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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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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
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