Fluid dynamics : theoretical and computational approaches

著者

• Warsi, Z. U. A.

書誌事項

Fluid dynamics : theoretical and computational approaches

Z.U.A. Warsi

CRC Press, c2006

3rd ed

注記

Includes bibliographical references and index

内容説明・目次

内容説明

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? New section on free surface flow New section on instability of flows through Chaos and nonlinear dissipative systems New section on formulation of the large eddy simulation (LES) problem New example problems and exercises that reflect new and important topics of current interest 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.

目次

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-I) 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

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詳細情報

• NII書誌ID(NCID): BA7331733X
• ISBN:
  • 0849333970
• LCCN: 2005040579
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Boca Raton, Fla.
• ページ数/冊数: 845 p.
• 大きさ: 26 cm
• 分類:
  • LCC : QC151
  • DC21 : 532/.05
• 件名:
  • LCSH : Fluid dynamics