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 |  موضوع: كتاب Multiphysics Modeling Using COMSOL 5 and MATLAB الثلاثاء 10 مايو 2022, 12:40 am | |
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Multiphysics Modeling Using COMSOL 5 and MATLAB
Second Edition
Roger W. Pryor, Ph.D.
COMSOL Certified Consultant
و المحتوى كما يلي :
Multiphysics Modeling Using COMSOL 5 and MATLAB
Second Edition
Roger W. Pryor, Ph.D.
COMSOL Certified Consultant
Contents
Preface xi
Introduction xiii
Chapter 1: Modeling Methodology Using COMSOL
Multiphysics 5.x 1
Guidelines for New COMSOL Multiphysics 5.x Modelers 1
Hardware Considerations 2
Simple Model Setup Overview 4
Basic Problem Formulation and Implicit Assumptions 12
1D Window Heat Flow Models 13
1D 1 Pane Window Heat Flow Model 13
1D 2 Pane Window Heat Flow Model 35
1D 3 Pane Window Heat Flow Model 49
First Principles as Applied to Model Definition 60
Some Common Sources of Modeling Errors 62
References 63
Suggested Modeling Exercises 63
Chapter 2: Materials Properties Using COMSOL Multiphysics 5.x 65
Materials Properties Guidelines and Considerations 65
COMSOL Materials Properties Sources 66
Other Materials Properties Sources 68vi • Contents
Material Property Entry Techniques 69
Multipane Window Model 69
Set Boundary Conditions 86
References 88
Chapter 3: 0D Electrical Circuit Interface Modeling Using
COMSOL Multiphysics 5.x 89
Guidelines for Electrical Circuit Interface Modeling in 5.x 90
Electrical / Electronic Circuit Considerations 90
Simple Electrical Circuit Interface Model
Setup Overview 99
Basic Problem Formulation and Implicit Assumptions 104
0D Basic Circuit Models 105
0D Resistor-Capacitor Series Circuit Model 105
0D Inductor-Resistor Series Circuit Model 112
0D Series-Resistor Parallel-Inductor-Capacitor
Circuit Model 118
0D Basic Circuit Models Analysis and Conclusions 125
First Principles as Applied to 0D Model Definition 126
References 127
Suggested Modeling Exercises 128
Chapter 4: 1D Modeling Using COMSOL Multiphysics 5.x 129
Guidelines for 1D Modeling in 5.x 129
1D Modeling Considerations 130
1D Basic Models 131
1D KdV Equation Model 131
1D Telegraph Equation Model 148
1D Spherically Symmetric Transport Model 167
1D Spherically Symmetric Transport Model Animation 184
1D Advanced Model 186
1D Silicon Inversion Layer Model: A Comparison
of the Results obtained from using the
Density-Gradient (DG) Theory and the
Schrodinger-Poisson (SP) Theory Methodologies 186Contents • vii
First Principles as Applied to 1D Model Definition 223
References 224
Suggested Modeling Exercises 226
Chapter 5: 2D Modeling Using COMSOL Multiphysics 5.x 227
Guidelines for 2D Modeling in 5.x 227
2D Modeling Considerations 228
2D Basic Models 233
2D Electrochemical Polishing Model 233
2D Hall Effect Model 256
First Principles as Applied to 2D Model Definition 270
References 271
Suggested Modeling Exercises 272
Chapter 6: 2D Axisymmetric Modeling Using COMSOL
Multiphysics 5.x 273
Guidelines for 2D Axisymmetric Modeling in 5.x 273
2D Axisymmetric Modeling Considerations 274
2D Axisymmetric Heat Conduction in a Cylinder Model 278
2D Axisymmetric Basic Models 278
2D Axisymmetric Cylinder Conduction Model 278
2D Axisymmetric Transient Heat Transfer Model 290
First Principles as Applied to 2D Axisymmetric
Model Definition 303
References 304
Suggested Modeling Exercises 304
Chapter 7: 2D Simple and Advanced Mixed Mode Modeling
Using COMSOL Multiphysics 5.x 307
Guidelines for 2D Simple Mixed Mode Modeling in 5.x 307
2D Simple Mixed Mode Modeling Considerations 308
2D Simple Mixed Mode Models 313
2D Electric Impedance Sensor Model 313
2D Metal Layer on a Dielectric Block Model 332
Heat Transfer 2 (ht2) Interface 346
Heat Transfer in Solids (ht) Interface 358viii • Contents
First Principles as Applied to 2D Simple Mixed Mode
Model Definition 363
References 364
Suggested Modeling Exercises 365
Chapter 8: 2D Complex Mixed Mode Modeling Using COMSOL
Multiphysics 5.x 367
Guidelines for 2D Complex Mixed Mode Modeling in 5.x 367
2D Complex Mixed Mode Modeling Considerations 368
2D Complex Mixed Mode Models Using the RF Module 370
Finding the Impedance of a Two (2) Wire,
Parallel-Wire, Air-Dielectric, Transmission Line 370
2D Finding the Impedance of a Two (2) Wire,
Parallel-Wire, Air-Dielectric, Transmission Line Model
Summary and Conclusions 389
2D Finding the Impedance of a Concentric,
Two (2) Wire, Transmission Line (Coaxial Cable) 389
2D Finding the Impedance of a Concentric,
Two (2) Wire 405
2D Axisymmetric Transient Modeling of a
Coaxial Cable 405
First Principles as Applied to 2D Complex Mixed Mode
Model Definition 431
References 431
Suggested Modeling Exercises 432
Chapter 9: 3D Modeling Using COMSOL Multiphysics 5.x 433
Guidelines for 3D Modeling in 5.x 433
3D Modeling Considerations 434
3D Models 438
3D Spiral Coil Microinductor Model 438
3D Linear Microresistor Beam Model 455
Multiphysics Thermal Linear Elastic 1 (te1) 476
Heat Transfer in Solids (ht) 477
First Principles as Applied to 3D Model Definition 489
References 489
Suggested Modeling Exercises 490Contents • ix
Chapter 10: Perfectly Matched Layer Models Using COMSOL
Multiphysics 5.x 493
Guidelines for Perfectly Matched Layer (PML)
Modeling in 5.x 493
Perfectly Matched Layer (PML) Modeling
Guidelines and Coordinate Considerations 494
Perfectly Matched Layer Models 497
Building the 2D Concave Metallic Mirror PML Model 497
Building the 2D Energy Concentrator PML Model 517
First Principles as Applied to PML Model Definition 539
References 540
Suggested Modeling Exercises 540
Chapter 11: Bioheat Models Using COMSOL Multiphysics 5.x 543
Guidelines for Bioheat Modeling in 5.x 543
Bioheat Modeling Considerations 544
Bioheat Transfer Models 547
2D Axisymmetric Microwave Cancer Therapy Model 574
First Principles as Applied to Bioheat Model Definition 601
References 602
Suggested Modeling Exercises 602
Appendix: A Brief Introduction to LiveLinkTM for MATLAB
Using COMSOL Multiphysics 5.x 605
Guidelines for LiveLink Exploration through
Modeling in 5.x 605
Getting Started using LiveLink for MATLAB
with COMSOL Multiphysics 5.x on a
Windows 10 platform 606
First Principles as Applied to Scripting and GUI Model
Definition 614
References 615
Suggested Modeling Exercises 615
Index
A
Axisymmetric modeling, 2D
coordinate system, 275
First Principles Analysis, 303
heat conduction theory, 276–277
heat transfer theory, 275–276
numerical solution model, 277
Axisymmetric transient heat transfer
model, 2D
axisymmetric sphere, 292–295
building, 290–292
computed results, 300–301
3D results, 301–302
Fick’s First Law, 288–289
Fick’s Second Law, 289–290
heat transfer in solids, 295–297
mesh type, 298
study settings, 299–300
Axisymmetric transient modeling of a
coaxial cable, 405–430
B
Bioheat Models
bioheat equation theory, 544–546
First Principles Analysis, 601–602
tumor laser irradiation theory, 546
C
Concave metallic mirror, 497
Concept of impedance, 311
D
Distributed memory parallelism, 2
E
Electrochemical polishing model,
229–232
animation, 250–251
building, 233
computed results, 249–250
deformed geometry (dg) interface,
241–243
electric currents (ec) interface, 243–246
mesh type, 247
parameters, 234
time dependent study type, 248
variables, 235–241
Electromagnetic induction
discovery, 436
mutual inductance, 437
self-inductance, 436
F
Fick’s First Law, 288–289
Fick’s Second Law, 289–290
First Principles Analysis
bioheat models, 601–602
1D modeling, 223–224
2D axisymmetric modeling, 303
2D complex mixed mode modeling, 431
2D Hall Effect model, 270–271618 • Index
2D simple mixed mode modeling,
363–364
3D modeling, 489
LiveLink for MATLAB , 614
modeling methodology, 60–61
perfectly matched layer (pml) models,
539
0D electrical circuit interface modeling,
126–127
Fourier’s Law, 277
H
Hall Effect model
animation, 269–270
building, 256–257
computed results, 268–269
current conservation edit windows,
262–263
discovery, 254
electric currents (ec) interface, 259
First Principles Analysis, 270–271
Lorentz Force, 254
mesh type, 266
model geometry
electric insulation 2 boundaries, 263
electric potential 1, 264
floating potential 1 setting, 265
floating potential 2 setting, 265
ground 1 boundary, 263
Ohm’s Law, 252
parameters edit window, 257–258
rectangle entry windows, 259
resistance, 253
sensors, 253
settings electric currents, 260–261
silicon conductivity parameters,
261–262
study settings, 267–268
Heat conduction theory, 276–277
Heat transfer theory, 275–276
Hyperthermic oncology, 574
K
Kirchhoff’s law
Current Law, 94–95
Voltage Law, 95–96
L
LiveLink for MATLAB
First Principles Analysis, 614
on Windows 10 platform
COMSOL and MATLAB, 611–614
installation, 606
MATLAB Command Window, 607
M
Materials properties
guidelines and considerations, 65–66
multipane window model
Add Physics window, 70
geometry building, 74–77
material definition, 77
from newly built material, 77–81
parameter setting, 72–74
saved Initial Model Build, 72
Select Study Type window, 71
user defined direct entry, 84–86
user defined parameters, 82–84
set boundary conditions
meshing and solution computations,
87–88
sources, 66–69
Meshing, 32
Microwave cancer therapy theory, 574
bioheat transfer models, 575
2D axisymmetric model, 574–575
building, 575–576
domains, 579
electromagnetic waves, frequency
domain, 590–593
heat transfer (ht), 593–595
materials, 584–590Index • 619
mesh type, 595–597
parameters, 577–579
results, 598–600
settings union, 580
study settings, 597–598
union operation, 580–581
vector coordinates, 582
Modeling methodology
Desktop Display, 5
Geometric coordinate systems, 6
Model Wizard window, 5
1D heat flow model, 35
1 pane window heat flow model,
13–35
2 pane window heat flow model,
35–48
3 pane window heat flow model,
49–59
First Principles Analysis, 60–61
hardware considerations
installation, 3
platform, 2–3
rules, 2
problem formulation and implicit
assumptions, 12–13
Right-Hand-Rule, 4
Select Space Dimension
1D button, 9
Desktop Display, 11
Physics Interface, 11
Select Physics page, 10
sources of modeling errors, 62–63
Mutual-inductance, 97
N
Newton’s Law of Cooling, 276–277
O
Ohm’s Law, 91, 252
1D Cartesian Coordinate Geometry, 7
1D modeling
considerations, 130
First Principles Analysis, 223–224
KdV Equation
animation, 146–147
build, 133–139
mesh type, 139–141
nonlinear partial differential
equations, 131
results, 144–146
solver type, 142–144
in standard notation, 131
time dependent study type,
141–142
silicon inversion layer model
Add Physics window, 207
analytic doping model window, 196
build, 187–188
DG and SP theory methodologies,
187
ECC settings, 204–205
Electron Concentration Plot Settings,
206
electrostatics, 210–213, 215
Geometry 1, 188–190
Global Definitions, 190–192
materials, 192–194
Mesh 1, 199–202
metal contact model window, 197
multiphysics, 213
Parametric sweep settings, 216
results, 221
Schrodinger equation, 207–210
Schrodinger-Poisson Coupling
Settings, 214
Schrodinger-Poisson modified
settings, 221
semiconductor material model
window, 195
semiconductor window, 194
Study 1 and 2 settings, 202, 217
thin insulator gate window values,
198
spherically symmetric transport model
animation, 184–185620 • Index
build, 171–173
1D Plot Group 1, 181–183
1D Plot Group 2, 183–184
Geometry 1 window, 174–175
Global Definitions, 173–174
Initial Values 1, 176–179
Mesh Type, 179–180
PDE, 175–176
results, 181
study step, 180
time-dependent heat conduction,
168–170
Telegraph Equation Model
animation, 165–166
build, 150–152
default solver, 158–159
differential equations for Voltage and
Current, 148
1D Plot Group 2, 159–165
Geometry 1 Window, 153
initial values coefficients, 155
lumped-constant circuit, 148
Mesh Type, 156–157
PDE, 153–154
results, 159
study step, 157
Zero Flux 1, 155
1D 1 pane window heat flow model
control button array, 17
Desktop Display, 16–17
with built geometry, 21
Geometry 1 entry, 19
Global Definitions Parameters 1
selection menu, 16
initial model build, 15
materials selection button
add material library, 22–23
Domain-boundary selection window,
32
expanded built-in material list, 23
expanded Heat Transfer in Solids, 27
Function List, 22
Heat Transfer in Solids Selection
window, 28–29
Initial Boundaries Heat Flux window,
29
meshed 1D domain, 32
scrolled list with silica glass visible, 24
Solid 1 window Settings, 27
Twistie before built-in, 23
model wizard
add physics window, 13
Done button, select study type
window, 14
parameters entry table, 17–18
settings - interval window, 20–21
1D 2 pane window heat flow model, 35–48
1D 3 pane window heat flow model,
49–59
P
Perfectly matched layer (PML) models
2D concave metallic mirror
boundary selection, 506
computed solution, 516–517
electromagnetic waves (emw), 513
energy concentration systems, 517
general extrusion, 507–513
geometry, 500–505
in Graphics window, 505
materials, 506–507
mesh type, 514
parameters, 498
study settings, 514–516
variables, 499–500
2D energy concentrator
boundaries selection, 526–529
computed solution, 538–539
difference, 525
domain, 522
electromagnetic waves (emw),
529–531
far-field calculation, 533–534
formation, 523–524Index • 621
general extrusion, 535
geometry, 521
impedance boundary condition,
532
materials, 527–528
mesh type, 535–536
parameters, 518–519
rectangle, 524–525
study settings, 536–538
variables, 520
discovery, 494
First Principles Analysis, 539
wave equation solution, 496
R
Resonance, 125–126
S
Schrodinger equation, 207–210
Self-inductance, 97
Sensors, 253
Series-parallel resistive circuit, 94
Series-resistor parallel-inductor-capacitor
circuit model, 118–125
Shared memory parallelism, 2
Spherically symmetric transport model
animation, 184–185
build, 171–173
1D Plot Group 1, 181–183
1D Plot Group 2, 183–184
Geometry 1 window, 174–175
Global Definitions, 173–174
Initial Values 1, 176–179
Mesh Type, 179–180
PDE, 175–176
results, 181
study step, 180
time-dependent heat conduction,
168–170
T
Telegraph equation model, 1D modeling
animation, 165–166
build, 150–152
default solver, 158–159
differential equations for Voltage and
Current, 148
1D Plot Group 2, 159–165
Geometry 1 Window, 153
initial values coefficients, 155
lumped-constant circuit, 148
Mesh Type, 156–157
PDE, 153–154
results, 159
study step, 157
Zero Flux 1, 155
Thermodynamics, 276
2D axisymmetric heat conduction in
cylinder model, 277
building, 278–282
computed results, 287–288
default contour plot, 288
heat flux edit windows, 285
heat transfer in solids, 282
mesh type, 285–286
stationary study type, 286–287
2D axisymmetric tumor laser irradiation model
bioheat transfer, 558
boolean operations, 551–552
computed solution, 571–573
domains, 550–551, 558–565
domains formation, 553–554
geometry, 550
heat flux, 567–569
heat source, 566–567
initial values, 566
mesh type, 569–570
parameters, 548–550
study settings, 570–571
variables, 554–558
2D Cartesian Coordinate Geometry, 7622 • Index
2D complex mixed mode modeling
axisymmetric transient modeling of a
coaxial cable, 405–430
coordinate system, 369
First Principles Analysis, 431
radio frequency waves, 370
two (2) wire, parallel-wire, air-dielectric,
transmission line model, 370–381
coaxial cables, 389–404
electromagnetic waves, frequency
domain (emw), 382–389
2D metal layer on a diamond block model
building, 353–354
computed results, 362–363
geometry, 354–356
heat transfer in solids (ht) interface,
358–361
materials, 356–358
mesh type, 361
study settings, 361–362
2D metal layer on a dielectric block model
building, 332–333
computed results, 340–341
Fick’s First Law, 330
Fick’s Second Law, 331
geometry, 333–334
heat transfer in solids (ht) interface,
335–339
materials, 334–335
mesh type, 339
second study
computed results, 350–351
geometry, 342–344
heat transfer 2 (ht2) interface,
346–349
materials, 344–346
mesh type, 349
study settings, 349–350
vs. study 1 results, 351–353
study settings, 339–340
2D modeling
coordinate system, 229
electrochemical polishing theory,
229–232 (see also Electrochemical
polishing model)
2D simple mixed mode modeling
coordinate system, 309–310
electrical impedance theory, 310–313
electric impedance sensor model
building, 313–316
computed results, 325–329
electric currents (ec) interface,
318–321
geometry, 317–318
mesh type, 321–322
study settings, 322–325
First Principles Analysis, 363–364
out-of-plane thickness, 309–310
3D Cartesian Coordinate Geometry, 6
3D modeling
considerations
coordinate system, 435–436
inductance theory, 436–438
First Principles Analysis, 489
heat transfer in solids, 477–488
linear microresistor beam model
building, 457–458
electric currents (ec), 473–474
electric potential boundary
specification, 475–476
extrude, 462–463, 467–468
fillets, 466–467
form union, 469
geometry, 459–460
intersection, 468–469
materials, 471–473
parameters, 458–459
polygon settings, 460–462, 465–466
selections, 469–471
Settings Ground window, 475
work plane, 460
Work Plane 2, 463–465
multiphysics thermal linear elastic 1,
476–477Index • 623
spiral coil microinductor model
building, 438–439
color and style plot settings, 450
3D Plot Group 2, 451–454
environment, 442–443
geometry, 439–441
inductance calculation, 454–455
magnetic and electric fields, 445–449
materials, 443–445
selected spiral coil boundaries, 451
Z
0D electrical circuit interface modeling
electrical circuit interface model setup,
99–104
electrical / electronic circuit
considerations
connection sequences, 91–92
Kirchhoff law, 94–96
Maxwell-Faraday formulation, 97
Ohm’s law, 91
parallel resistive circuit, 93
self-inductance and mutual-inductance,
97
series-parallel resistive circuit,
94
First Principles Analysis, 126–127
inductor-resistor series circuit model,
112–118
problem formulation and implicit
assumptions, 104
resistor-capacitor series circuit model,
105–111
series-resistor parallel-inductor-capacitor
circuit model, 118–125
0D Space Dimension, 9
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