Computational Fluid Dynamics I

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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

Course Curriculum

Motivation for CFD and Introduction to the CFD approach Details 57:29
Illustration of the CFD approach through a worked out example Details 52:54
Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation Details 55:29
Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation Details 1:34
Forces acting on a control volume; Stress tensor; Details 1:5:40
Kinematics of deformation in fluid flow; Stress vs strain rate relation Details 1:1:26
Equations governing flow of incompressible flow; Details 55:15
Cut out the first 30s; Spatial discretization of a simple flow domain; Details 57:57
Finite difference approximation of pth order of accuracy for qth order derivative; Details 54:18
One-sided high order accurate approximations,Explicit and implicit formulations Details 54:39
Numerical solution of the unsteady advection equation using different finite. Details 53:44
Need for analysis of a discretization scheme; Concepts of consistency Details 1:3:42
Statement of the stability problem Details 1:19
Consistency and stability analysis of the unsteady diffusion equation Details 54:26
Interpretation of the stability condition,Stability analysis of the generic scalar equ Details 1:1:27
Template for the generic scalar transport equation and its extension to the solution Details 49:27
Illustration of application of the template using the MacCormack scheme Details 59:5
Stability limits of MacCormack scheme Details 46:5
Artificial compressibility method and the streamfunction-vorticity method Details 46:39
Pressur e equation method for the solution of NS equations Details 44:34
Pressure-correction approach to the solution of NS equations on a staggered grid Details 1:11:7
Need for effici ent solution of linear algebraic equations Details 1:6:18
Direct methods for linear algebraic equations; Gaussian elimination method Details 39:38
Gauss-Jordan method; LU decomposition method; TDMA and Thomas algorithm Details 1:3:39
Basic iterative methods for linear algebraic equations: Description of point -Jacobi Details 49:43
Convergence analysis of basic iterative schemes,Diagonal dominance condition Details 53:39
Application to the Laplace equation Details 29:28
Advanced iterative methods: Alternating Direction Implicit Method; Operator splitting Details 48:51
Advanced iterative methods,Strongly Implicit Procedure,Conjugate gradient method Details 1:1:10
Illustration of the Multigrid method for the Laplace equation Details 38:8
Overview of the approach of numerical solution of NS equations for simple domains Details 29:2
Derivation of the energy conservation equation Details 51:12
Derivation of the species conservation equation; dealing with chemical reactions Details 47:6
Turbulence,Characteri stics of turbulent flow,Dealing with fluctuations Details 1:3:59
Derivation of the Reynolds -averaged Navier -Stokes equations Details 54:48
Reynol ds stresses in turbulent flow,Time and length scales of turbulence Details 1:41
One-equation model for turbulent flow Details 50:27
Two -equation model for turbulent flow; Numerical calculation of turbulent Details 1:1:23
Calculation of near-wall region in turbulent flow; wall function approach Details 54:45
Need for special methods for dealing with irregular fl ow geometry Details 50:56
Transformation of the governing equations; Illustration for the Laplace equation Details 51:59
Finite volume method for complicated flow domain Details 47:57
Finite volume method for the general case Details 57:42
Generation of a structured grid for irregular flow domain; Algebraic methods Details 58:47
Unstructured grid generation,Domain nodalization Details 53:31
Delaunay triangulation method for unstructured grid generation Details 55:34
Co -located grid approach for irregular geometries; Pressure correction equations Details 55:9

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