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1
Motivation
2
Flow in a rectangular duct: Discretiztion of flow domain
3
Flow in a rectangular duct: Problem formulation
4
Tutorial 1: Converting PDE to algebraic equation using FD approximation
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Tutorial 1 contd.: Solution for algebraic equations using Gauss- Seidel Method
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Flow in a triangular duct: Problem formulation
7
Flow in a triangular duct: Discretiztion of flow domain
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Tutorial 2: Converting PDE to algebraic equation using Finite Volume method
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Tutorial 2 contd.: Description of FV method and solution using G-S Method
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Effect of grid spacing & upcoming course outline
11
Mass conservation equations
12
Momentum conservation equations
13
Forces acting on control volume
14
Kinematics of deformation in fluid flow
15
Equations governing fluid flow in incompressible fluid
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Navier-Stokes equation for simple cases of flow
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Energy conservation equations
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Practical cases of fluid flow with heat transfer in CFD point of view
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Practical cases of fluid flow with mass transfer in CFD point of view
20
Equations governing fluid flow with chemical reactions
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Concept of wellposedness of mathematical problems
22
Introduction to finite difference methods
23
Finite difference approximation on an uniform mesh
24
Higher order and mixed derivatives
25
Solution of Poisson equation in rectangular duct- Turorial
26
Discretization of time domain
27
FD approx. on a non-uniform mesh and need of analysis of obtained discretization
28
Need for the analysis of discretized equation
29
Properties of Numerical Schemes: Accuracy, Conservation property, Boundedness, Consistency
30
Properties of Numerical Schemes: Stability analysis
31
Tutorial on Stability Analysis
32
Analysis of Generic 1-d scalar transport equation
33
Introduction to the solution of coupled N-S equations
34
N-S equation in compressible flow- Mac Cormack Scheme
35
Stability limits of Mac-Cormack Scheme and the intro to Beam-Warming Scheme
36
Implicit Beam-Warming Scheme
37
Compressible flow to Incompressible flow
38
Solution of coupled equations: Incompressible flow
39
Artificial compressiblity method, Stream function-vorticity method
40
Pressure equation method, Staggered grid system
41
Pressure Correction Method
42
Tutorial on Pressure Correction Method
43
Tutorial on Pressure Correction Method contd.
44
Introduction to the basic numerical methods
45
Direct Methods: solution of the system of algebraic equations
46
Tri-diagonal Matrix Algorithm: Derivation
47
TDMA and other iterative methods
48
Recap of basic iterative methods.
49
Mod 5_ Week 2_Lec 5.6_Convergence analysis of basic iterative methods
50
Successive Over Relaxation (SOR) method
51
Alternating Direction Implicit (ADI) method
52
Strongly Implicit Procedure (ILU) method
53
Multigrid method
54
Body Fitted Grid Approach
55
Formulation Of Finite Volume Method
56
Methods For Unstructured Grid Generation
57
Triangulation: The Advancing Front Method
58
The Advancing Front Method continuation
59
Time and length scale of turbulance
60
The turbulent closure problem
61
The generic formulation for turbulence
62
More generic formulation and summary
Description:
The course deals with the numerical solution of equations governing fluid flow and would be of interest to engineers and scientists? both aspiring and professional? with chemical/ mechanical/ civil/ aerospace engineering applications. In all these fields, one needs to deal extensively with fluid flow related phenomena and one needs to resolve flow-related features of the processes and equipment. Although the equations governing fluid flow have been formulated more than 150 years ago, it is only in recent years that these are being solved in the practical applications in which the flow occurs. The course deals with the basic techniques that enable the numerical solution of these equations.

Computational Fluid Dynamics

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#Science #Physics #Fluid Mechanics #Fluid Dynamics #Computational Fluid Dynamics #Engineering #Mathematics #Applied Mathematics #Numerical Methods #Computer Science #Computational Modeling #Finite Volume Method
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Motivation