1. The document describes COMSOL Multiphysics software, which is an interactive environment for modeling and solving scientific and engineering problems based on partial differential equations. 2. It can model coupled physics phenomena simultaneously using finite element analysis. It has various application modules for topics like acoustics, electromagnetics, heat transfer, fluid flow, and more. 3. An example is provided of modeling laminar fluid flow between two parallel plates to study inlet effects using the Chemical Engineering Module of COMSOL Multiphysics.

1. In The Name of Absolute PowerIn The Name of Absolute Power
& Absolute Knowledge& Absolute Knowledge

2. COMSOL MultiphisicsCOMSOL Multiphisics
Prepared by:
Mastaneh Hajipour
Supervisor:
Dr. Pishvaie
January 2010
Sharif University of Technology
Department of chemical and petroleum engineering

3. 3
COMSOL Multiphysics
COMSOL Multiphysics is a powerful interactive
environment for modeling and solving all kinds of scientific
and engineering problems based on partial differential
equations (PDEs).
With this software you can easily extend conventional
models for one type of physics into multiphysics models
that solve coupled physics phenomena - and do so
simultaneously.

4. 4
COMSOL Multiphysics
It is possible to build models by defining the physical quantities
- such as material properties, loads, constraints, sources, and
fluxes - rather than by defining the underlying equations.
You can always apply these variables, expressions, or numbers
directly to solid domains, boundaries, edges, and points
independently of the computational mesh.
COMSOL then internally compiles a set of PDEs representing
the entire model. You access the power of COMSOL through a
flexible graphical user interface, or by script programming in
the COMSOL Script language.

5. 5
COMSOL Multiphysics
PDEs form the basis for the laws of science and provide the
foundation for modeling a wide range of scientific and
engineering phenomena.
When solving the PDEs, COMSOL Multiphysics uses the
finite element method (FEM). The software runs the finite
element analysis together with adaptive meshing and error
control using a variety of numerical solvers.

6. 6
COMSOL Application
You can use COMSOL Multiphysics in many application
areas, just a few examples being:
 Chemical reactions
 Diffusion
 Fluid dynamics
 Fuel cells and electrochemistry
 Bioscience
 Acoustics
 Electromagnetics
 Geophysics

7. 7
COMSOL Application
 Heat transfer
 Microelectromechanical systems (MEMS)
 Microwave engineering
 Optics
 Photonics
 Porous media flow
 Quantum mechanics
 Radio-frequency components
 Semiconductor devices
 Structural mechanics
 Transport phenomena
 Wave propagation

8. 8
COMSOL M-file
You can build models of all types in the COMSOL user
interface. For additional flexibility, COMSOL also provides
its own scripting language, COMSOL Script, where you can
access the model as a Model M-file or a data structure.
COMSOL Multiphysics also provides a seamless interface to
MATLAB. This gives you the freedom to combine PDE-based
modeling, simulation, and analysis with other modeling
techniques. For instance, it is possible to create a model in
COMSOL and then export it to Simulink as part of a control-
system design.

9. 9
COMSOL Multiphysics
 Many real-world applications involve simultaneous couplings
in a system of PDEs - multiphysics.
 COMSOL Multiphysics offers modeling and analysis power
for many application areas. For several of the key application
areas optional modules are provided. These application-
specific modules use terminology and solution methods
specific to the particular discipline, which simplifies creating
and analyzing models. The COMSOL 3.4 product family
includes the following modules:

10. 10
The COMSOL Modules
1. AC/DC Module
2. Acoustics Module
3. Chemical Engineering Module
4. Earth Science Module
5. Heat Transfer Module
6. MEMS Module
7. RF Module
8. Structural Mechanics Module
The optional modules are optimized for specific application
areas. They offer discipline standard terminology and
interfaces, materials libraries, specialized solvers, elements,
and visualization tools.

11. 11
The AC/DC Module
The AC/DC Module provides a unique environment for
simulation of AC/DC electromagnetics in 2D and 3D. The
AC/DC Module is a powerful tool for detailed analysis of coils,
capacitors, and electrical machinery. With this module you can
run static, quasi-static, transient, and time-harmonic simulations
in an easy-to-use graphical user interface.

12. 12
The AC/DC Module
The available application modes cover the following types of
Electromagnetics field simulations:
 Electrostatics
 Conductive media DC
 Magnetostatics
 Low-frequency electromagnetics

13. 13
The Acoustics Module
The Acoustics Module provides an environment for modeling of
acoustics in fluids and solids. The module supports time-
harmonic, modal, and transient analyses for fluid pressure as
well as static, transient, eigenfrequency, and frequency-response
analyses for structures. The available application modes
include:
 Pressure acoustics
 Aeroacoustics (acoustics in an ideal gas with an irrotational
mean flow)
 Compressible irrotational flow

14. 14
The Acoustics Module
Typical application areas for the Acoustics Module include:
 Modeling of loudspeakers and microphones
 Aeroacoustics
 Underwater acoustics
 Automotive applications such as mufflers and car interiors

15. 15
The Chemical Engineering Module
The Chemical Engineering Module presents a powerful way of
modeling equipment and processes in chemical engineering.
It provides customized interfaces and formulations for
momentum, mass, and heat transport coupled with chemical
reactions for applications such as:
 Reaction engineering and design
 Heterogeneous catalysis
 Separation processes
 Fuel cells and industrial electrolysis
 Process control together with Simulink

16. 16
The Chemical Engineering Module …
COMSOL Multiphysics excels in solving systems of coupled
nonlinear PDEs that can include:
 Heat transfer
 Mass transfer through diffusion and convection
 Fluid dynamics
 Chemical reaction kinetics
 Varying material properties
The multiphysics capabilities of COMSOL can fully couple and
simultaneously model fluid flow, mass and heat transport, and
chemical reactions.

17. 17
The Chemical Engineering Module …
In fluid dynamics you can model fluid flow through porous media
or characterize flow with the Navier-Stokes equations.
It is easy to represent chemical reactions by source or sink terms
in mass and heat balances.
All formulations exist for both Cartesian and Cylindrical
coordinates (for axisymmetric models) as well as for stationary
and time-dependent cases.

18. 18
The Chemical Engineering Module …
The available application modes are:
1. Momentum balances
 Incompressible Navier-Stokes equations
 Darcy’s law
 Brinkman equations
 Non-Newtonian flow
 Nonisothermal and weakly compressible flow
 Turbulent flow, k-ε turbulence model
 Turbulent flow, k-ω turbulence model
 Multiphase flow

19. 19
The Chemical Engineering Module …
2. Energy balances
 Heat conduction
 Heat convection and conduction
3. Mass balances
 Diffusion
 Convection and diffusion
 Electrokinetic flow
 Maxwell-Stefan diffusion and convection
 Nernst-Planck transport equations

20. 20
The Earth Science Module
The Earth Science Module combines application modes for fundamental
processes and structural mechanics and electromagnetics analyses.
Available application modes are:
 Darcy’s law for hydraulic head, pressure head, and pressure
 Solute transport in saturated and variably saturated porous media
 Richards’ equation including nonlinear material properties.
 Heat transfer by conduction and convection in porous media with
one mobile fluid, one immobile fluid, and up to five solids
 Brinkman equations
 Incompressible Navier-Stokes equations

21. 21
The Heat Transfer Module
The Heat Transfer Module supports all fundamental mechanisms
of heat transfer.
Available application modes are:
 General heat transfer, including conduction, convection, and
surface-to-surface radiation
 Bioheat equation for heat transfer in biomedical systems
 Highly conductive layer for modeling of heat transfer in thin
structures.
 Nonisothermal flow appliction mode .
 Turbulent flow, k-ε turbulence model
 applications in electronics and power systems, process
industries, and manufacturing industries.

22. 22
The MEMS Module
One of the most exciting areas of technology to emerge in
recent years is MEMS (microelectromechanical systems),
where engineers design and build systems with physical
dimensions of micrometers.
These miniature devices require multiphysics design and
simulation tools because virtually all MEMS devices
involve combinations of electrical, mechanical, and fluid-
flow phenomena.

23. 23
The MEMS Module
Available application modes are:
 Plane stress
 Plane strain
 Electrokinetic flow
 Axisymmetry, stress-strain
 Piezoelectric modeling in 2D plane stress and plane strain,
axisymmetry, and 3D solids.
 3D solids
 General laminar flow

24. 24
The RF Module
The RF Module provides a unique environment for the
simulation of electromagnetic waves in 2D and 3D.
The RF Module is useful for component design in virtually all
areas where you find electromagnetic waves, such as:
 Optical fibers
 Antennas
 Waveguides and cavity resonators in microwave engineering
 Photonic waveguides
 Photonic crystals
 Active devices in photonics

25. 25
The RF Module
The available application modes cover the following types of
electromagnetics field simulations:
 In-plane wave propagation
 Axisymmetric wave propagation
 Full 3D vector wave propagation
 Full vector mode analysis in 2D and 3D

26. 26
The Structural Mechanics Module
The Structural Mechanics Module solves problems in structural
and solid mechanics, adding special element types—beam, plate,
and shell elements—for engineering simplifications.
Available application modes are:
 Plane stress/ strain
 Axisymmetry, stress-strain
 Piezoelectric modeling
 2D beams, Euler theory
 3D beams, Euler theory
 3D solids
 Shells

27. 27
The Modeling Process
The modeling process in COMSOL consists of six main steps:
1. Selecting the appropriate application mode in the Model
Navigator.
2. Drawing or importing the model geometry in the Draw
Mode.
3. Setting up the subdomain equations and boundary conditions
in the Physics Mode.
4. Meshing in the Mesh Mode.
5. Solving in the Solve Mode.
6. Postprocessing in the Postprocessing Mode.

28. 28
1. The Model Navigator
When starting COMSOL Multiphysics, you are greeted by the
Model Navigator. Here you begin the modeling process and
control all program settings. It lets you select space dimension
and application modes to begin working on a new model, open
an existing model you have already created, or open an entry in
the Model Library.
COMSOL Multiphysics provides an integrated graphical user
interface where you can build and solve models by using
predefined physics modes

29. 29
2. Creating Geometry
An important part of the modeling process is creating the
geometry. The COMSOL Multiphysics user interface contains
a set of CAD tools for geometry modeling in 1D, 2D, and 3D.
The CAD Import Module provides an interface for import of
Parasolid, SAT (ACIS), STEP, and IGES formats.
In combination with the programming tools, you can even use
images and magnetic resonance imaging (MRI) data to create a
geometry.

30. 30
Axes and Grid
In the COMSOL Multiphysics user interface you can set limits
for the model axes and adjust the grid lines. The grid and axis
settings help you get just the right view to produce a model
geometry. To change these settings, use the Axes/Grid
Settings dialog box that you open from the Options menu.
You can also set the axis limits with the zoom functions.

31. 31
Axes and Grid
The default names for coordinate systems vary with the space
dimension:
 Models that you open using the space dimensions 1D, 2D,
and 3D use the Cartesian coordinates x, y, and z.
 In 1D axisymmetric geometries the default coordinate is r,
the radial direction. The x-axis represents r.
 In 2D axisymmetric geometries the x-axis represents r, the
radial direction, and the y-axis represents z, the height
coordinate.

32. 32
3. Modeling Physics and Equations
From the Physics menu you can specify all the physics and
equations that define a model including:
 Boundary and interface conditions
 Domain equations
 Material properties
 Initial conditions

33. 33
4. Creating Mesh
When the geometry is complete and the parameters are defined,
COMSOL Multiphysics automatically meshes the geometry.
However, you can take charge of the mesh-generation process
through a set of control parameters.
For a 2D geometry the mesh generator partitions the subdomains
into triangular or quadrilateral mesh elements.
Similarly, in 3D the mesh generator partitions the subdomains
into tetrahedral, hexahedral, or prism mesh elements.

34. 34
5. Solution
Next comes the solution stage. Here COMSOL Multiphysics
comes with a suite of solvers for stationary, eigenvalue, and
time-dependent problems.
For solving linear systems, the software features both direct and
iterative solvers. A range of preconditioners are available for
the iterative solvers. COMSOL sets up solver defaults
appropriate for the chosen application mode and automatically
detects linearity and symmetry in the model.
A segregated solver provides efficient solution schemes for large
multiphysics models, turbulence modeling, and other
challenging applications.

35. 35
6. Postprocessing
For postprocessing, COMSOL provides tools for plotting and
postprocessing any model quantity or parameter:
 Surface plots
 Slice plots
 Isosurfaces
 Contour plots
 Arrow plots
 Streamline plots and particle tracing
 Cross-sectional plots
 Animations
 Data display and interpolation
 Integration on boundaries and subdomains

36. 36
Report Generator
To document your models, the COMSOL Report Generator
provides a comprehensive report of the entire model,
including graphics of the geometry, mesh, and postprocessing
quantities.
You can print the report directly or save it as an HTML file for
viewing through a web browser and further editing.

37. 37
Expression Variables
Add symbolic expression variables or expressions using the
dialog boxes that you open from the Expressions submenu on
the Options menu.
Global expressions are available globally in the model, and scalar
expressions are defined the same anywhere in the current
geometry.
With boundary expressions, subdomain expressions, point
expressions, and interior mesh boundary expressions you can
also create expressions that have different meanings in
different parts of the model.

38. 38
Expression Variables
Expression variables can make a model easier to understand by
introducing short names for complicated expressions.
Another use for expression variables is during postprocessing. If
you need to view a field variable throughout the model, but it
has different names in different domains, create an expression
variable made up of the different domains and then plot that
variable.

39. 39
Example 1: fluid flow between two parallel plates
This example models the developing flow between two parallel
plates. The purpose is to study the inlet effects in laminar flow
at moderate Reynolds numbers, in this case around 40.
The model’s input data are tabulated below.

40. 40
Step 1: The Model Navigator
Selecting the appropriate application mode in the Model
Navigator.
In the Model Navigator, click the New page.
Select:
Chemical Engineering Module>Momentum Transport>
Laminar Flow>Incompressible Navier-Stokes.

41. 41
Step 2: Creating Geometry
Drawing or importing the model geometry in the Draw Mode.
 Simultaneously press the Shift key and click the
Rectangle/Square button.
 Type the values below in the respective edit fields for the
rectangle dimensions.
 Use the Draw Point button to
place two points by clicking
at (−0.01, 0.01) and (0.01, 0.01).

42. 42
Step 3: Modeling Physics and Equations
The first step of the modeling process is to create a temporary
data base for the input data. Define the constants in the
Constants dialog box in the Option menu.
Setting up the subdomain equations and boundary conditions in
the Physics Mode.
Select Subdomain Settings, select Subdomain 1, Define the
physical properties of the fluid.

43. 43
Boundary Conditions
From the Physics menu, select Boundary Settings.
Enter boundary conditions according to the following table.

44. 44
Step 4: Mesh Generation
In this case you want to customize some settings for the initial
mesh.
1. From the Mesh menu, select Free Mesh Parameters.
2. On the Boundary page, select Boundaries 3 and 6 from the
Boundary Selection list.
3. In the Maximum element size edit field, type 1e-3. This
creates elements with a maximum edge length of 10-3
m for
Edges 3 and 6.
4. Click the Remesh button.

45. 45
Step 5 : Solve
Computing the solution,
Click the Solve button on the Main toolbar.
Step 6 : Postprocessing
The resulting plots show how the velocity profile develops
along the flow direction. At the outlet, the flow is almost a
fully developed parabolic velocity profile.

46. 46
Velocity Field Surface Plot

47. 47
Example 2: Coupled Free and Porous Media Flow
This is a model of the coupling between flow of a gas in an open
channel and in a porous catalyst attached to one of the channel
walls. The flow is described by the Navier-Stokes equation in
the free region and the Brinkman equations in the porous region.

48. 48
Step 1: The Model Navigator
Selecting the appropriate application mode in the Model
Navigator.
In the Model Navigator, click the New page.
Select:
Chemical Engineering Module>Momentum Transport>
Laminar Flow>Incompressible Navier-Stokes.

49. 49
Step 2: Creating Geometry
Drawing or importing the model geometry in the Draw Mode.
 Simultaneously press the Shift key and click the
Rectangle/Square button.
 Type the values below in the respective edit fields for the
rectangle dimensions.

50. 50
Step 3: Modeling Physics and Equations
Define the constants in the Constants dialog box in the Option
menu.
Setting up the subdomain equations and boundary conditions in
the Physics Mode.
Select Subdomain Settings, select Subdomain 1, Set ρ to rho and
η to eta.
Select Subdomain 2, select the Flow in porous media (Brinkman
equations) check box.
Set ρ to rho, η to eta, εp to epsilon, and k to k.

51. 51
Boundary Conditions
From the Physics menu, select Boundary Settings.
Enter boundary conditions according to the following table.

52. 52
Step 4: Mesh Generation
In order to resolve the velocity profile close to the interface
between the open channel and the porous domain, a finer mesh
is required at this boundary.
1. From the Mesh menu, select Free Mesh Parameters.
2. Click the Custom mesh size option button.
3. In the Maximum element size edit field, type 2e-4.
4. In the Boundary tab, Select Edge 5, then type 1e-4 in the
Maximum element size edit field.
5. Click the Remesh button.

53. 53
Step 5 : Solve
Click the Solve button on the Main toolbar.
Step 6 : Postprocessing
To visualize the velocity in a horizontal cross-section across
the channel and the porous domain, follow these steps:
1. From the Postprocessing menu, select Cross-Section Plot
Parameters.
2. Specify the following
Cross-section line data:

54. 54
Cross Section Plot of Velocity Field