Multiphysics Modeling Using COMSOL- A First Principles Approach.pdf

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M ultiphysics
M odeling USING
COMSOL ®
A F I R S T
P R I N C I P L E S
A P P R O A C H
R ogeR W. P RyoR
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Copyright © 2011 by Jones and Bartlett Publishers, LLC
All rights reserved. No part of the material protected by this copyright may be reproduced or utilized in any form,
electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system,
without written permission from the copyright owner.
COMSOL and COMSOL Multiphysics are trademarks of COMSOL AB. COMSOL materials are reprinted with the
permission of COMSOL AB.
Production Credits
Publisher: David Pallai
Editorial Assistant: Molly Whitman
Production Director: Amy Rose
Associate Production Editor: Tiffany Sliter
Associate Marketing Manager: Lindsay Ruggiero
V.P., Manufacturing and Inventory Control: Therese Connell
Composition: Glyph International
Cover Design: Scott Moden
Cover Image: © Photo courtesy of
COMSOL, Inc. (www.comsol.com)
Printing and Binding: Malloy, Inc.
Cover Printing: Malloy, Inc.
Library of Congress Cataloging-in-Publication Data
Pryor, Roger W.
Multiphysics modeling using COMSOL : a first principles approach / Roger W. Pryor.
p. cm.
Includes index.
ISBN-13: 978-0-7637-7999-3 (casebound)
ISBN-10: 0-7637-7999-7 (casebound)
1. Physics—Data processing. 2. Physics—Mathematical models. 3. Physics—Computer simulation. 4.
Engineering—Data processing. 5. Engineering—Mathematical models. 6. Engineering—Computer
simulation. 7. COMSOL Multiphysics. I. Title.
QC52.P793 2010
530.15'18—dc22
2009033347
6048
Printed in the United States of America
13 12 11 10 09 10 9 8 7 6 5 4 3 2 1
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Contents
Preface ix
Introduction
x
Chapter 1
Modeling Methodology
1
Guidelines for New COMSOL ® Multiphysics ® Modelers
1
Hardware Considerations
1
Coordinate Systems 2
Implicit Assumptions 5
1D Window Panes Heat Flow Models
6
1D Single-Pane Heat Flow Model 6
1D Dual-Pane Heat Flow Model 16
1D Triple-Pane Heat Flow Model 27
First Principles Applied to Model Definition
35
Common Sources of Modeling Errors
37
Exercises
38
Chapter 2
Materials and Databases
39
Materials and Database Guidelines and Considerations
39
COMSOL ® Material Library Module: Searchable
Materials Library 40
MatWeb: Searchable Materials Properties Website 43
PKS-MPD: Searchable Materials Properties Database
48
References
61
Exercises
62
Chapter 3
1D Modeling
63
1D Guidelines for New COMSOL ® Multiphysics ® Modelers
63
1D Modeling Considerations
63
Coordinate System
64
iii
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iv
C ONTENTS
1D KdV Equation: Solitons and Optical Fibers
64
COMSOL KdV Equation Model 65
First Variation on the KdV Equation Model 77
Second Variation on the KdV Equation Model 83
1D KdV Equation Models: Summary and Conclusions
90
1D Telegraph Equation 90
COMSOL 1D Telegraph Equation Model 92
First Variation on the Telegraph Equation Model 98
Second Variation on the Telegraph Equation Model
105
1D Telegraph Equation Models: Summary
and Conclusions
110
References
112
Exercises
112
Chapter 4
2D Modeling
113
2D Guidelines for New COMSOL ® Multiphysics ® Modelers
113
2D Modeling Considerations
113
Coordinate System 114
2D Electrochemical Polishing (Electropolishing) Theory
115
COMSOL 2D Electrochemical Polishing Model 118
First Variation on the 2D Electrochemical Polishing Model
130
Second Variation on the 2D Electrochemical
Polishing Model 147
2D Electrochemical Polishing Models:
Summary and Conclusions 165
2D Hall Effect Model Considerations
167
2D Hall Effect Model 171
First Variation on the 2D Hall Effect Model 186
Second Variation on the 2D Hall Effect Model 203
2D Hall Effect Models: Summary and Conclusions
221
References
222
Exercises
223
Chapter 5
2D Axisymmetric Modeling
225
2D Axisymmetric Guidelines for New COMSOL ®
Multiphysics ® Modelers 225
2D Axisymmetric Modeling Considerations
225
2D Axisymmetric Coordinate System
227
Heat Conduction Theory
228
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