Fluid dynamics : theoretical and computational approaches /: theoretical and computational approaches. (2005)

• Record Type: Book
• Further Information: Note: Z.U.A. Warsi.
• Other Names: Warsi, Z. U. A
• Contents: 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
• Edition: 3rd ed
• Publisher Details: Place of publication not identified : CRC Press
• Publication Date: 2005
• Extent: 1 online resource, illustrations
• Subjects: 532.05; Fluid dynamics
• Languages: English
• ISBNs: 9781420057881
• Related ISBNs: 142005788X
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.