The COMSOL Multiphysics User’s Guide

Comsol Multiphysics

User?s Guide

VERSION 4.3

?

COMSOL Multiphysics User��s Guide

? 1998�C2012 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 (sla) and may be used or copied only under the terms of the license agreement.

COMSOL, COMSOL Desktop, COMSOL Multiphysics, and LiveLink are registered trademarks or trademarks of COMSOL AB. Other product or brand names are trademarks or registered trademarks of their

respective holders.

Version:

May 2012

COMSOL 4.3

Contact Information

Visit contact for a searchable list of all COMSOL offices and local

representatives. From this web page, search the contacts and find a local sales

representative, go to other COMSOL websites, request information and pricing, submit

technical support queries, subscribe to the monthly eNews email newsletter, and much

more.

If you need to contact Technical Support, an online request form is located at

support/contact.

Other useful links include:

? Technical Support support

? Software updates: support/updates

? Online community: munity

? Events, conferences, and training: events

? Tutorials: products/tutorials

? Knowledge Base: support/knowledgebase

Part No. CM020002

C o n t e n t s

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

CONTENTS

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Chapter 2: The COMSOL Modeling Environment

The COMSOL Desktop Environment

Introduction

68

. . . . . . . . . . . . . . . . . . . . . . . . 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

4 | CONTENTS

The Help Window . . . . . . . . . . . . . . . . . . . . .

100

The Model Library Window

106

. . . . . . . . . . . . . . . . .

The Material Browser Window . . . . . . . . . . . . . . . .

108

The External Process Window. . . . . . . . . . . . . . . . .

108

Errors and Warnings . . . . . . . . . . . . . . . . . . . .

109

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

CONTENTS

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