Introduction to Computational Fluid Dynamics

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. student...

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Detalles Bibliográficos
Otros Autores:	Niyogi, Pradip Author (author), Laha, Manas Kumar Contributor (contributor), Chakrabartty, Sunil Kumar Contributor
Formato:	Libro electrónico
Idioma:	Inglés
Publicado:	[Place of publication not identified] Pearson Education Canada 2009
Edición:	1st edition
Materias:	Fluid dynamics > Mathematics > Textbooks. Numerical analysis > Textbooks.
Ver en Biblioteca Universitat Ramon Llull:	https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009628040606719

Tabla de Contenidos:

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.

Introduction to Computational Fluid Dynamics

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