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
5 Tutorial 1 contd.: Solution for algebraic equations using Gauss- Seidel Method
6 Flow in a triangular duct: Problem formulation
7 Flow in a triangular duct: Discretiztion of flow domain
8 Tutorial 2: Converting PDE to algebraic equation using Finite Volume method
9 Tutorial 2 contd.: Description of FV method and solution using G-S Method
10 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
16 Navier-Stokes equation for simple cases of flow
17 Energy conservation equations
18 Practical cases of fluid flow with heat transfer in CFD point of view
19 Practical cases of fluid flow with mass transfer in CFD point of view
20 Equations governing fluid flow with chemical reactions
21 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