unavailable |

44 | Generation of a structured grid for irregular flow domain; Algebraic methods; Elliptic grid generation method | PDF unavailable |

45 | Unstructured grid generation; Domain nodalization; Advancing front method for triangulation | PDF unavailable |

46 | Delaunay triangulation method for unstructured grid generation | PDF unavailable |

47 | Co -located grid approach for irregular geometries; Pressure correction equation for a co -located structured grid; Pressure correction equation for a co-located unstructured grid. | PDF unavailable |

Sl.No | Language | Book link |
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1 | English | Not Available |

2 | Bengali | Not Available |

3 | Gujarati | Not Available |

4 | Hindi | Not Available |

5 | Kannada | Not Available |

6 | Malayalam | Not Available |

7 | Marathi | Not Available |

8 | Tamil | Not Available |

9 | Telugu | Not Available |