Holdings: Fluid dynamics :: THWS Bibkatalog

Fluid dynamics: theoretical and computational approaches

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Bibliographic Details
Main Author:	Warsi, Zahir U. A. (Author)
Format:	Book
Language:	English
Published:	Boca Raton [u.a.] CRC Press 1999
Edition:	2. ed.
Subjects:	Dynamica Idealen (wiskunde) Navier-Stokes-vergelijkingen Reologie Turbulentie Viscositeit Fluid dynamics Strömungsmechanik
Online Access:	Inhaltsverzeichnis
Physical Description:	726 S. graph. Darst.
ISBN:	0849324076

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adam_text	Table of Contents Chapter 1 KINEMATICS OF FLUID MOTION 1 1 Introduction to Continuum Motion 1 1 2 Fluid Particles 1 1 3 Inertial Coordinate Frames 1 1 4 Motion of a Continuum 2 1 5 The Time Derivatives 5 1 6 Velocity and Acceleration 5 1 7 Steady and Nonsteady Flow 9 1 8 Trajectories of Fluid Particles and Streamlines 9 1 9 Material Volume and Surface 10 1 10 Relation Between Elemental Volumes 11 1 11 The Kinematics Formulae of Euler and Reynolds 12 1 12 Control Volume and Surface 14 1 13 Kinematics of Deformation 15 1 14 Kinematics of Vorticity and Circulation 20 Vortex Line 20 Vortex Tbbe 20 Rate of Change of Circulation 22 Reference 23 Problems 23 Chapter 2 THE CONSERVATION LAWS AND THE KINETICS OF FLOW 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15 2 16 Fluid Density and the Conservation of Mass 29 Principle of Mass Conservation 29 Time Variation of pP 30 Particular Forms of the Continuity Equation 30 Mass Conservation Using a Control Volume 31 Kinetics of Fluid Flow 31 Stress Principle of Cauchy 32 Conservation of Linear and Angular Momentum 32 Conservation of Linear Momentum 32 Conservation of Angular Momentum 33 Nature of the Stress Vector 33 Symmetry of T 36 Equations of Linear and Angular Momentum 37 Momentum Conservation Using a Control Volume 38 Conservation of Energy 39 Energy Conservation Using a Control Volume 42 General Conservation Principle 42 The Closure Problem 42 Stokes’ Law of Friction 45 The Postulates of Stokes 46 Stokesian Stress Tensor 47 The Interpretation of Pressure 50 The Dissipation Function 51 Constitutive Equation for Non-Newtonian Fluids 52 Thermodynamic Aspects of Pressure and Viscosity 54 Ideal Gases 55 Concept of Viscosity in Fluids 57 Sutherland Formula for Viscosity 58 2 17 Equations of Motion in Lagrangian Coordinates 59 References 62 Problems 63 Chapter 3 THE NAVIER-STOKES EQUATIONS 3 1 Formulation of the Problem 65 Cartesian Coordinates 65 Curvilinear Coordinates 66 3 2 Viscous Compressible Flow Equations 67 Conservation of Mass 67 Conservation of Momentum 67 Equations of Mechanical Energy 68 Equations of Internal Energy 68 Equations of Entropy and Enthalpy 68 Equations of Energy 69 Conservation of Total Kinetic Energy 69 3 3 Viscous Incompressible Flow Equations 70 Conservation of Mass 70 Conservation of Momentum 70 Equation of Vorticity 70 Equation of Internal Energy 71 Equation of Pressure 71 3 4 Equations of Inviscid Flow (Euler’s Equations) 72 Conservation of Mass 72 Conservation of Momentum 73 Equations of Entropy and Enthalpy 73 Conservation of Energy 73 Conservation of Total Kinetic Energy 73 Inviscid Barotropic Row 73 3 5 Initial and Boundary Conditions 74 3 6 Mathematical Nature of the Equations 75 3 7 Vorticity and Circulation 75 Vorticity and Circulation for Inviscid Ruids 76 The Bernoulli Equation 77 3 8 Some Results Based on the Equations of Motion 79 Force Acting on a Solid Body 79 Stress Vector and Tensor at a Surface 80 Vorticity Vector at the Surface 81 Rate-of-Strain Tensor at a Surface 81 3 9 Nondimensional Parameters in Ruid Motion 82 Principle of Similarity 85 Dynamic Similarity 85 Variable Nondimensional Parameters 86 Principles of Reynold’s Number Similarity 86 3 10 Coordinate Transformation , 88 Orthogonal Coordinates 88 Navier-Stokes’ Equations in Orthogonal Coordinates 93 Nonorthogonal Curvilinear Coordinates 94 Steady Eulerian Coordinates 94 Nonsteady Eulerian Coordinates 97 Equations in General Coordinates 102 Equations in General Coordinates Using Contravariant Components 103 3 11 3 12 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 4 10 4 11 4 12 Equations in General Coo Equations in General Coo Equations in Nonsteady E Equations in Curvilinear Streamlines and Stream S Two-Dimensional Stream Three-Dimensional Stre Navier-Stokes’ Equations Two-Dimensional and Axi Three-Dimensional Rows References Problems FL Introduction Parti The Bernoulli Constant Irrotational Rows Boundary Conditions Two-Dimensional Irrotati Examples of Analytic Fu Blausius Formulae for Fo Method of Conformal Ma Kutta-Joukowskii’s Trans Pure Circulatory Motion Row Past a Wing Profile An Iterative Method for t Sources, Sinks, and Doub Sources and Sinks in Thr Doublets in Three Dimen Induced Velocities Due t Part Basic Thermodynamics First Law of Thermodyn Second Law of Thermod Deductions from the Two Specific Heats Enthalpy Maxwell Equations Isentropic State Speed of Sound Thermodynamic Relatio Perfect Gases Subsonic and Supersonic Critical and Stagnation Isentropic Ideal Gas Rel One-Dimensional Unste Steady Plane Row of In Stream Function Formul Irrotational Row of an I Case of Small Perturbati Subsonic Row Supersonic Row Theory of Shock Waves 58 Coordinates 59 62 63 Chapter 3 -STOKES EQUATIONS tions y ergy uations r’s Equations) py nergy ations iscid Fluids ations of Motion rface ce Fluid Motion eters r Similarity rthogonal Coordinates ordinates es tes tes Using Contravariant Components 65 65 66 67 67 67 68 68 68 69 69 70 70 70 70 71 71 72 72 73 73 73 73 73 74 75 75 76 77 79 79 80 81 81 82 85 85 86 86 88 88 93 94 94 97 102 103 Equations in General Coordinates Using Covariant Components 104 Equations in General Coordinates with Vectors and Tensor Densities 104 Equations in Nonsteady Eulerian Coordinates 106 Equations in Curvilinear Coordinates with Cartesian Velocity Components 110 Streamlines and Stream Surfaces Ill Two-Dimensional Stream Function : Ill Three-Dimensional Stream Functions 113 Navier-Stokes’ Equations in Stream Function Form 114 Two-Dimensional and Axially Symmetric Flows 114 Three-Dimensional Flows 116 References 123 Problems 124 Chapter 4 FLOW OF INVISCID FLUIDS Introduction 135 Part I: Inviscid Incompressible Flow The Bernoulli Constant 136 Irrotational Flows 136 Boundary Conditions 137 Two-Dimensional Irrotational Flows 138 Examples of Analytic Functions for Inviscid Flows 140 Blausius Formulae for Force and Moment 145 Method of Conformal Mapping in Inviscid Flows 148 Kutta-Joukowskii’s Transformation 150 Pure Circulatory Motion Around a Plate 152 Flow Past a Wing Profile 152 An Iterative Method for the Numerical Generation of z =f(Q 155 Sources, Sinks, and Doublets in Three Dimensions 157 Sources and Sinks in Three Dimensions 158 Doublets in Three Dimensions 159 Induced Velocities Due to Line and Sheet Vortices 160 Part II: Inviscid Compressible Flow Basic Thermodynamics 162 First Law of Thermodynamics 163 Second Law of Thermodynamics 164 Deductions from the Two Thermodynamic Laws 166 Specific Heats 168 Enthalpy 169 Maxwell Equations 170 Isentropic State 171 Speed of Sound 172 Thermodynamic Relations for an Ideal Gas 172 Perfect Gases 173 Subsonic and Supersonic Flow 174 Critical and Stagnation Quantities 175 Isentropic Ideal Gas Relations 177 One-Dimensional Unsteady Inviscid Compressible Flow 178 Steady Plane Flow of Inviscid Gases 186 Stream Function Formulation 187 Irrotational Flow of an Inviscid Gas 188 Case of Small Perturbations 189 Subsonic Row 190 Supersonic Flow 191 Theory of Shock Waves 193 Shock Relations for an Arbitrarily Moving Shock 193 First Shock Condition 194 Second Shock Condition 195 Third Shock Condition 195 Fourth Shock Condition 195 Shock Surface, Slip surface, and Contact Discontinuity 197 Energy Equation for a Shock Surface 197 Hugonoit Equation 198 Summary of All Shock Relations 198 The Role of Entropy 200 Stationary Shocks 201 Stationary Normal Shock 201 Stationary Oblique Shocks 202 Prandtl’s Relation 203 Shock Polar for Stationary Oblique Shocks 205 References 206 Problems 206 Chapter 5 LAMINAR VISCOUS FLOW Part I: Exact Solutions 5 1 Introduction 5 2 Exact Solutions Flow on an Infinite Plate Flow Between Two Infinite Parallel Plates Flow Between Rotating Coaxial Cylinders (Circular Couette Row) Steady Row Through a Cylindrical Pipe (Hagen-Poiseuille Row) Row in the Entrance Region of a Circular Pipe Nonsteady Unidirectional How Stokes Problems Ekman Layer Problems Motion Produced Due to a Vortex Filament Two-Dimensional Stagnation Point Row (Heimenz Row) Axially Symmetric Stagnation Point Row (Homann Row) Motion Between Two Inclined Plates Exact Solutions in Slow Motion Row Past a Rigid Sphere Row Past a Rigid Circular Cylinder Part II: Boundary Layers Introduction Formulation of the Boundary Layer Problem Method of Inner and Outer Limits Boundary Layer on Two-Dimensional Curved Surfaces Boundary Layer Parameters Separation of the Two-Dimensional Steady Boundary Layers Transformed Boundary Layer Equations Similar Boundary Layers Boundary Layer on a Semi-Infinite Plate Solution of the Blausius Equation Boundary Layer on a Wedge Numerical Solution of the Falkner-Skan Equation Nonsimilar Boundary Layers Gortler’s Series Solution 5 9 Momentum Integral Equation Solution of the Momentum Integral Equation 5 3 5 4 5 5 5 6 5 7 5 8 221 221 221 222 223 225 227 228 228 230 232 234 234 235 238 239 243 248 249 „254 „255 257 259 264 265 „267 „268 271 „ 273 „274 „275 280 281 5 10 5 11 5 12 5 13 5 14 5 15 5 16 5 17 5 18 5 19 5 20 5 21 5 22 Choice of the Velocity Free Boundary Layers Row in the Wake of a Two-Dimensional Jet Axially Symmetric Jet Numerical Solution of Numerical Solution of Errors: Truncation and Crank and Nicolson Dufort and Frankel Three-Point Scheme Solution of the Bound The Box Method Three-Dimensional Bou The Metric Coefficients The Matching Conditio Equations in Rotating C Choice of Surface Co or Internal Cartesian Coor Nondevelopable Surfa Physical Consequences Intrinsic Coordinates Domains of Dependenc Momentum Integral Eq Separation and Attachm Limiting Streamlines an Boundary Layers on Bo Mangler’s Transformati Boundary Layer on Ya Cross Row Transformed Equations Three-Dimensional Sta Boundary Layer on Rot Numerical Solution of Unsteady Boundary La Purely Unsteady Bound Periodic Boundary Lay Separation of Unsteady Mathematical Formula! Numerical Method of S Second Order Boun Method of Matched As Outer Expansion Some Important Deriva Inner Expansion The First and Second O Matching of Inner and A Unified Second Orde Matching Inverse Problems in Bo Inverse Formulation wi Formulation of the Co Estimation of the Visco External Row Equatio Particular Cases Numerical Solution of Moving Shock 193 194 195 195 195 Contact Discontinuity 197 ace 197 198 198 200 201 201 202 203 ue Shocks 205 206 206 Chapter 5 R VISCOUS FLOW I: Exact Solutions 221 221 221 lei Plates 222 Cylinders (Circular Couette Flow) 223 cal Pipe (Hagen-Poiseuille Flow) 225 a Circular Pipe 227 228 228 230 x Filament 232 int Flow (Heimenz Flow) 234 oint Flow (Homann Flow) 234 lates 235 238 239 nder 243 : Boundary Layers 248 yer Problem ‘ 249 its 254 sional Curved Surfaces 255 257 onal Steady Boundary Layers 259 uations 264 265 nite Plate 267 on 268 271 er-Skan Equation 273 274 275 280 gral Equation 281 Choice of the Velocity Profile 284 5 10 Free Boundary Layers 285 Flow in the Wake of a Flat Plate 285 Two-Dimensional Jet 287 Axially Symmetric Jet 289 5 11 Numerical Solution of the Boundary Layer Equation 290 Numerical Solution of the Diffusion Equation 291 Errors: Truncation and Round-Off 291 Crank and Nicolson 293 Dufort and Frankel 293 Three-Point Scheme 293 Solution of the Boundary Layer Equation 294 The Box Method 296 5 12 Three-Dimensional Boundary Layers 299 The Metric Coefficients 300 The Matching Conditions 301 Equations in Rotating Coordinates 303 Choice of Surface Coordinates 305 Internal Cartesian Coordinates 307 Nondevelopable Surfaces 308 Physical Consequences of Three Dimensionality 309 Intrinsic Coordinates 309 Domains of Dependence and Influence 310 5 13 Momentum Integral Equations in Three Dimensions 311 5 14 Separation and Attachment in Three Dimensions 312 Limiting Streamlines and Vortex Lines 314 5 15 Boundary Layers on Bodies of Revolution and Yawed Cylinders 315 Mangler’s Transformation 317 Boundary Layer on Yawed Cylinders 317 Cross Flow 319 Transformed Equations for Yawed Cylinders 320 5 16 Three-Dimensional Stagnation Point Flow 320 5 17 Boundary Layer on Rotating Blades 321 5 18 Numerical Solution of 3-D Boundary Layer Equations 322 5 19 Unsteady Boundary Layers 324 Purely Unsteady Boundary Layers 324 Periodic Boundary Layers 326 Separation of Unsteady Boundary Layers 329 Mathematical Formulation of the M-R-S Principle 330 Numerical Method of Solution of Unsteady Equations 331 5 20 Second Order Boundary Layer Theory 332 Method of Matched Asymptotic Expansion 334 Outer Expansion 334 Some Important Derivatives at the Wall 338 Inner Expansion 338 The First and Second Order Boundary Layer Problems 339 Matching of Inner and Outer Solutions 340 A Unified Second Order Correct Viscous Model 342 Matching 343 5 21 Inverse Problems in Boundary Layers 346 Inverse Formulation with Assigned Displacement Thickness 347 5 22 Formulation of the Compressible Boundary Layer Problem 348 Estimation of the Viscous Terms 350 External Flow Equations and the Boundary Conditions 353 Particular Cases 354 Numerical Solution of Compressible Boundary Layer Equations 354 5 23 5 24 5 25 5 26 5 27 5 28 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 Part HI: Navier-Stokes’ Formulation Incompressible Flow 358 Formulation of the Problem in Primitive Variables 259 Ad Hoc Modification 360 Formulation of the Problem in Vorticity/Potential Form 360 Vorticity-Stream Function Formulation 361 Vorticity-Potential Function Formulation 362 Integro-Differential Formulation 364 Application of the Boundary Conditions 365 Basic Computational Aspects 366 Compressible Flow 366 Determination of Temperature 368 Hyperbolic Equations and Conservation Laws 272 System of Quasilinear Equations from the Conservation Equations 380 Hyperbolic Equations in Higher Dimensions 284 Numerical Transformation and Grid Generation 385 Equations for Grid Generation 385 Gaussian Equations for Grid Generation 387 Numerical Algorithms for Viscous Compressible Flows 387 Nature of the Difference Schemes 393 Formulation for Compressible Navier-Stokes’ Equations 397 Thin-Layer Navier-Stokes’ Equations (TLNS) 401 Parabolized Navier-Stokes’ Equations (PNS) 401 References 402 Problems 406 Chapter 6 TURBULENT FLOW Part I: Stability Theory and the Statistical Description of Turbulence Introduction 421 Stability of Laminar Flows 421 Formulation of the Problem 421 Formulation for Plane Parallel Laminar Flows 424 Squire’s Theorem 426 Temporal and Spatial Instabilities 427 Boundary Conditions for the Orr-Sommerfeld Equation 428 Temporal Stability 430 Temporal Stability at Infinite Reynolds’ Number 431 Rayleigh’s First Theorem 432 Rayleigh’s Second Theorem 432 Numerical Algorithm for the Orr-Sommerfeld Equation 435 Transition to Turbulence 438 Statistical Methods in Turbulent Continuum Mechanics 439 Average or Mean ofTXirbulent Quantities 440 Time and Space Averaging 440 Time Average 441 Ensemble Average 441 Space Average 443 Basic Axioms of Averaging 444 Statistical Concepts 445 Probability Distribution Functions 445 Probability Density 446 Mathematical Expectation 447 Correlation Functions 448 Stationary Processes 448 Characteristic Functions Gaussian Distribution 6 9 Internal Structure in the Physical Space Second and Third Order Correlations Dynamic Equation of Correlations Homogeneous Turbulence Homogeneous Shear Türbulence Isotropic Turbulence Analysis of Isotropic Turbulence Longitudinal and Lateral Correlations Approximate Analysis Dynamic Equation for Isotropic Turbulence 6 10 Internal Structure in the Wave Number Space Some General Definitions Dynamic Equation of Homogeneous Turbulence in the k-Space Analysis of Isotropic Tbrbulence in the k-Space Connection Between u2f(r, t) and E(k, /) Formulation of One-Dimensional Spectrum Taylor’s Formulae 6 11 The Theory of Universal Equilibrium i Determination of E(k, t) Based on Kolmogorov’s Hypothesis Transfer Theories Comparison of Taylor’s and Kolmogorov’s Dissipation Lengths Integral Length and Time Scales Part II: Development of the Averaged Equations 6 12 Introduction 6 13 Averaged Equations for Incompressible Flow Equation of Tiirbulence Kinetic Energy Equations of Mean-Square Vorticity Fluctuations Rate Equation for the Reynolds’ Stresses Rate Equation for the Dissipation e Physical Interpretation of the Terms Analysis of the Pressure-Strain Correlation 6 14 Average Equations for Compressible Row Equation of the Turbulence Energy and the Reynolds’ Stress Dissipation Function 6 15 Tbrbulent Boundary Layer Equations Equations in Rectangular Cartesian Coordinates Two-Dimensional Equations Three-Dimensional Equations Equations in Orthogonal Curvilinear Coordinates Part III: Basic Empirical and Boundary Layer Results in Tiirbulence 6 16 The Closure Problem 6 17 Prandtl’s Mixing Length Hypothesis Turbulent Row Near a Wall Experimental Determination of ht Application of the Logarithmic Formula in Pipe Row Power Laws for the Velocity Distribution Rough Pipes 6 18 Wall-Bound TXirbulent Rows 6 19 Analysis of Turbulent Boundary Layer Velocity Profiles Law of the Wall for Compressible Flow 6 20 Momentum Integral Methods in Boundary Layers Method of Tfuckenbrodt Method of Head 449 450 451 451 453 454 456 456 457 459 461 463 464 464 466 467 470 472 474 475 476 477 481 482 483 484 486 489 490 491 492 493 495 498 500 501 501 504 504 506 507 507 508 511 512 513 515 515 523 530 531 534 539 6 21 6 22 6 23 6 24 6 25 6 26 6 27 6 28 6 29 6 30 6 31 6 32 6 33 1 2 3 4 5 6 7 8 9 10 11 12 Differential Equation Methods in Two-Dimensional Boundary Layers Zero-Equation Modeling in Boundary Layers One-Equation Model of Glushko Part IV: Tbrbulence Modeling Generalization of Boussinesq’s Hypothesis Specification of the Length Scale Zero-Equation Modeling in Shear Layers Thin Shear Layers One-Equation Modeling Choice of the Constants b,, b3, and b5 Modifications Due to the Explicit Effects of Viscosity Two-Equation (K- g ) Modeling Modeling of the Dissipation Rate Equation Modeling for Separated Flows Reynolds’ Stress Equation Modeling Determination of the Constants c, and c2 Another Modeling of the Energy Equation The Wall Boundary Conditions Application to Two-Dimensional Thin Shear Layers Algebraic Reynolds’ Stress Closure Development of a Nonlinear Constitutive Equation Extension to Compressible Flow Current Approaches to Nonlinear Modeling Heuristic Modeling Modeling for Compressible Flow Stokes’ Law of Friction Complete Stress Tensor Heat Flux Production of Turbulence Energy Model Equations Justification of the Modeling Constants for Compressible Flow Three-Dimensional Boundary Layers Eddy Viscosity Approach to 3-D Boundary Layers References Problems 541 543 544 547 548 550 550 551 552 554 556 557 558 558 561 562 563 564 566 568 571 578 582 583 584 584 585 586 586 588 588 592 593 596 Mathematical Exposition 1 BASE VECTORS AND VARIOUS REPRESENTATIONS Introduction 609 Representations in Rectangular Cartesian Systems 610 Scalars, Vectors, and Tensors 611 Differential Operations on Tensors 612 Gradient 612 Divergence 613 Curl 614 Multiplication of a Tensor and a Vector 614 Scalar Multiplication of Two Tensors 615 A Collection of Usable Formulae 616 Taylor’s Expansion in Vector Form 618 Principal Axes of a Tensor 618 Transformation of T to the Principal Axes 620 Quadratic Form and the Eigenvalue Problem 622 Representation in Curvilinear Coordinates 622 Fundamental Metric Components 625 Elemental Displacement Vector 627 o-Dimensional Boundary Layers ary Layers rbulence Modeling pothesis 541 543 544 547 548 Layers 550 550 551 b5 552 Effects of Viscosity 554 556 Equation 557 558 558 561 uation 562 563 in Shear Layers 564 re 566 stitutive Equation 568 571 578 582 583 584 584 585 586 586 stants for Compressible Flow 588 588 Boundary Layers 592 593 596 matical Exposition 1 VARIOUS REPRESENTATIONS 609 artesian Systems 610 : 611 612 613 614 614 615 616 618 618 cipal Axes 620 alue Problem 622 oordinates 622 627 Vector r sors e rm Differentiation of Base Vectors 628 Gradient of a Vector 630 Divergence and Curl of Vectors 631 Divergence of Second Order Tensors 632 Christoffel Symbols in Three Dimensions 633 First Kind 633 Second Kind 634 Some Derivative Relations 637 Normal Derivative of Functions 638 Physical Components in Curvilinear Coordinates 638 Scalar and Double Dot Products of Two Tensors 639 Mathematical Exposition 2 THEOREMS OF GAUSS, GREEN, AND STOKES Gauss’ Theorem 641 Green’s Theorem 641 Stokes’ Theorem * 642 Mathematical Exposition 3 GEOMETRY OF SPACE AND PLANE CURVES Basic Theory of Curves 645 Tangent Vector 646 Principal Normal 646 Binormal Vector 647 Serret-Frenet Equations 647 Plane Curves 647 Mathematical Exposition 4 FORMULAE FOR COORDINATE TRANSFORMATION Introduction 651 Transformation Laws for Scalars 651 Transformation Laws for Vectors 652 Transformation Laws for Tensors 654 Transformation Laws for the Christoffel Symbols 656 Some Formulae in Cartesian and Curvilinear Coordinates 656 Laplacian of an Absolute Scalar 657 Mathematical Exposition 5 POTENTIAL THEORY Introduction 659 Formulae of Green 659 Green’s Formulae for Laplace Operator 660 Potential Theory 660 Integral Representation 661 The Delta Function 662 Integral Representation of Delta Function 663 Delta Function in Higher Dimensions 664 Delta Function and Fundamental Solution of the Laplace Equation 664 The Dirichlet Problem for the Poisson Equation 665 Particular Solution of Poisson’s Equation 666 General Representation of a Vector 666 Application of Green’s First Formula 667 Mathematical Exposition 6 SINGULARITIES OF THE FIRST ORDER ODES 1 Introduction 669 2 Singularities and Their Classification 669 Mathematical Exposition 7 GEOMETRY OF SURFACES 1 1 INTI 1 Basic Definitions 673 2 Formulae of Gauss 673 Christoffel Symbols Based on Surface Coefficients 674 3 Formulae of Weingarten 676 4 Equations of Gauss 676 5 Normal and Geodesic Curvatures 676 Longitudinal and Transverse Curvatures 679 6 Grid Generation in Surfaces 680 Mathematical Exposition 8 FINITE DIFFERENCE APPROXIMATION APPLIED TO PDE’S 1 Introduction 681 2 Calculus of Finite Difference 681 Methods of Interpolation 683 Cubic Spline Functions 684 3 Iterative Root-Finding 685 4 Numerical Integration 687 5 Finite Difference Approximations of Partial Derivatives 688 First Derivatives 688 Second Derivatives 688 6 Finite Difference Approximation of Parabolic PDE 689 Stable Schemes for Parabolic Equations 692 Crank-Nicolson’s Method 692 Alternating Direction Implicit (ADI) Method 693 Leapfrog DuFort-Frankel Method 693 7 Finite Difference Approximation of Elliptic Equations 693 Point- and Line-Jacobi Method 696 Gauss-Seidel Iterative Method 696 Successive-Over-Relaxation (SOR) 697 The a contii part i Since volut X 1( on a in th« of m value sumi throi scop T1 is in disti gase the l weaJ and orig betv neig cohe thro diff 1 2 FLl Mathematical Exposition 9 FRAME INVARIANCY 1 Introduction 699 2 Orthogonal Tensor 699 Time Differentiation 700 Change of Basis 700 3 Arbitrary Rectangular Frames of Reference 701 4 Check for Frame Invariancy 702 5 Use of Q 703 References for the Mathematical Expositions 704 Index 707 In c geo flui eg are to t san 1 3 IN It i
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id	DE-604.BV012516430
illustrated	Illustrated
indexdate	2024-07-09T18:28:56Z
institution	BVB
isbn	0849324076
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-008496333
oclc_num	39052176
open_access_boolean
owner	DE-703 DE-1046 DE-29T DE-91 DE-BY-TUM DE-522 DE-634 DE-11
owner_facet	DE-703 DE-1046 DE-29T DE-91 DE-BY-TUM DE-522 DE-634 DE-11
physical	726 S. graph. Darst.
publishDate	1999
publishDateSearch	1999
publishDateSort	1999
publisher	CRC Press
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spelling	Warsi, Zahir U. A. Verfasser aut Fluid dynamics theoretical and computational approaches Z. U. A. Warsi 2. ed. Boca Raton [u.a.] CRC Press 1999 726 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dynamica gtt Idealen (wiskunde) gtt Navier-Stokes-vergelijkingen gtt Reologie gtt Turbulentie gtt Viscositeit gtt Fluid dynamics Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008496333&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Warsi, Zahir U. A. Fluid dynamics theoretical and computational approaches Dynamica gtt Idealen (wiskunde) gtt Navier-Stokes-vergelijkingen gtt Reologie gtt Turbulentie gtt Viscositeit gtt Fluid dynamics Strömungsmechanik (DE-588)4077970-1 gnd
subject_GND	(DE-588)4077970-1
title	Fluid dynamics theoretical and computational approaches
title_auth	Fluid dynamics theoretical and computational approaches
title_exact_search	Fluid dynamics theoretical and computational approaches
title_full	Fluid dynamics theoretical and computational approaches Z. U. A. Warsi
title_fullStr	Fluid dynamics theoretical and computational approaches Z. U. A. Warsi
title_full_unstemmed	Fluid dynamics theoretical and computational approaches Z. U. A. Warsi
title_short	Fluid dynamics
title_sort	fluid dynamics theoretical and computational approaches
title_sub	theoretical and computational approaches
topic	Dynamica gtt Idealen (wiskunde) gtt Navier-Stokes-vergelijkingen gtt Reologie gtt Turbulentie gtt Viscositeit gtt Fluid dynamics Strömungsmechanik (DE-588)4077970-1 gnd
topic_facet	Dynamica Idealen (wiskunde) Navier-Stokes-vergelijkingen Reologie Turbulentie Viscositeit Fluid dynamics Strömungsmechanik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008496333&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT warsizahirua fluiddynamicstheoreticalandcomputationalapproaches

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