Modules / Lectures

Sl.No Chapter Name English
1Motivation for CFD and Introduction to the CFD approachPDF unavailable
2Illustration of the CFD approach through a worked out examplePDF unavailable
3Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation and Statement of the momentum conservation equationPDF unavailable
4Forces acting on a control volume; Stress tensor; Derivation of the momentum conservation equation ; Closure problem; Deformation of a fluid element in fluid flowPDF unavailable
5Kinematics of deformation in fluid flow; Stress vs strain rate relation; Derivation of the Navier-Stokes equations PDF unavailable
6Equations governing flow of incompressible flow; Initial and boundary conditions; Wellposedness of a fluid flow problem PDF unavailable
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. PDF unavailable
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 apPDF 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
10One -sided high order accurate approximations; Explicit and implicit formulations for the time derivatives PDF unavailable
11Numerical solution of the unsteady advection equation using different finite difference approximations PDF unavailable
12Need for analysis of a discretization scheme; Concepts of consistency, stability and convergence and the equivalence theorem of Lax ; Analysis for consistency PDF unavailable
13Statement of the stability problem; von Neumann stability analysis of the first order wave equationPDF unavailable
14Consistency and stability analysis of the unsteady diffusion equation; Analysis for two- and three -dimensional cases; Stability of implicit schemes PDF unavailable
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 PDF unavailable
16Template for the generic scalar transport equation and its extension to the solution of Navier-Stokes equa tions for a compressible flow. PDF unavailable
17Illustration of application of the template using the MacCormack scheme for a three-dimensional compressible flowPDF unavailable
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 PDF unavailable
19Artificial compressibility method and the streamfunction-vorticity method for the solution of NS equations and their limitations PDF unavailable
20Pressur e equation method for the solution of NS equations PDF unavailable
21Pressure-correction approach to the solution of NS equations on a staggered grid; SIMPLE and its family of methods PDF unavailable
22Need for effici ent solution of linear algebraic equations; Classification of approaches for the solution of linear algebraic equations. PDF unavailable
23Direct methods for linear algebraic equations; Gaussian elimination methodPDF unavailable
24Gauss-Jordan method; LU decomposition method; TDMA and Thomas algorithm PDF unavailable
25Basic iterative methods for linear algebraic equations: Description of point -Jacobi, Gauss-Seidel and SOR methods PDF unavailable
26Convergence analysis of basic iterative schemes; Diagonal dominance condition for convergence; Influence of source terms on the diagonal dominance condition; Rate of convergence PDF unavailable
27Application to the Laplace equation PDF unavailable
28Advanced iterative methods: Alternating Direction Implicit Method; Operator splittingPDF unavailable
29Advanced iterative methods; Strongly Implicit Proc edure; Conjugate gradient method; Multigrid method PDF unavailable
30Illustration of the Multigrid method for the Laplace equationPDF unavailable
31Overview 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 reactionsPDF unavailable
34Turbulence; 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
36Reynol ds stresses in turbulent flow; Time and length scales of turbulence; Energy cascade; Mixing length model for eddy viscosity PDF unavailable
37One-equation model for turbulent flow PDF unavailable
38 Two -equation model for turbulent flow; Numerical calculation of turbulent reacting flows PDF unavailable
39Calculation of near-wall region in turbulent flow; wall function approach; near-wall turbulence models PDF unavailable
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 systemPDF unavailable
41Transformation of the governing equations; Illustration for the Laplace equation; Appearance and significance of cross -derivative terms; Concepts of structured and unstructured grids.PDF unavailable
42Finite vol ume method for complicated flow domain; Illustration for the case of flow through a duct of triangular cross -section. PDF unavailable
43Finite volume method for the general case PDF unavailable
44Generation 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 triangulationPDF unavailable
46Delaunay triangulation method for unstructured grid generation PDF unavailable
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.PDF unavailable

Sl.No Language Book link
1EnglishNot Available
2BengaliNot Available
3GujaratiNot Available
4HindiNot Available
5KannadaNot Available
6MalayalamNot Available
7MarathiNot Available
8TamilNot Available
9TeluguNot Available