IIT Madras Course , Prof. Sreenivas Jayanti

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IIT Madras Course , Prof. Sreenivas Jayanti

Illustration of the CFD approach; CFD as an engineering analysis tool - Derivation of flow governing equations - Initial and boundary conditions; wellposedness - Turbulence modeling - Discretization of the governing equations using finite difference / volume methods - Concepts of consistency, stability and convergence - Template for the discretization of a generic unsteady transport equation - Spectral analysis of errors and TVD schemes - Solution of discretized linear algebraic equations: direct methods; classical iterative methods; convergence analysis - Advanced methods for the solution of discretized equations - Solution of coupled equations: methods for compressible flows - On evaluation of pressure in incompressible flows - Pressure-velocity coupling algorithms - Template for the solution of governing equations - Structured and unstructured grids - Structured grid generation methods - Unstructured grid generation methods - Benchmarking and calibration

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Computational Fluid Dynamics by Prof. Sreenivas Jayanti, Department of Chemical Engineering, IIT Madras. For more details on NPTEL visit httpnptel.iitm.ac.in

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- 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
- 4.Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation
- 5.Forces acting on a control volume; Stress tensor;
- 6.Kinematics of deformation in fluid flow; Stress vs strain rate relation
- 7.Equations governing flow of incompressible flow;
- 8.Cut out the first 30s; Spatial discretization of a simple flow domain;
- 9.Finite difference approximation of pth order of accuracy for qth order derivative;
- 10.One-sided high order accurate approximations,Explicit and implicit formulations
- 11.Numerical solution of the unsteady advection equation using different finite.
- 12.Need for analysis of a discretization scheme; Concepts of consistency
- 13.Statement of the stability problem
- 14.Consistency and stability analysis of the unsteady diffusion equation
- 15.Interpretation of the stability condition,Stability analysis of the generic scalar equ
- 16.Template for the generic scalar transport equation and its extension to the solution
- 17.Illustration of application of the template using the MacCormack scheme
- 18.Stability limits of MacCormack scheme
- 19.Artificial compressibility method and the streamfunction-vorticity method
- 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
- 22.Need for effici ent 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
- 26.Convergence analysis of basic iterative schemes,Diagonal dominance condition
- 27.Application to the Laplace equation
- 28.Advanced iterative methods Alternating Direction Implicit Method; Operator splitting
- 29.Advanced iterative methods,Strongly Implicit Procedure,Conjugate gradient 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
- 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
- 35.Derivation of the Reynolds -averaged Navier -Stokes equations
- 36.Reynol ds stresses in turbulent flow,Time and length scales of turbulence
- 37.One-equation model for turbulent flow
- 38.Two -equation model for turbulent flow; Numerical calculation of turbulent
- 39.Calculation of near-wall region in turbulent flow; wall function approach
- 40.Need for special methods for dealing with irregular fl ow geometry
- 41.Transformation of the governing equations; Illustration for the Laplace equation
- 42.Finite volume method for complicated flow domain
- 43.Finite volume method for the general case
- 44.Generation of a structured grid for irregular flow domain; Algebraic methods
- 45.Unstructured grid generation,Domain nodalization
- 46.Delaunay triangulation method for unstructured grid generation
- 47.Co -located grid approach for irregular geometries; Pressure correction equations

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