Anna University , Chennai

Department of B.E-Aeronautical Engg

Seventh Semester

AE2402 Computational Fluid Dynamics

Scanned Lecture Notes - All Units (Subhamathi Edition)

(Regulation 2008)

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Content :

UNIT-1

Introduction

Continuity equation

Momentum equation

Energy equation

Basic equation of fluid dynamics

Model of the flow

Substantial derivation

Physical meaning of divergence of a vector

Continuity

Conservation form of continuity equation

Momentum equation

1. Physical principle

2. Fluid model

Application of physical principle into fluid model

Energy equation

Work done due to body force

Rate of change of energy

Continuity equation

Incompressible invisid flow

Source and vortex flow

Elementary flows

Uniform flow

Source flow

Vortex flow

Non-lifting flow over arbitrary 2-D body source panel method

Source sheet

The vortex panel numerical method

Mathematical properties of the fluid dynamic equation

Quasi-linear system

Characteristic lines

Method of characteristics

Hyperbolic equation

Unsteady invisid compressible flow

Parabolic equation

Elliptic equation

1. Trichlet condition

2. Newmann condition

3. Wellposed problem

Discretization of PDE

Derivation of elementary

First order accuracy

Truncation error

First order forward difference

First order rearward difference

Second order central difference

Mixed derivation

Reflection boundary condition

Basic aspects of finite difference equation

Consistent

Finite difference solution

Explicit approach

Advantages

Disadvantages

Implicit approach

Advantages

Disadvantages

Errors and an analysis of stability

Discretization error

Round off error

Stability

Vonnewmannis method

Evaluating the inequality in above equation

UNIT-2

GRID GENERATION

Introduction

Computational plane

General transformation of the equation

Need for grid transformation

Types of grid generation

1. Structural grid generation

2. Unstructural grid generation

Types of grid

1. O-type grid

2. C-type grid

3. H-type grid

Grid generation techniques

Stretch or compressed grids

Elliptic grid generation

UNIT-3

DISCRETIZATION

Introduction

Boundary layers flow along a wall

Order of magnitude analysis

Surface oriented co-ordinate system

Transformation of the boundary layer equation

Choice of discretization model

Generalized implicit method

UNIT-4

INTRODUCTION TO FINITE ELEMENTS TECHNIQUES

Introduction

Advantages of FEM over FDM and FVM

Strong formulation

Weighted residual formulation

Point collocation method

Subdomain collocation method

Galerkin method

Weak formulation

Natural boundary condition

Essential boundary condition

Variational formulation

Finite elements

1. Triangular elements

2. Quadrilateral lagrange elements

3. Quadrilateral serendipity elements

4. Iso parametric elements

UNIT-5

FINITE VOLUME TECHNIQUES

Introduction

Cells

Nodes

1. Structural quadrilateral

2. Structural triangular

3. Unstructural triangular

Comparision of FVM over FDM and FEM

FEM like finite volume methods

Cell centred

Cell vertex on triangular grid

Cell centred formulation

Rader electronic warfare

1. Electronic warfare support measure

2. Electronic counter measure

3. Electronic protective measure

Lax-wendroff time steping

Runge-kutta method

Discipative terms

Numerical flux

accuracy

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