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| موضوع: كتاب Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer الخميس 06 فبراير 2014, 5:21 pm | |
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أخوانى فى الله أحضرت لكم كتاب
Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer Ben Q. Li Series Editor: Klaus-Jürgen Bathe Massachusetts Institute of Technology Cambridge, MA, USA Advisors: Franco Brezzi University of Pavia Pavia, Italy Olivier Pironneau Université Pierre et Marie Curie Paris, France
ويتناول الموضوعات الأتية :
1 Introduction 1 11Conservation Laws for a Continuum Medium 1 111Conservation of Mass1 112Conservation of Momentum 2 113Conservation of Energy2 114 Constitutive Relations 3 12Governing Equations in Terms of Primitive Variables 5 121 Vector Form 5 122Component Form in Cartesian Coordinates 5 123Component Form in Cylindrical Coordinates 6 124 Summary813 Species Transport Equations 8 14Governing Equations in Translating and Rotating Frames of Reference 915 Boundary and Initial Conditions 9 151 General Boundary Conditions10 152 Free Boundary Conditions 11 153 Moving Interface Conditions 12154 Phase Change Conditions1216Governing Equations for Flows Through Porous Media13 17 Governing Equations in Conservation Form15 Exercises 17 References 18 2Discontinuous Finite Element Procedures 21 21The Concept of Discontinuous Finite Elements 22 211 Weakly Imposed Cross-element Continuity23 212Numerical Boundary Fluxes for Discontinuity 25 213 Boundary Constraint Minimization26 214Treatment of Discontinuity for Non-conservative Systems 27 215 Transient Problems2822Discontinuous Finite Element Formulation29 xii Contents 221 Integral Formulation29222 Time Integration3023 Solution Procedures31 24Advantages and Disadvantages of Discontinuous Finite Element Formulations32241 Advantages32242 Disadvantages 3325 Examples 34 Exercises 42 References 42 3Shape Functions and Elemental Calculations 45 31 Shape Functions 46 3111-D Shape Functions46 3122-D Shape Functions50 3121 Triangular Elements 50 3122 Quadrilateral Elements 54 3133-D Shape Functions58 3131 Tetrahedral Elements58 3132 Hexahedral Elements60 32 Construction of Special Elements65 321 Non-standard Elements 65 322Construction of Element Shape Functions by Node Collapsing66 323 Spectral Elements6733Hierarchical Shape Functions69 331 1-D Hierarchical Correction69 332Canonical Square and Cubic Elements 71 333 Triangular and Tetrahedral Elements73 334Obtaining Hierarchical Elements Through Coordinate Transformations 77 335 Orthogonal Mass Matrix Construction7834 Interpolation Error Analysis80 341Hilbert Space and Various Error Measures80 342Interpolation Error Analysis for 1-D Elements 84 343Interpolation Error Analysis for 2-D/3-D Elements87 35 Numerical Integration88 351 1-D Numerical Integration 88 3522-D and 3-D Numerical Integration 90 353Integration for Triangular and Tetrahedral Elements91 36 Elemental Calculations93 361 Domain Calculations93362 Boundary Calculations98Exercises 102 References 103 Contents xiii 4Conduction Heat Transfer and Potential Flows 105 411-D Steady State Heat Conduction106 42Steady State Heat Conduction in Multidimensions113 43 1-D Transient Heat Conduction122 431 Alternating Upwinding Scheme124432 Central Fluxes 125433 Unified Representation125434 Numerical Implementation126435 RungeKutta Time Integration 128 436 Computational Procedures 12944Transient Heat Conduction in Multidimensions131 45Potential Flows and Flows in Porous Media 137 46 Selection of Numerical Fluxes 138 461 Stability for Steady StateProblems139 4611 Stability and Numerical Fluxes 139 4612Discontinuous and Mixed Finite Element Formulations142 462 Stability for Time Dependent Problems1444621Numerical Fluxes for Transient Problems144 4622Stability Analysis Using Matrix 145 463 Fourier Analysis147Exercises 152 References 155 5 Convection-dominated Problems 157 51 Pure Convection Problems 158 511 1-D Pure Convection158 5111 Method of Characteristics158 5112Discontinuous Finite Element Formulation162 512 Pure Convection in Multidimensions166513 Stability Analysis 169 5131 L2 -Stability – Integral Analysis 169 5132 L2 -Stability – Discretized Analysis 171 5133 Fourier Analysis 176 52 Steady State Convection-diffusion 181 521 1-D Problem181522 Origin of Oscillatory Stability185523 Steady Convection-Diffusion in Multidimensions18753 Transient Convection-diffusion191 531 Multidimensional Problem191532 Stability Analysis 195 5321 L2 -Stability – Integral Analysis 195 5322 L2 -Stability – Discretized Analysis 198 5323 Fourier Analysis 199 54 Nonlinear Problems202 541 1-D Inviscid Burgers’ Equation 202 5411 Basic Considerations 202 xiv Contents 5412Discontinuous Finite Element Formulation204 542Multidimensional Inviscid Burgers’ Equation 209 5421Discontinuous Finite Element Formulation209 5422 Characteristic Decomposition211 543Higher Order Approximations and TVD Formulations 212 5431Concept of Total Variation Diminishing 212 5432 Flux Limiters 214 5433 Slope Limiters 218 5434 TVD-RungeKutta Schemes227 55 Viscous Burgers’ Equations 235 551 1-D Burgers’ Equation 235 5522-D Viscous Burgers’ Equation 239 Exercises 241 References 243 6 Incompressible Flows 247 61Primitive Variable Approach248 62Fractional Step (Projection) Approach258 63Vorticity and Stream Function Approach260 64Coupled Flow and Heat Transfer265 Exercises 269 References 270 7 Compressible Fluid Flows 273 71 1-D Compressible Flows274 711Governing Equations274 712Basic Properties of the Euler Equations275 713 The Rankine–Hugoniot Conditions278 7141-D Riemann Solver – Exact Solution 281 7151-D Riemann Solver – Approximate Solution 283 716Discontinuous Finite Element Formulation 284 717 Low Order (Finite Volume) Approximations2877171The Godunov Scheme 288 7172The Roe Scheme289 718High Order TVD Approximations 290 719 Numerical Examples 29172Multidimensional Inviscid Compressible Flows 295 721 Governing Equations295 722Basic Properties of the Split 3-D Euler Equations 296 723Discontinuous Finite Element Formulation 298 73Multidimensional Compressible Viscous Flows 299 74 ALE Formulation 304 741 ALE Kinematic Description304 742Conservation of Mass308 743Conservation of Momentum 309 744Conservation of Energy310 745Summary of ALE Equations311 Contents xv 746 Constitutive Relations 311 747ALE Description of Compressible Flows 311 748Discontinuous Finite Element Formulation 312 Exercises 313 References 316 8External Radiative Heat Transfer 319 81Integral Equation for Surface Radiation Exchanges320 811 Governing Equation 320812 Kernel Functions32382Discontinuous Galerkin Finite Element Formulation325 83 Shadowing Algorithms327 831Shadowing Algorithm for 2-D Geometry 329 832 Shadowing Algorithm for Axisymmetric Configurations334 833Shadowing Algorithm for 3-D Geometry 339 84Coupling with Other Heat Transfer Calculations 345 841 Direct Coupling347 842 Iterative Coupling 34885 Numerical Examples 349 Exercises 359 References 360 9Radiative Transfer In Participating Media 363 91Governing Equation and Boundary Conditions364 911 Radiative Transfer Equation364912 Boundary Conditions 36692 Approximation Methods367 921 The Discrete Ordinate Method368922 The Spherical Harmonics Method36893 Discontinuous Finite Element Formulation376 94 Numerical Implementation389 941 2-D Calculations 389942 3-D Calculations 396 943Integration of the Source Term 399 9431 The Emitting Contribution399 9432 The Scattering Contribution 400 95 Radiation In Systems of Axisymmetry403 951Governing Equation in Cylindrical Coordinates 403 952 Volume Integration 405 953Surface Integration Over *p 406 954 Integration Over *M 408 955 Mapping410 956Treatment of the Emitting and Scattering Term411 96 Use of RTE for External Radiation Calculations 412 97Coupling of the Discontinuous Method with Other Methods415 98 Constant Element Approximation 416 Exercises 424 References 426 xvi Contents 10Free and Moving Boundary Problems 429 101Free and Moving Boundaries 430 102Basic Relations fora Curved Surface431 1021 Description of a Surface431 1022 Differential and Integral Relations for Curved Surfaces436 103Physical Constraints at a Moving Boundary 441 1031 Kinematic Conditions at a Moving Boundary441 1032 Stress Condition at a Moving Interface442 1033 Thermal Conditions at a Moving Interface 444 104Moving Grids vs Fixed Grids for Numerical Solutions447 105 Moving Grid Methods448 1051 Moving Boundaries Between Fluids4491052 Moving Phase Boundaries454 10521 SolidLiquid Phase Transition454 10522 LiquidVapor Phase Transition457 106 Fixed Gridmethods458 1061 Volume of Fluid Method459 10611 Structured Mesh460 10612 Unstructured Mesh 464 1062 The Marker-and-Cell Method 4681063 The Level Set Method469 1064 Fixed Grid Methods for Phase Change Problems 473 10641 Flow-based Methods 473 10642 Enthalpy-based Methods 474 107Phase Field Modeling of Moving Boundaries476 1071 Basic Ideas of Phase Field Models476 1072 Governing Equations for Interfacial Phenomena 479 1073 Discontinuous Finite Element Formulation 482 1074 Phase Field Modeling of Microstructure Evolution 483 10741 Governing Equations483 10742 Discontinuous Formulation 485 10743 Numerical Examples486 1075 Flow and Orientation Effects on Microstructure Evolution 489 10751 Flow Effects on Microstructure Evolution 489 10752Microstructure Evolution During Polycystalline Solidification 490 Exercises 494 References 498 11Micro and Nano Scale Fluid Flow and Heat Transfer 501 111 Micro Scale Heat Conduction 502 1111 Two-temperature Equations5021112 Phonon Scattering Equation503 1113 Phonon Radiative Transfer Equation 506 112Discontinuous Finite Element Formulation507 113Micro and Nano Fluid Flow and Heat Transfer513 Contents xvii 114The Boltzmann Transport Equation and Numerical Solution517 1141 The Boltzmann Integral-Differential Equation 518 1142 Numerical Solution of the Boltzmann Transport Equation523 115 The BoltzmanBGK Equation and Numerical Solution 524 1151 The BoltzmannBGK Equation524 1152 Discontinuous Finite Element Formulation 525 116The Lattice Boltzman Equation and Numerical Solution526 1161 Derivation of the Lattice Boltzmann Equation527 1162 Boundary Conditions 53311621Bounce Back Boundary Conditions (No Slip)533 11622Symmetric Boundary Conditions (Free Slip) 533 11623Inflow and Outflow Boundary Conditions (No Gradient)534 11624 Force Field Conditions 534 11625Moving Wall Conditions 534 1163 Discontinuous Finite Element Formulation 534 Exercises 538 References 540 12Fluid Flow and Heat Transfer in Electromagnetic Fields 543 121Maxwell Equations and Boundary Conditions544 1211 Maxwell Equations 5441212 Boundary Conditions 545 12121 Interface Boundary Condition 545 12122 Perfect Conducting Surface546 12123 Impedance Condition547 12124Sommerfield Radiation Condition547 12125 Symmetry Boundary Condition548 122 Maxwell Stresses and Energy Sources 548 123Discontinuous Formulation of the Maxwell Equations549 1231 Solution in Time Domain549 1232 Solution in Frequency Domain 5501233 Solution in Other Forms550124 Electroosmotic Flows550 1241 Governing Equations551 1242 Discontinuous Finite Element Formulation 553 125 Microwave Heating 556 126 Electrically Deformed Free Surfaces557 127Compressible flows in Magnetic Fields 566 Exercises568 References 569 Index
أتمنى أن تستفيدوا منه وأن ينال إعجابكم رابط تنزيل كتاب Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer
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