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