Introduction to Computational Fluid Dynamics

Format:

Book

Author/Creator:

Niyogi, Pradip, Author.

Contributor:

Laha, Manas Kumar, Contributor.

Chakrabartty, Sunil Kumar, Contributor.

Language:

English

Subjects (All):

Fluid dynamics--Mathematics--Textbooks.

Fluid dynamics.

Numerical analysis--Textbooks.

Numerical analysis.

Physical Description:

1 online resource (1 v.) : ill.

Edition:

1st edition

Place of Publication:

[Place of publication not identified] Pearson Education Canada 2009

Language Note:

English

System Details:

text file

Summary:

Introduction to Computational Fluid Dynamics is a self-contained introduction to a new subject, arising through the amalgamation of classical fluid dynamics and numerical analysis supported by powerful computers. Written in the style of a text book for advanced level B.Tech, M.Tech and M.Sc. students of various science and engineering disciplines. It introduces the reader to finite-difference and finite-volume methods for studying and analyzing linear and non-linear problems of fluid flow governed by inviscid incompressible and compressible Euler equations as also incompressible and compressible viscous flows governed by boundary-layer and Navier-Stokes equations. Simple turbulence modelling has been presented.

Contents:

Cover

About the Authors

Preface

Acknowledgements

Contents

Part I: Finite Difference Method for Partial Differential Equations

Chapter 1: Introduction and Mathematical Preliminaries

1.1 Introduction

1.2 Typical Partial Differential Equations in Fluid Dynamics

1.3 Types of Second-order Equations

1.3.1 Characteristics of Second-Order Equations

1.4 Well-posed Problems

1.4.1 Examples of Well-Posed Problems

1.4.2 An Ill-Posed Problem

1.5 Properties of Linear and Quasilinear Equations

1.5.1 Qualitative Properties of Partial Differential Equations

1.6 Physical Character of Subsonic and Supersonic Flows

1.7 Second-order Wave Equations

1.7.1 Cauchy Problem for the Wave Equation

1.7.2 Domain of Dependence and Range of Influence

1.8 System of First-order Equations

1.8.1 Classification and Types of First-Order Systems

1.8.2 Conservation Form and Conservation-Law Form

1.9 Weak Solutions

1.10 Summary

1.11 Key Terms

Chapter 2: Finite Difference and Finite Volume Discretisations

2.1 Introduction

2.2 Finite Difference Discretisation

2.3 Discretisation of Derivatives

2.4 Consistency, Convergence, and Stability

2.5 Finite Volume Discretisation

2.5.1 Cell-Centred Scheme

2.6 Face Area and Cell Volume

2.6.1 Equivalence Between Finite Difference and Finite Volume Methods

2.7 Summary

2.8 Key Terms

2.9 Exercise 2

Chapter 3: Equations of Parabolic Type

3.1 Introduction

3.2 Finite Difference Scheme for Heat Conduction Equation

3.2.1 FTCS Scheme: Truncation Error and Consistency

3.2.2 Modified Equation

3.2.3 FTCS Scheme: Convergence

3.2.4 FTCS Scheme: Stability

3.2.5 Derivative Boundary Conditions

3.3 Crank-Nicholson Implicit Scheme

3.4 Analogy with Schemes for Ordinary Differential Equations.

3.4.1 Thomas Algorithm for Tridiagonal Systems

3.4.2 Crank-Nicholson Scheme: Truncation Error, Consistency, and Convergence

3.4.3 Dissipative and Dispersive Errors

3.4.4 Stability of the Crank-Nicholson Scheme

3.5 A Note on Implicit Methods

3.6 Leap-frog and DuFort-Frankel Schemes

3.6.1 Truncation Error of the DuFort-Frankel Scheme

3.6.2 Stability of DuFort-Frankel Scheme

3.7 Operator Notation

3.8 The Alternating Direction Implicit (ADI) Method

3.8.1 ADI Scheme

3.8.2 Splitting and Approximate Factorisation

3.8.3 Stability of the ADI Scheme

3.8.4 Program 3.1: adi.f

3.9 Summary

3.10 Key Terms

3.11 Exercise 3

Chapter 4: Equations of Hyperbolic Type

4.1 Introduction

4.2 Explicit Schemes

4.2.1 FTCS Scheme

4.2.2 FTFS Scheme

4.2.3 Upwind Scheme: First Order

4.2.4 Upwind Scheme: Modified Equation

4.2.5 The Lax Scheme

4.2.6 Consistency of Lax Scheme

4.2.7 Lax Scheme: Modified Equation

4.2.8 The Leap-Frog Scheme

4.3 Lax-Wendroff Scheme and Variants

4.3.1 Lax-Wendroff Scheme: Modified Equation

4.3.2 Two-Step Lax-Wendroff Scheme

4.3.3 The MacCormack Scheme

4.3.4 Upwind Scheme: Warming-Beam

4.4 Implicit Schemes

4.5 More on Upwind Schemes

4.6 Scalar Conservation Law: Lax-Wendroff and Related Schemes

4.6.1 Program 4.1: Ixmc.f

4.6.2 Implicit Schemes for Scalar Conservation Law

4.7 Hyperbolic System of Conservation Laws

4.7.1 System of Conservation Laws

4.8 Second-order Wave Equation

4.8.1 Stability of the Leap-Frog Scheme for the Wave Equation

4.8.2 An Implicit Scheme for the Second-Order Wave Equation

4.8.3 Stability of the Implicit Scheme

4.9 Method of Characteristics for Second-order Hyperbolic Equations

4.10 Model Convection-Diffusion Equation

4.10.1 Steady Convection-Diffusion Equation.

4.10.2 Linear Convection-Diffusion Equation: FTCS Scheme

4.10.3 First-Order Upwind Scheme for Convection-Diffusion Equation

4.10.4 Burgers Equation

4.11 Summary

4.12 Key Terms

4.13 Exercise 4

Chapter 5: Equations of Elliptic Type

5.1 Introduction

5.2 The Laplace Equation in Two Dimension

5.3 Iterative Methods for Solution of Linear Algebraic Systems

5.3.1 The Jacobi and the Gauss-Seidel Schemes

5.4 Solution of the Pentadiagonal System

5.4.1 Program 5.1: sor.f

5.5 Approximate Factorisation Schemes

5.5.1 Analysis of Line Gauss-Seidel Scheme for the Laplace Equation

5.5.2 Time-Dependent Analogy

5.5.3 Program 5.2: afl.f

5.6 Grid Generation Example

5.7 Body-fitted Grid Generation Using Elliptic-type Equations

5.7.1 Solution of the Algebraic Equations by AFI Scheme

5.8 Some Observations of AF Schemes

5.9 Multi-grid Method

5.9.1 Program 5.3: mgc.f

5.10 Summary

5.11 Key Terms

5.12 Exercise 5

Chapter 6: Equations of Mixed Elliptic-Hyperbolic Type

6.1 Introduction

6.2 Tricomi Equation

6.3 Transonic Computations Based on TSP Model

6.3.1 Finite Difference Discretisation

6.3.2 Implementation of Boundary Conditions

6.3.3 Iterative Solution of the Discretised Equations

6.3.4 Artificial Viscosity and Conservative Schemes

6.3.5 Computational Results

6.3.6 Program 6.1 tsc.f

6.4 Summary

6.5 Key Terms

6.6 Exercise 6

Part II: Computational Fluid Dynamics

Chapter 7: The Basic Equations of Fluid Dynamics

7.1 Introduction

7.2 Basic Conservation Principles

7.3 Unsteady Navier-Stokes Equations in Integral Form

7.4 Navier-Stokes Equations in Differential Form

7.4.1 Compressible Two-Dimensional Equations in Vector Form

7.4.2 Incompressible Navier-Stokes Equations in Cartesian Coordinates

7.4.3 Dimensionless Form of the Basic Equations.

7.4.4 Incompressible Two-Dimensional Equations: Dimensionless Form

7.4.5 Observations on the Basic Equations

7.5 Boundary Conditions for Navier-Stokes Equations

7.6 Reynolds Averaged Navier-Stokes Equations

7.7 Boundary-layer, Thin-layer and Associated Approximations

7.8 Euler Equations for Inviscid Flows

7.8.1 Certain Observations on Euler and Navier-Stokes Equations

7.9 Boundary Conditions for Euler Equations

7.9.1 Far-field Boundary Conditions for Euler Equations

7.10 The Full Potential Equation

7.10.1 Potential Equation in Conservative Form

7.10.2 Boundary Conditions for the Full Potential Equation

7.10.3 Transonic Small Perturbation Model

7.10.4 Oswatitsch Reduction

7.10.5 Cole's and Other Forms of the TSP Equation

7.11 Inviscid Incompressible Irrotational Flow

7.12 Summary

7.13 Key Terms

Chapter 8: Grid Generation

8.1 Introduction

8.2 Co-ordinate Transformation

8.3 Differential Equation Methods

8.4 Algebraic Methods

8.4.1 Calculation of the Arc Length

8.4.2 Desired Arc Length Distribution

8.4.3 Calculation of the Angle θ on the Aerofoil and Cut

8.4.4 Calculation of ymin and nmax

8.4.5 Δn - Distribution on the Aerofoil and the Cut

8.4.6 Mesh Spacing in n-Direction

8.4.7 Calculation of x and y at Nodal Points

8.4.8 Cubic Spline

8.5 Transfinite Interpolation Methods

8.6 Unstructured Grid Generation

8.7 Mesh Adaptation

8.7.1 Moving Mesh

8.7.2 Mesh Enrichment

8.8 Summary

8.9 Key Terms

8.10 Exercise 8

Chapter 9: Inviscid Incompressible Flow

9.1 Introduction

9.2 Potential Flow Problem

9.3 Panel Methods

9.3.1 AMO Smith Method for a Lifting Airfoil

9.3.2 Influence Coefficients

9.4 Panel Methods (Continued)

9.4.1 Mathematical Preliminaries for Morino-Kuo Method

9.4.2 Flow Past an Aerofoil.

9.4.3 A Constant-Potential Panel Method

9.4.4 Morino-Kuo Method

9.4.4.1 Pressure coefficient, forces, and moments

9.4.5 Program 9.1: Morinoprogram.c

9.4.6 Discretisation Error in Panel Methods

9.5 More on Panel Methods

9.6 Panel Methods for Subsonic and Supersonic Flows

9.7 Summary

9.8 Key Terms

9.9 Exercise 9

Chapter 10: Inviscid Compressible Flow

10.1 Introduction

10.1.1 Transonic Controversy

10.2 Small-perturbation Flow

10.2.1 Subsonic Flow Past a Thin Profile

10.2.2 Supersonic Small-Perturbation Flow

10.3 Numerical Solution of the Full Potential Equation

10.3.1 Rotated Difference Scheme

10.3.2 Conservative Schemes for the Potential Equation

10.4 Full Potential Solution in Generalised Coordinates

10.4.1 Spatial Differencing and Artificial Viscosity

10.4.2 AF2 Iteration Scheme

10.4.3 Boundary Conditions

10.4.4 Computational Results of Full-Potential Solution

10.5 Observations on the Full Potential Model

10.6 Euler Model

10.6.1 Governing Equations in Two Dimension

10.6.2 Numerical Methods for the Euler Model

10.6.3 Explicit and Implicit Schemes

10.6.4 Review of Acceleration Techniques

10.6.5 Finite Volume Discretisation

10.6.6 Artificial Dissipation

10.7 Boundary Conditions

10.7.1 Time Stepping Scheme

10.7.2 Acceleration Techniques

10.8 Computed Examples Based on the Euler Model

10.9 Supersonic Flow Field Computation

10.9.1 Examples of Supersonic Flow Computation

10.10 Summary

10.11 Key Terms

10.12 Exercise 10

Chapter 11: Boundary Layer Flow

11.1 Introduction

11.2 The Boundary Layer: Physical Considerations

11.2.1 Separation of the Boundary Layer from the Surface

11.2.2 Turbulence

1 1.2.3 Measures of Boundary Layer Thickness

11.3 The Boundary Layer Equations

1 1.3.1 Assumptions of the Boundary Layer Theory.

11.3.2 The Boundary Layer Equations for Laminar Flow.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references.

Description based on publisher supplied metadata and other sources.

ISBN:

9789332501324

9332501327

OCLC:

842893247