Computational Fluid Dynamics and Heat Transfer 2nd Edition by Pradip Majumdar ISBN 9781498703741 1498703747

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ISBN 10: 1498703747
ISBN 13: 9781498703741
Author: Pradip Majumdar

Computational Fluid Dynamics and Heat Transfer 2nd Edition Table of contents:

Part I Basic Equations and Numerical Analysis

Chapter 1 Review of Basic Laws and Equations

1.1 Basic Equations

1.2 Fluid Flow

1.2.1 Fluid Properties

1.2.1.1 Kinematics of Fluid and Kinematic Properties

1.2.2 Basic Equations in Integral Form

1.2.2.1 Basic Equations for a System

1.2.2.2 Basic Equations for a Control Volume

1.2.3 Differential Analysis of Fluid Motion

1.2.3.1 Conservation of Mass

1.2.4 Boundary Conditions for Flow Field

1.2.4.1 Solid–Fluid Interface

1.2.4.2 Fluid–Fluid Interface

1.3 Heat Transfer

1.3.1 Basic Modes and Transport Rate Equation

1.3.2 The First Law of Thermodynamics and Heat Equation

1.3.3 Initial and Boundary Conditions for Heat Transfer

1.4 Mass Transfer

1.4.1 Basic Modes and Transport Rate Equation

1.4.2 Conservation of Mass Species and Mass Concentration Equation

1.4.3 Initial and Boundary Conditions for Mass Transfer

1.5 Generalized Form of Transport Equation

1.6 Mathematical Classification of Governing Equations

Problems

Chapter 2 Approximations and Errors

2.1 Truncation Error

2.2 Round-off Error

2.2.1 Significant Figures or Digits

2.2.2 Computer Number System

2.2.3 Machine Epsilon

2.3 Error Definitions

2.4 Approximate Error

2.5 Convergence Criteria

Problems

Chapter 3 Numerical Solutions of Systems of Equations

3.1 Mathematical Background

3.1.1 Representation of the System of Equations

3.1.2 Cramer’s Rule and the Elimination of Unknowns

3.2 Direct Methods

3.2.1 Gaussian Elimination

3.2.2 Gauss–Jordan Elimination Method

3.2.3 Decomposition or Factorization Methods

3.2.4 Banded Systems

3.2.5 Error Equation and Iterative Refinement

3.3 Iterative Methods

3.3.1 Jacobi Method

3.3.2 Gauss–Seidel Method

3.3.3 Convergence Criterion for Iterative Methods

3.3.4 The SOR Method

3.3.5 CG Method

3.3.6 Preconditioned CG Method

3.3.7 Generalized Minimal Residuals Method

3.3.8 GMRES Method

Problems

Chapter 4 Numerical Integration

4.1 Newton–Cotes Integration Formulas

4.1.1 The Trapezoidal Rule

4.1.2 Simpson’s Integration Formula

4.1.3 Summary of Newton–Cotes Integration Formulas

4.2 Romberg Integration

4.3 Gauss Quadrature

4.3.1 Two-Point Gauss–Legendre Formula

4.3.2 Higher-Point Gauss–Legendre Formulas

4.4 Multidimensional Numerical Integration

Problems

Part II Finite Difference – Control Volume Method

Chapter 5 Basic Steps in Finite Difference–Control Volume Method

5.1 Introduction and Basic Steps in Finite Difference Method

5.2 Discretization of the Domain

5.3 Discretization of the Mathematical Model

5.3.1 The Taylor Series Method

5.3.1.1 Numerical Differentiation – Finite Difference Formulas

5.3.2 Control Volume Method

5.4 One-Dimensional Steady-State Diffusion

5.5 Variable Source Term

5.6 Boundary Conditions

5.7 Grid Size Distribution

5.8 Nonuniform Transport Property

5.9 Nonlinearity

5.10 Linearization of a Variable Source Term

Problems

Chapter 6 Finite Difference–Control Volume Method: Multidimensional Problems

6.1 Two-Dimensional Steady-State Problems

6.2 Boundary Conditions

6.2.1 Corner Boundary Nodes

6.3 Irregular Geometries

6.4 Three-Dimensional Steady-State Problems

6.5 Solution Techniques and Computer Implementation

6.5.1 Solution Algorithm Based on the Gauss–Seidel Method

6.5.2 Solution by Combination of TDMA and Gauss–Seidel Method (Line-by-Line Method)

Problems

Chapter 7 Finite Difference–Control Volume Method: Unsteady State Diffusion Equation

7.1 Time Discretization Procedure

7.2 Explicit Scheme

7.2.1 Discretization Equation by Control Volume Approach

7.2.2 Finite Difference Equation by Taylor Series Expansion

7.2.3 Stability Consideration

7.2.4 Other Explicit Schemes

7.2.5 Boundary Conditions

7.3 Implicit Scheme

7.3.1 Discretization Equation by Control Volume Approach

7.3.2 Finite Difference Equation by Taylor Series Expansion

7.3.3 A General Formulation of Fully Implicit Scheme for One-Dimensional Problems

7.3.4 A General Formulation of Fully Implicit Scheme for Two-Dimensional Problems

7.3.5 Solution Methods for a Two-Dimensional Implicit Scheme

7.3.6 Boundary Conditions for Implicit Scheme

7.4 Crank–Nicolson Scheme

7.4.1 Solution Methods for Crank–Nicolson Method

7.5 Splitting Methods

7.5.1 ADI Method

7.5.2 ADE Method

Problems

Chapter 8 Finite Difference–Control Volume Method: Convection Problems

8.1 Spatial Discretization Using Control Volume Method

8.1.1 Central Difference Scheme

8.1.2 Upwind Scheme

8.1.3 Exponential Scheme

8.1.4 Hybrid Scheme

8.1.5 Power Law Scheme

8.1.6 Generalized Convection–Diffusion Scheme

8.1.7 Higher-Order Discretization Schemes for Convective Terms

8.1.7.1 Second-Order Upwind Scheme

8.1.7.2 Third-Order QUICK Scheme

8.1.7.3 Derivation of Discretization Equation Using QUICK Scheme

8.1.7.4 MUSCL Scheme: Monotonic Upstream-Centered Scheme for Conservation Laws

8.2 Discretization of a General Transport Equation

8.2.1 One-Dimensional Unsteady-State Problems

8.2.2 Two-Dimensional Unsteady-State Problem

8.2.3 Three-Dimensional Unsteady-State Problem

8.3 Solution of Flow Field

8.3.1 Stream Function–Vorticity-Based Method

8.3.2 Direct Solution with the Primitive Variables

Problems

Chapter 9 Additional Features in Computational Model and Mesh Generations

9.1 Boundary Conditions

9.1.1 Inlet Conditions

9.1.1.1 Restrictions on the Selection Inlet Location

9.1.2 Outlet Conditions

9.1.2.1 Restrictions of Assigning Fully Developed Outflow Conditions

9.1.3 Wall Boundary Conditions

9.1.4 Pressure Conditions at the Inlets and Outlets

9.1.5 Symmetric and Periodic Boundary Conditions

9.1.5.1 Symmetric Boundary Planes and Conditions

9.1.6 Periodic Boundary Planes and Boundary Conditions

9.2 Mesh Types and Mesh Generation

9.2.1 Mesh Types

9.2.1.1 Two-Dimensional Mesh

9.2.1.2 Three-Dimensional Meshes

9.2.2 Mesh Size Distributions

9.2.2.1 Unstructured Mesh

9.2.2.2 Hybrid Mesh

9.2.2.3 Skewness

9.2.3 Mesh Generation Procedure

9.2.4 Multiblock Mesh System

9.2.5 Prism Layer

9.3 Multigrid (MG) Method

9.3.1 Algebraic Multigrid Method

Chapter 10 Turbulent Flow Modeling

10.1 Physical Description of Turbulence

10.2 Governing Equations for Turbulent Fluid Flow Analysis

10.3 Computational Model for Turbulence Flow

10.3.1 Direct Numerical Simulation

10.3.2 Averaged or Filtered Simulation

10.3.2.1 Large Eddy Simulation

10.4 Reynolds Averaged Navier-Stokes Model

10.4.1 Turbulence Kinetic Energy Transport Equation

10.4.2 Boussinesq Eddy Viscosity Concept and Prandtl Mixing Length Model

10.4.2.1 Boussinesq Eddy Viscosity

10.4.2.2 Prandtl Mixing Length

10.5 Different Classes of Turbulence Closure Models

10.6 Classification of Turbulence Models

10.6.1 Algebraic Turbulence Model or Zero-Equation Models

10.6.2 One-Equation Model

10.6.2.1 Prandtl–Emmons–Glushko Model

10.6.2.2 Spalart–Allmaras Model

10.6.2.3 Baldwin–Barth Model

10.6.3 Two-Equation Model

10.6.3.1 k − ε Turbulence Model

10.6.3.2 Two-Equation k − ω Turbulence Models

10.6.3.3 Low Reynolds Turbulence Model

10.7 Reynolds Stress Model

10.8 Near-Wall Region Modeling

10.9 Estimation of y-Plus

10.9.1 Procedure to Estimate y+ in Wall Function Treatment

10.10 Boundary Condition for Turbulence Quantities

10.10.1 Inlet Turbulence

10.10.2 Wall Boundary Condition

Part III Finite Element Method

Chapter 11 Introduction and Basic Steps in Finite Element Method

11.1 Comparison between Finite Difference–Control Volume Method and FEM

11.2 Basic Steps in FEMs

11.3 Integral Formulation

11.3.1 Variational Formulation

11.3.2 Method of Weighted Residuals

11.4 Variational Methods

11.4.1 The Rayleigh–Ritz Variational Method

11.4.2 Weighted Residual Variational Methods

Problems

Chapter 12 Element Shape Functions

12.1 One-Dimensional Element

12.1.1 One-Dimensional Linear Element

12.1.2 One-Dimensional Quadratic Line Element

12.1.3 One-Dimensional Cubic Element

12.2 Two-Dimensional Element

12.2.1 Linear Triangular Element

12.2.2 Quadratic Triangular Element

12.2.3 Two-Dimensional Quadrilateral Elements

12.3 Three-Dimensional Element

12.3.1 Three-Dimensional Tetrahedron Element

12.3.2 Three-Dimensional Hexahedron Element

Problems

Chapter 13 Finite Element Method: One-Dimensional Steady State Problems

13.1 Finite Element Formulation Using Galerkin Method

13.2 Finite Element Formulation Using Variational Approach

13.3 Boundary Conditions

13.3.1 Boundary Condition of the Second Kind or Constant

13.3.2 Mixed Boundary Conditions

13.4 Variable Source Term

13.5 Axisymmetric Problems

Problems

Chapter 14 Finite Element Method: Multidimensional Steady-State Problems

14.1 Two-Dimensional Steady-State Diffusion Equation

14.1.1 Step 1: Mesh Generation or Discretization of the Solution Domain

14.1.2 Step 2: Element and Node Numbering

14.1.3 Step 3: Selection of Approximate Solution Function

14.1.4 Step 4: Formulation of an Integral Statement Using Galerkin’s Approach

14.1.5 Step 5: Formation of Element Characteristics Equation

14.1.6 Step 6: Assembly of Element Equations and Formation of Global System

14.2 Three-Dimensional Problems

14.4 Point Source

Problems

Chapter 15 Finite Element Method: Unsteady-State Problems

15.1 Discretization Scheme

15.2 One-Dimensional Unsteady-State Problem

15.2.1 Semi-Discrete Finite Element Formulation

15.2.2 Time Approximation

15.2.3 Stability Consideration

15.3 Two-Dimensional Unsteady-State Diffusion Equation

15.4 Three-Dimensional Unsteady-State Diffusion Equation

Problems

Chapter 16 Finite Element Method: Convection Problems

16.1 Classification of Finite Element Methods for Convection Problems

16.2 Velocity-Pressure or Mixed Formulation

16.2.1 One-Dimensional Convection-Diffusion Problem

16.2.2 Two-Dimensional Viscous Incompressible Flow

16.2.3 Unsteady Two-Dimensional Viscous Incompressible Flow

16.2.4 Unsteady Three-Dimensional Viscous Incompressible Flow

16.2.5 Convective Heat and Mass Transfer

16.3 Solution Methods

16.3.1 Steady-State Problems

16.3.1.1 Picard Method

16.3.1.2 Newton-Raphson Method

16.3.1.3 Velocity-Pressure Correction Method

16.3.2 Unsteady-State Problem

Problems

Appendix A

Appendix B

Bibliography

Index

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Tags: Pradip Majumdar, Computational, Fluid Dynamics, Heat Transfer