COMSOLMultiphysicsUsersGuide926

VERSION 4.3
User´s Guide
Comsol Multiphysics®

Contact Information
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Part No. CM020002
COMSOL Multiphysics User’s Guide
 1998–2012 COMSOL
Protected by U.S. Patents 7,519,518; 7,596,474; and 7,623,991. Patents pending.
This Documentation and the Programs described herein are furnished under the COMSOL Software License
Agreement (www.comsol.com/sla) and may be used or copied only under the terms of the license agree-
ment.
COMSOL, COMSOL Desktop, COMSOL Multiphysics, and LiveLink are registered trademarks or trade-
marks of COMSOL AB. Other product or brand names are trademarks or registered trademarks of their
respective holders.
Version: May 2012 COMSOL 4.3

CONTENTS | 3
Contents
Chapter 1: Introduction
About COMSOL Multiphysics 34
The COMSOL Modules 37
AC/DC Module . . . . . . . . . . . . . . . . . . . . . . . 38
Acoustics Module . . . . . . . . . . . . . . . . . . . . . . 39
Batteries & Fuel Cells Module . . . . . . . . . . . . . . . . . . 40
CFD Module . . . . . . . . . . . . . . . . . . . . . . . . 41
Chemical Reaction Engineering Module . . . . . . . . . . . . . . 42
Corrosion Module . . . . . . . . . . . . . . . . . . . . . . 43
Geomechanics Module. . . . . . . . . . . . . . . . . . . . . 44
Heat Transfer Module . . . . . . . . . . . . . . . . . . . . . 45
MEMS Module . . . . . . . . . . . . . . . . . . . . . . . . 45
Microfluidics Module . . . . . . . . . . . . . . . . . . . . . 46
Nonlinear Structural Materials Module . . . . . . . . . . . . . . 47
Optimization Module . . . . . . . . . . . . . . . . . . . . . 47
Particle Tracing Module . . . . . . . . . . . . . . . . . . . . 48
Pipe Flow Module . . . . . . . . . . . . . . . . . . . . . . 49
Plasma Module. . . . . . . . . . . . . . . . . . . . . . . . 51
RF Module . . . . . . . . . . . . . . . . . . . . . . . . . 52
Structural Mechanics Module . . . . . . . . . . . . . . . . . . 53
Subsurface Flow Module . . . . . . . . . . . . . . . . . . . . 54
CAD Import and LiveLink Connections . . . . . . . . . . . . . . 55
LiveLink for MATLAB . . . . . . . . . . . . . . . . . . . . . 56
Overview of the User’s Guide 57
The COMSOL Documentation Set 61
Where Do I Access the Documentation and Model Library? . . . . . . 62
Checking for Software Updates . . . . . . . . . . . . . . . . . 63
Typographical Conventions . . . . . . . . . . . . . . . . . . . 64

4 | CONTENTS
Chapter 2: The COMSOL Modeling Environment
The COMSOL Desktop Environment 68
Introduction . . . . . . . . . . . . . . . . . . . . . . . . 68
Changing the COMSOL Desktop Layout . . . . . . . . . . . . . . 69
Moving Between Windows and Sections on the COMSOL Desktop . . . 70
Changing the COMSOL Desktop Language . . . . . . . . . . . . . 71
Printing from the COMSOL Desktop . . . . . . . . . . . . . . . 72
The Main Menu and Toolbar . . . . . . . . . . . . . . . . . . 73
Introduction to the Model Wizard and the Model Builder 76
The Model Wizard . . . . . . . . . . . . . . . . . . . . . . 76
Basic Steps to Build a Model . . . . . . . . . . . . . . . . . . 79
The Model Builder Window . . . . . . . . . . . . . . . . . . 80
About Sequencing in COMSOL Multiphysics . . . . . . . . . . . . 84
Opening a Context Menu to Add Nodes . . . . . . . . . . . . . . 85
Moving Nodes in the Model Tree. . . . . . . . . . . . . . . . . 87
Going to the Source Node . . . . . . . . . . . . . . . . . . . 88
Copying, Pasting, and Duplicating Nodes . . . . . . . . . . . . . . 88
Expanding and Collapsing All Nodes . . . . . . . . . . . . . . . 90
Undoing and Redoing Operations . . . . . . . . . . . . . . . . 90
Clearing All Meshes and Clearing all Solutions . . . . . . . . . . . . 90
Sorting Nodes by Space Dimension and Type . . . . . . . . . . . . 91
Introduction to the COMSOL Windows 95
The Node Settings Windows . . . . . . . . . . . . . . . . . . 95
The Graphics Window . . . . . . . . . . . . . . . . . . . . 96
Plot Windows . . . . . . . . . . . . . . . . . . . . . . . . 97
The Messages Window . . . . . . . . . . . . . . . . . . . . 97
The Progress Window. . . . . . . . . . . . . . . . . . . . . 98
The Log Window. . . . . . . . . . . . . . . . . . . . . . . 98
The Results Window . . . . . . . . . . . . . . . . . . . . . 99
The Help Window . . . . . . . . . . . . . . . . . . . . . 100
The Model Library Window . . . . . . . . . . . . . . . . . 106
The Material Browser Window . . . . . . . . . . . . . . . . 108
The External Process Window. . . . . . . . . . . . . . . . . 108
Errors and Warnings . . . . . . . . . . . . . . . . . . . . 109

CONTENTS | 5
The About COMSOL Multiphysics Box . . . . . . . . . . . . . 110
Keyboard Shortcuts 111
Key to the Nodes and Toolbar Buttons 113
Chapter 3: Global and Local Definitions
About Global and Local Definitions 120
Global Definitions . . . . . . . . . . . . . . . . . . . . . 120
Local Definitions . . . . . . . . . . . . . . . . . . . . . . 121
Load Group. . . . . . . . . . . . . . . . . . . . . . . . 122
Constraint Group . . . . . . . . . . . . . . . . . . . . . 123
About Building Expressions . . . . . . . . . . . . . . . . . . 123
Operators, Functions, and Variables Reference 125
Unary and Binary Operators . . . . . . . . . . . . . . . . . 126
Special Operators . . . . . . . . . . . . . . . . . . . . . 126
Mathematical Functions . . . . . . . . . . . . . . . . . . . 141
Physical Constants . . . . . . . . . . . . . . . . . . . . . 143
Reference . . . . . . . . . . . . . . . . . . . . . . . . 144
Global Parameters 145
About the Global Parameters . . . . . . . . . . . . . . . . . 145
Defining, Saving, or Importing Global Parameters. . . . . . . . . . 145
Loading Parameters from a Text File . . . . . . . . . . . . . . 146
Variables 147
About Global and Local Variables . . . . . . . . . . . . . . . 147
Predefined Physics Interface Variables . . . . . . . . . . . . . . 149
Variable Naming Convention and Scope . . . . . . . . . . . . . 150
Variable Classification and Geometric Scope . . . . . . . . . . . 151
Specifying Varying Coefficients and Material Properties . . . . . . . 152
Variables for Time, Frequency, and Eigenvalues . . . . . . . . . . 153
Geometric Variables . . . . . . . . . . . . . . . . . . . . 155
Shape Function Variables . . . . . . . . . . . . . . . . . . . 160