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Many introductions to fluid dynamics offer an illustrative approach that demonstrates some aspects of fluid behavior, but often leave you without the tools necessary to confront new problems. For more than a decade, Fluid Dynamics: Theoretical and Computational Approaches has supplied these missing tools with a constructive approach that made the book a bestseller. Now in its third edition, it supplies even more computational skills in addition to a solid foundation in theory.
After laying the groundwork in theoretical fluid dynamics, independent of any particular coordinate system in order to allow coordinate transformation of the equations, the author turns to the technique of writing Navier–Stokes and Euler’s equations, flow of inviscid fluids, laminar viscous flow, and turbulent flow. He also includes requisite mathematics in several “Mathematical Expositions” at the end of the book and provides abundant end-of-chapter problems.
What’s New in the Third Edition?
By integrating a strong theoretical foundation with practical computational tools, Fluid Dynamics: Theoretical and Computational Approaches, Third Edition is an indispensable guide to the methods needed to solve new and unfamiliar problems in fluid dynamics.
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Contenuti
Important Nomenclature
Kinematics of Fluid Motion
Introduction to Continuum Motion
Fluid Particles
Inertial Coordinate Frames
Motion of a Continuum
The Time Derivatives
Velocity and Acceleration
Steady and Nonsteady Flow
Trajectories of Fluid Particles and Streamlines
Material Volume and Surface
Relation between Elemental Volumes
Kinematic Formulas of Euler and Reynolds
Control Volume and Surface
Kinematics of Deformation
Kinematics of Vorticity and Circulation
References
Problems
The Conservation Laws and the Kinetics of Flow
Fluid Density and the Conservation of Mass
Principle of Mass Conservation
Mass Conservation Using a Control Volume
Kinetics of Fluid Flow
Conservation of Linear and Angular Momentum
Equations of Linear and Angular Momentum
Momentum Conservation Using a Control Volume
Conservation of Energy
Energy Conservation Using a Control Volume
General Conservation Principle
The Closure Problem
Stokes’ Law of Friction
Interpretation of Pressure
The Dissipation Function
Constitutive Equation for Non-Newtonian Fluids
Thermodynamic Aspects of Pressure and Viscosity
Equations of Motion in Lagrangian Coordinates
References
Problems
The Navier–Stokes Equations
Formulation of the Problem
Viscous Compressible Flow Equations
Viscous Incompressible Flow Equations
Equations of Inviscid Flow (Euler’s Equations)
Initial and Boundary Conditions
Mathematical Nature of the Equations
Vorticity and Circulation
Some Results Based on the Equations of Motion
Nondimensional Parameters in Fluid Motion
Coordinate Transformation
Streamlines and Stream Surfaces
Navier–Stokes Equations in Stream Function Form
References
Problems
Flow of Inviscid Fluids
Introduction
Part I: Inviscid Incompressible Flow
The Bernoulli Constant
Method of Conformal Mapping in Inviscid Flows
Sources, Sinks, and Doublets in Three Dimensions
Part II: Inviscid Compressible Flow
Basic Thermodynamics
Subsonic and Supersonic Flow
Critical and Stagnation Quantities
Isentropic Ideal Gas Relations
Unsteady Inviscid Compressible Flow in One-dimension
Steady Plane Flow of Inviscid Gases
Theory of Shock Waves
References
Problems
Laminar Viscous Flow
Part I: Exact Solutions
Introduction
Exact Solutions
Exact Solutions for Slow Motion
Part II: Boundary Layers
Introduction
Formulation of the Boundary Layer Problem
Boundary Layer on 2-D Curved Surfaces
Separation of the 2-D Steady Boundary Layers
Transformed Boundary Layer Equations
Momentum Integral Equation
Free Boundary Layers
Numerical Solution of the Boundary Layer Equation
Three-Dimensional Boundary Layers
Momentum Integral Equations in Three Dimensions
Separation and Attachment in Three Dimensions
Boundary Layers on Bodies of Revolution and Yawed Cylinders
Three-Dimensional Stagnation Point Flow
Boundary Layer On Rotating Blades
Numerical Solution of 3-D Boundary Layer Equations
Unsteady Boundary Layers
Second-Order Boundary Layer Theory
Inverse Problems in Boundary Layers
Formulation of the Compressible Boundary Layer Problem
Part III: Navier–Stokes Formulation
Incompressible Flow
Compressible Flow
Hyperbolic Equations and Conservation Laws
Numerical Transformation and Grid Generation
Numerical Algorithms for Viscous Compressible Flows
Thin-Layer Navier–Stokes Equations (TLNS)
References
Problems
Turbulent Flow
Part I: Stability Theory and the Statistical Description of Turbulence
Introduction
Stability of Laminar Flows
Formulation for Plane-Parallel Laminar Flows
Temporal Stability at Infinite Reynolds Number
Numerical Algorithm for the Orr–Sommerfeld Equation
Transition to Turbulence
Statistical Methods in Turbulent Continuum Mechanics
Statistical Concepts
Internal Structure in Physical Space
Internal Structure in the Wave-Number Space
Theory of Universal Equilibrium
Part II: Development of Averaged Equations
Introduction
Averaged Equations for Incompressible Flow
Averaged Equations for Compressible Flow
Turbulent Boundary Layer Equations
Part III: Basic Empirical and Boundary Layer Results in Turbulence
The Closure Problem
Prandtl’s Mixing-Length Hypothesis
Wall-Bound Turbulent Flows
Analysis of Turbulent Boundary Layer Velocity Profiles
Momentum Integral Methods in Boundary Layers
Differential Equation Methods in 2-D Boundary Layers
Part IV: Turbulence Modeling
Generalization of Boussinesq’s Hypothesis
Zero-Equation Modeling in Shear Layers
One-Equation Modeling
Two-Equation ( K-Î) Modeling
Reynolds’ Stress Equation Modeling
Application to 2-D Thin Shear Layers
Algebraic Reynolds’ Stress Closure
Development of A Nonlinear Constitutive Equation
Current Approaches to Nonlinear Modeling
Heuristic Modeling
Modeling for Compressible Flow
Three-Dimensional Boundary Layers
Illustrative Analysis of Instability
Basic Formulation of Large Eddy Simulation
References
Problems
Mathematical Exposition 1: Base Vectors and Various Representations
Introduction
Representations in Rectangular Cartesian Systems
Scalars, Vectors, and Tensors
Differential Operations On Tensors
Multiplication of A Tensor and A Vector
Scalar Multiplication of Two Tensors
A Collection of Usable Formulas
Taylor Expansion in Vector Form
Principal Axes of a Tensor
Transformation of T to the Principal Axes
Quadratic Form and the Eigenvalue Problem
Representation in Curvilinear Coordinates
Christoffel Symbols in Three Dimensions
Some Derivative Relations
Scalar and Double Dot Products of Two Tensors
Mathematical Exposition 2: Theorems of Gauss, Green, and Stokes
Gauss’ Theorem
Green’s Theorem
Stokes’ Theorem
Mathematical Exposition 3: Geometry of Space and Plane Curves
Basic Theory of Curves
Mathematical Exposition 4: Formulas for Coordinate Transformation
Introduction
Transformation Law for Scalars
Transformation Laws for Vectors
Transformation Laws for Tensors
Transformation Laws for the Christoffel Symbols
Some Formulas in Cartesian and Curvilinear Coordinates
Mathematical Exposition 5: Potential Theory
Introduction
Formulas of Green
Potential Theory
General Representation of a Vector
An Application of Green’s First Formula
Mathematical Exposition 6: Singularities of the First-Order ODEs
Introduction
Singularities and Their Classification
Mathematical Exposition 7: Geometry of Surfaces
Basic Definitions
Formulas of Gauss
Formulas of Weingarten
Equations of Gauss
Normal and Geodesic Curvatures
Grid Generation in Surfaces
Mathematical Exposition 8: Finite Difference Approximation Applied to PDEs
Introduction
Calculus of Finite Differences
Iterative Root Finding
Numerical Integration
Finite Difference Approximations of Partial Derivatives
Finite Difference Approximation of Parabolic PDEs
Finite Difference Approximation of Elliptic Equations
Mathematical Exposition 9: Frame Invariancy
Introduction
Orthogonal Tensor
Arbitrary Rectangular Frames of Reference
Check for Frame Invariancy
Use of Q
References for the Mathematical Expositions
Index
Product Description
Book by Warsi ZUA
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