Computational Fluid Dynamics and Heat Transfer (Computational & Physical Processes in Mechanics & Thermal Scienc)

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Author
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 −ɛ̌Turbulence 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[sup(+)] 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 D iscretization 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: Review of Vectors and Matrices
Appendix B: Integral Theorems
Bibliography
Index