Computational Fluid Dynamics Video Lectures

Computational Fluid Dynamics
'Computational Fluid Dynamics' Video Lectures by Prof. Sreenivas Jayanti from IIT Madras
"Computational Fluid Dynamics" - Video Lectures
1. Motivation for CFD and Introduction to the CFD approach
2. Illustration of the CFD approach through a worked out example
3. Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation and Statement of the momentum conservation equation
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
5. Kinematics of deformation in fluid flow; Stress vs strain rate relation; Derivation of the Navier-Stokes equations
6. Equations governing flow of incompressible flow; Initial and boundary conditions; Wellposedness of a fluid flow problem
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.
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 app
9. Finite difference approximation of pth order of accuracy for qth order derivative; cross -derivatives; Examples of high order accurate formulae for several derivatives
10. One -sided high order accurate approximations; Explicit and implicit formulations for the time derivatives
11. Numerical solution of the unsteady advection equation using different finite difference approximations
12. Need for analysis of a discretization scheme; Concepts of consistency, stability and convergence and the equivalence theorem of Lax ; Analysis for consistency
13. Statement of the stability problem; von Neumann stability analysis of the first order wave equation
14. Consistency and stability analysis of the unsteady diffusion equation; Analysis for two- and three -dimensional cases; Stability of implicit schemes
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 t
16. Template for the generic scalar transport equation and its extension to the solution of Navier-Stokes equa tions for a compressible flow.
17. Illustration of application of the template using the MacCormack scheme for a three-dimensional compressible flow
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 vario
19. Artificial compressibility method and the streamfunction-vorticity method for the solution of NS equations and their limitations
20. Pressur e equation method for the solution of NS equations
21. Pressure-correction approach to the solution of NS equations on a staggered grid; SIMPLE and its family of methods
22. Need for effici ent solution of linear algebraic equations; Classification of approaches for the solution of linear algebraic equations.
23. Direct methods for linear algebraic equations; Gaussian elimination method
24. Gauss-Jordan method; LU decomposition method; TDMA and Thomas algorithm
25. Basic iterative methods for linear algebraic equations: Description of point -Jacobi, Gauss-Seidel and SOR methods
26. Convergence analysis of basic iterative schemes; Diagonal dominance condition for convergence; Influence of source terms on the diagonal dominance condition; Rate of convergence
27. Application to the Laplace equation
28. Advanced iterative methods: Alternating Direction Implicit Method; Operator splitting
29. Advanced iterative methods; Strongly Implicit Proc edure; Conjugate gradient method; Multigrid method
30. Illustration of the Multigrid method for the Laplace equation
31. Overview of the approach of numerical solution of NS equations for simple domains; Introduction to complexity arising from physics and geometry
32. Derivation of the energy conservation equation
33. Derivation of the species conservation equation; dealing with chemical reactions
34. Turbulence; Characteri stics of turbulent flow; Dealing with fluctuations and the concept of time-averaging
35. Derivation of the Reynolds -averaged Navier -Stokes equations; identification of the closure problem of turbulence; Boussinesq hypothesis and eddy viscosity
36. Reynol ds stresses in turbulent flow; Time and length scales of turbulence; Energy cascade; Mixing length model for eddy viscosity
37. One-equation model for turbulent flow
38. Two -equation model for turbulent flow; Numerical calculation of turbulent reacting flows
39. Calculation of near-wall region in turbulent flow; wall function approach; near-wall turbulence models
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
41. Transformation of the governing equations; Illustration for the Laplace equation; Appearance and significance of cross -derivative terms; Concepts of structured and unstructured grids.
42. Finite vol ume method for complicated flow domain; Illustration for the case of flow through a duct of triangular cross -section.
43. Finite volume method for the general case
44. Generation of a structured grid for irregular flow domain; Algebraic methods; Elliptic grid generation method
45. Unstructured grid generation; Domain nodalization; Advancing front method for triangulation
46. Delaunay triangulation method for unstructured grid generation
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.
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