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Introduction to finite difference methods
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Classroom Contents
Computational Fluid Dynamics
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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
- 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
