Comsol Handbook Series

COMSOL HANDBOOK SERIES
CUT POINTS AND EVALUATIONS
Essentials of Postprocessing
and Visualization in
COMSOL Multiphysics®
ESSENTIALS OF POSTPROCESSING AND VISUALIZATION IN COMSOL MULTIPHYSICS 2

Essentials of Postprocessing and Visualization in
COMSOL Multiphysics
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© November 2014.
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Further Resources
Further writing and tutorials on postprocessing in COMSOL are
available here:
VIDEOS
www.comsol.com/search/?s=postprocessing&subset=video
BLOG ARTICLES
www.comsol.com/search/?s=postprocessing&subset=blog
DISCUSSION FORUM
www.comsol.com/community/forums/results-and-visualization/
SUPPORT KNOWLEDGE BASE

www.comsol.com/support/knowledgebase/
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TABLE OF CONTENTS
INTRODUCTION 1
DATA SETS, DERIVED VALUES, AND TABLES
▪ Solutions 2
▪ Cut Points and Evaluations 3
▪ Tables 6
PLOT TYPES
▪ Choosing a Plot Type 8
▪ 3D Plots 8
▪ 2D Plots 15
▪ 1D Plots 21
USING POSTPROCESSING FOR RESULTS INTERPRETATION 24
EXPORTING RESULTS
▪ Data, Tables, and Mesh 25
▪ Reports 27
TIPS & TRICKS
▪ Shortcuts 28
▪ Rearranging the COMSOL Desktop 28
▪ Showing Meshes on Surface Plots 29
▪ Sliding and Interactive Positioning 30
CONCLUDING REMARKS 31
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INTRODUC TION
INTRODUCTION
The orientation, coloring, and arrangement of
an object created using computer modeling can
offer perspective on the geometry, function,
and success of a product. Visualization is an
incredibly important part of the engineering
process. Visually displaying the physics in a
simulation gives an explanation of what’s really
happening inside a device or design: heat
transfer takes on colors that help us understand
its distribution, points of structural failure
become visible and obvious, and the paths fluids
travel are suddenly traceable.
The postprocessing and visualization tools in

the COMSOL Multiphysics® software are a great
asset for helping you understand your results,
see what’s happening in your product, and
explain your work to colleagues, collaborators,
and customers. The demonstrations in this
guide will allow you to more easily identify
physics phenomena, opening up a visual avenue
for you to share your findings, communicate
your design ideas, and demonstrate limits and
challenges. As simulation is especially helpful
for verifying a design prior to prototyping, these
techniques also offer a way to quickly see how
changes to the dimensions, materials, or other
parameters will affect the quality of your device.
We have put together this material based on

requests from COMSOL® software users, many
of whom wish to use the postprocessing and
graphics tools in COMSOL more effectively.
Our goal is to offer techniques that will meet
your needs, enable and inspire you to discover
new ways of demonstrating your product’s
capabilities, and aid you in exploring the
incredible world of physics happening on, or
under, the surface of your work.
HELMHOLTZ COIL
Simulation of a parallel pair of identical circular
coils spaced one radius apart and wound so that
the current flows through both coils in the same
direction. Results show the uniform magnetic field
between the coils with the primary component
parallel to the axes of the two coils.

SOLUTIONS
DATA SETS, DERIVED VALUES, AND TABLES

Paradoxically, although we will explore in detail Open the COMSOL Multiphysics® software,
the techniques used to create visual results in go to Model Libraries, and open the stresses
the COMSOL® software, we must start with in pulley model from File > Model Libraries >
the numbers—the data needed to do so. This COMSOL Multiphysics > Structural Mechanics.
chapter will outline the data sets, derived values,
and tables that results plots draw from. The Results node for the solved model is shown
in Figure 3.
SOLUTIONS
Solutions are data sets that are stored by the
solvers. They rely on information such as
which solver is selected, which component the
solution applies to (for models with multiple
components), and the timestep or other variable
for which a solution is shown. Every solved
model will contain at least one solution.
To demonstrate the use of data sets, derived

values, and tables, let’s take a look at a model that
shows the stress distribution in a driving pulley: Solutions 1 and 2 have already been created.
They are different result sets from the same
study; Solution 2 includes an Adaptive Mesh
HINT
Refinement step, which refines the mesh
in certain areas of the model where greater
As we’ll see later, duplicating accuracy is needed. If we examine the first two
solutions is a very useful plot groups in the Results node (named “Stress
way to easily switch between (solid)” and “2D Plot Group 2,” respectively), we
views in a plot, for example, will see that they draw on data from Solution 1
to show results at different or Solution 2.
times or in different
locations. (This duplicates
only a view of the solution
and not the underlying data
in the numerical solvers,
and so does not increase
memory usage.)
Each of these plots shows the stress in the pulley

The solution to this model is found using a for a specific rpm, which is set in the Parameter
kinetostatic analysis, where the pulley is “frozen” value (n) field. You can also change the data set
at a moment in time and the center is assumed to Solution 2, and click Plot to see how the mesh
fixed. We can examine the stress distribution refinement affects the results.
and deformation for different rotational speeds
(the variable n represents the rpm).
2 COMSOL HANDBOOK SERIES

Go to the Cut Point 2D 1 node and click Plot.

The cut point will appear in the Graphics
CUT LINES & CUT PLANES
window at the top right corner of the pulley
cross-section, along the edge of one of the Cut points are used for
openings (only one quadrant is shown): evaluating variables at a
specific location; likewise,
cut lines can be used to
evaluate variables and
Let’s take a look at some of the other data sets in visualize results along a
this model. designated line. Cut planes
can be created to visualize
cross-sectional surface plots
CUT POINTS AND EVALUATIONS in three dimensions.
CUT POINTS
Cut points are points created in a solution that
do not affect the geometry of a model. They
create data sets that can be used for evaluating We’ll use this point later to create some new
variables at the exact location of the cut point. In plots. For now, take a look at 1D Plot Group 3 in
this model, we can plot the stress at a point for the Results node.
different rotational speeds (rpm), for example, to
see how the rpm affects the stress. The selected Data Set is Cut Point 2D 1, and the
results show how the stress changes with the
A cut point may be placed anywhere in a model rpm at coordinates (19, 54), with the location in
geometry. The coordinates of the cut point can millimeters:
be adjusted in the settings section.
In this model, the point (0,0) is at the center of

the pulley.
NOTES
All the models used in this guide are available in the Model Libraries for
COMSOL® software users. If you are not currently using COMSOL, contact
us at www.comsol.com/contact. You can find more information about the
HINT physics capabilities of COMSOL at www.comsol.com/products.
One useful feature of cut points is the “Snap to closest This guide assumes that you have updated the COMSOL Model Libraries.
boundary” capability—selecting this checkbox will move This can be done from File > Help > Update COMSOL Model Library. Then
the cut point to the boundary closest to your selected click Find Models and, if you’re looking for a specific model, click Uncheck
coordinates, which is very helpful if you want to create a all on the next screen. Navigate to the model that you’re looking for (in this
cut point right on the edge of the geometry. case, it would be COMSOL Multiphysics > Structural Mechanics > Stresses in
Pulley) and click Download.

DERIVED VALUES We can also add multiple variables to this table.

We’ve taken a look at all of the data sets that Change the expression to solid.mises (von
currently exist in the model. In this section, we Mises stress) by typing it in or clicking Replace
will discuss maxima and minima, integrals, and Expression and choosing Solid Mechanics >
point and global evaluations. These calculations Stress > von Mises stress (solid.mises). Change the
can be used to manipulate data for results plots. units to MPa and click Evaluate again.
Right-click Derived Values under the Results Table 1 will now show different values for the
node to see a list of values that can be calculated. maximum displacement and stress at each rpm.
Let’s find the maximum stress on the surface of
the cross section.
This allows us to evaluate the maximum of a

chosen variable over a surface domain. In the
MORE DERIVED VALUES Surface Maximum settings window, we’ll choose Voilà! We’ve got our data.
Solution 2 for the Data Set (this is the more
Other maxima and
refined of the two studies). Set the selection to
minima can be evaluated POINT EVALUATIONS
Domain 1 by clicking on the cross-section of the Now let’s create a Point Evaluation. Point
for a chosen variable along
pulley in the Graphics window. evaluations are used to evaluate a variable or
a line or over a volume.
Averages and integrals expression at a specific chosen point (in contrast
In the Expression section, check that the default to the maximum we just found, which was over
can be evaluated similarly,
expression is solid.disp (displacement) and the a whole domain). They can also be evaluated
available in the selection
unit is m (meters). Click Evaluate at the top over multiple points, for example, to explore the
list that appears when you
of the settings window. This will create a table deformation (or other effect) at several locations
right-click the Derived
with two columns, showing the maximum total in a model.
Values node.
displacement for each rpm value.
Right-click Derived Values and choose Point
Evaluation.

In the geometry shown in the Graphics window, GLOBAL EVALUATIONS

a set of points will appear on the pulley cross- Because the pulley will warp and deform slightly
as it spins, the diameter is not actually constant. VARIABLES
section. These are points that are drawn in the
model geometry. One or more of them must What if want to measure the diameter as it
It’s not necessary to keep the
be selected for the point evaluation (we can’t changes with rotational speed?
variable R in the function,
choose a point just anywhere, as in the case of a but in this case we did so
cut point). We’ll create a variable that describes the
in order to describe the
deformation of the cross-section by measuring
diameter. The variable
the change in distance between two points
expression
at different rpms. For this, we'll use a global
intop1(u) – intop2(u) would
evaluation.
also work, but would give us
the change between any two
First, create two integration nodes. We’re going
points.
to evaluate an integral over a point, which gives
the value of a function (which we’ll define) at that
point.
Expand Component 1 and the Definitions node.

Right-click Definitions and choose Component
Couplings > Integration. Do this twice.
Choose the points you want to select by clicking

on them in the Graphics window. Let’s choose
the two points on either side of the central hole,
left and right of (0,0).
Their names are added to the selection list when

you click on them (36 and 55). Change the
expression to solid.mises and the units to MPa.
Click Evaluate.
Click on the Integration 1 node. The Graphics
window now shows all points in the pulley
geometry, as it did when we created a Point
Evaluation earlier. For this evaluation, we’ll
again choose the points farthest from the center
to the left and right.
Under Geometric entity level, select Point. Click

on the far-right point (point 90) to select it.
Go to the Integration 2 node, again set the

geometric entity level to Point, and this time
select the far-left point (point 1).
Now we need to create the variable that we want

to measure. Right-click the Definitions node
again and choose Variables. In the Variables
We have now created Table 2, which shows the table, enter diam for the name and
stress at both points for each rpm. intop1(R+u)-intop2(-R+u) for the expression.

TABLES
The variable we just created measures the • The maximum stress and displacement
diameter at a given rpm. Note that we’ve used R in the cross section for different speeds.
and -R to account for both directions (left and • The table showing the change in
right of zero). distance between two points, created
using the global evaluation.
Now right-click Study 1 and choose Update
Solution. Because this model has already been Let’s take a quick look at the shortcuts that are
solved, we need to update the results. available for tables.
But rather than needing to compute
the study all over again, COMSOL
lets you add this component coupling,
then adjust the existing solution to
account for it. (This especially comes
in handy if you’ve forgotten to create
variables and couplings until after you
have already solved the simulation.)
Now let’s go back to the Results

node. Right-click Derived Values
and choose Global Evaluation. In the
Expression field, enter diam-2*R. This
represents the difference between the
original diameter (2*R) and the new variable
we just created, giving us the deformation in At the top of any table window underneath the
meters. title, you’ll see the following display of icons.
Click Evaluate. Table 3 will appear, showing the Several of these buttons are self-explanatory.
deformation. The first few entries (for n less Here’s a rundown of the others:
than 2500) will be negative, indicating that the
diameter has decreased. At n=2500, the results • Settings: opens the table settings
will become positive and grow increasingly large window in the center column.
as the rpm increases. • Full Precision: displays the complete
values in the table (to all decimal places).
We’ve completed our global evaluation.
• Table Graph: creates a graph plot using
the data from the table (read more about
TABLES this below). Similarly, the Table Surface
button creates a surface plot using data
HINT Almost done! We’ve seen how to gather and from the table.
organize data from the solvers in several
You can also import tables different ways. Let’s wrap up with a few • Export: exports the table data to a text
from data files by right- comments on using tables effectively. file (.txt).
clicking the Tables node • Display: displays the next table under
under Results, choosing You’ve probably noticed by now that the the Tables node. Clicking the arrow will
Table, and then using the evaluations we performed automatically show a list of all the tables created so far,
import function available generated tables. Tables store information from allowing you to switch between them.
in the settings window to data sets and derived values. Here’s a summary
upload a text or data file. of the tables we created in the pulley model:
This is particularly useful
for comparing results • The results from Cut Point 2D 1, where
from a simulation with we plotted the stress at (19, 54) over
experimental data. different rpms.

TABLES
A final note: tables are very useful for checking

the results at a certain time or parameter value,
for instance to see how a solution changes from
its initial value to its final. We can also use data
from a table in a results plot. As an example,
we’ll use the global evaluation we created at the
end of the last section.
Right-click Results and choose 1D Plot Group.

Right click the new node, 1D Plot Group 6, and
choose Table Graph. (You can also do this by
clicking the Table Graph icon from the table
window.) From the Table selection list, choose
Table 3 and click Plot.
Results show the table and graph indicating how

the deformation increases with higher rpms.

CHOOSING A PLOT T YPE
PLOT TYPES
So we have data, and we have learned a few ways
to use and manipulate it. Now let’s move on to
the fun part: visualizing results.
CHOOSING A PLOT TYPE

The COMSOL® software is so flexible that you
can, for instance, create a 3D plot from a 2D
model. Such extrusions are a very powerful tool
for getting a closer look at the physics in your
device. But when would you do this? For what
applications would you want to? Sometimes the The model analyzes thermal conduction,
best plot type for visualizing your results will be convection, and the temperature field across the
counterintuitive. Before we shed some light on surfaces.
this, we’ll cover the basics of creating plots; later,
we’ll move on to the fancier stuff. You can find the temperature plot by expanding
the Results node and clicking on the Temperature
We’ll start with the most realistic plot type, (nitf) plot group. But since we’re going to recreate
since this is how you would visualize an object it, go ahead and delete it (right-click and choose
in real life: 3D. Since reducing the dimension is Delete). Let’s also delete the Velocity (nitf) plot
intuitive—2D and 1D plots are often created by group, since we’ll recreate it later.
slicing cross-sections of 3D plots—we’ll examine
most plot techniques using a 3D model. Another piece of the puzzle that we’ll delete
and re-create is the view. The final results show
a limited geometry—part of the rectangular
3D PLOTS channel is hidden. Hiding entities like this is a
very helpful trick for visualizing physics inside
Let’s take the example of an aluminum heat
of a model, as we will see.
sink used for cooling components in electrical
circuits. If you have the Heat Transfer Module or
For now, let’s restore the view to show the
the CFD Module, this model can be found in the
whole geometry so that we can explore hiding
Model Libraries under File > Model Libraries >
components. Expand Component 1 > Definitions
Heat Transfer Module > Tutorial Models, Forced
> View 1 and delete the Hide Geometric Entities
and Natural Convection or under File > Model
1 node.
Libraries > CFD Module > Non-Isothermal Flow.
The model documentation, including steps to
SURFACE PLOTS
build the simulation, is also available there.
The first plot we’ll create on the heat sink
geometry is a surface plot to show the
One reason this model is a good example is that
temperature changing in the channel. Right-click
there’s plenty of physics going on here! This
the Results node and choose 3D Plot Group.
model studies fluid flow and heat transfer. The
Right-click the new node and choose Surface.
heat sink, made of aluminum with a cluster of
pillars for cooling, is mounted on a plate of silica
The expression we want (temperature) is already
glass. It sits inside a rectangular channel with an
in the field. If we needed to add it, however, we
inlet and an outlet for air flow. Initially, the base
could find it by clicking Replace Expression and
of the heat sink experiences 1 watt of heat flux,
choosing Conjugate Heat Transfer (Heat Transfer
generated by an external heat source.
in Solids) > Temperature (T).

3D PLOTS
If you don’t remember the location of the expression

you need, search for it by typing a keyword into the
HINT
field at the top of the expression window:
Another way to reach the
view node that applies to a
particular plot group is to
select the plot group (such
as 3D Plot Group 1) and
check the Plot Settings tab.
In the View field, you can
change which view applies
That looks a little better! However, we still to the plot group, or navigate
can’t see what’s going on inside the channel. directly to the view by
Remember when we deleted the Hide Geometric clicking the button next to
Entities node from View 1? Let’s go back there the drop-down list.
for a minute.
INVISIBILITY CLOAKS: HIDING ENTITIES

In some cases, it’s very helpful to be able to hide
certain parts of a geometry to get a good look
at what’s going on inside—especially with a
Click Plot. We now have a surface that, quite
complex model geometry that has an air domain
frankly, looks nothing like the final results that
around it, like the heat sink! Much of the time,
we’re aiming for! But we’ll adjust our view and
you won’t want to see the air box when you
plot settings until we’ve reached a look we like.
set up your results. At other times, you may
One reason the box looks so different from the
want a view that exposes the inside of a device,
results shown earlier is that the default color
hidden underneath several other geometric
scheme is set to Rainbow.
components. The trick we’re about to use
frequently comes in handy in postprocessing.
Back in the View 1 node, right-click the node

and choose Hide Geometric Entities. In the
settings window under Geometric entity level,
choose Boundary. (You can also hide points,
edges, and domains.)
ENTITIES VS. OBJECTS
In the Surface settings window, we can change There is also an option to Hide Geometric Objects, which hides objects created by a
this under the Coloring and Style tab. Using geometry feature. Hiding geometry objects only applies in certain nodes, such as the
the drop-down list, change the color table from View and Definitions nodes. Actions that hide geometric objects are not reflected
Rainbow to ThermalLight. in the Materials, Physics, Mesh and Results nodes, so Hide Geometric Entities is a
better option when you are not working in the Geometry branch of the model tree.
Now select the three faces of the channel that

block the view of the heat sink (boundaries 1,
2, and 4). They turn red when the mouse hovers
over them, and purple when selected (click to
select).

3D PLOTS
Also select boundary 121, the channel inlet. This

can be done by rotating the heat sink until the
face is visible, or by holding the mouse over the
area and scrolling until you see the edges of the
face turn red. Then click to select it.
For a simple geometry like this, it is easy enough

to rotate the model and select the face on the
other side. But for complicated geometries, or
faces that are covered by other faces and not
accessible from the outside of the model, the
scroll wheel (or the arrow keys, if your mouse
doesn’t have a scroll wheel) provides a much easier
way to cycle through the entities. This is also very
useful if you have carefully arranged a view and
you don’t want to reposition your model.
You can define your selection and give it a name.

It will appear as a new node in the Definitions:
Under the Results node, the new group will

appear as an option when creating selections of
the same entity type, so that you don’t need to
re-select the entities.
Go back to 3D Plot Group 1. We can see the

inside of the channel now. Let’s get rid of some
of those lines, though. Under the Plot Settings
tab, uncheck the Plot data set edges box and
click Plot. Now we see just the surface and the
geometry, without the lines.
For models where you will select the same set

of features several times, or where you need to
carefully select many entities, use the Create
Selection button next to the selection list.

3D PLOTS
LINE PLOTS These results were created using a Cut Line 3D

Although we just unplotted the data set edges solution.
in the heat sink, one plot type that we can add
to show results is a line plot. Line plots are used ARROW PLOTS
to display quantities on edges; the following line The next plot that we’ll add is an arrow plot.
plot shows the temperature on the edges of the Right-click 3D Plot Group 1 and choose Arrow
heat sink domain: Volume. This creates a plot of arrows that show
the velocity vector field of the airflow through
the channel and around the heat sink. The
length of the arrows indicates how fast the air is
moving—fastest above the heat sink and high up
in the channel, and slower around the floor of
the channel and the base of the heat sink.
Line plots can also be used to show results

at multiple locations in a model. Under the
Coloring and Style tab in the settings for a line
plot, the style can be set to line or to tube, with a
manually-adjustable radius.
The results below show a plot running along the

center of the heat sink channel, depicting the air
flow velocity between the inlet and the outlet: Your initial arrow plot won’t look like this, though;
to create the above image, you would need to add
more arrows, and would have to scale them down
so that the geometry underneath is visible.
Take a look at the Arrow Positioning tab. There

are listings for x-grid points, y-grid points, and
z-grid points. This means that we can change
how many arrow entries are shown along the
x-axis, along the y-axis, and along the z-axis.
The ideal number of arrows will normally
USING DEFORMATIONS
depend on the application, but for now, change
the x-grid points to 8, the y-grid to 4, and the The line plot shown here
z-grid to 4. (For a real graphic you would of includes a deformation
course want more arrows so that you can see the and a radius expression.
flow field, but for learning purposes it will be For an example of using
helpful to make everything large.) deformations, turn to page 18.

3D PLOTS
We can change the arrow size by changing the scale as arrows on planar surfaces or arrows on lines,
factor under the Coloring and Style tab. Check the respectively. The figure below shows arrow
Scale factor box and increase the scale factor to 0.05 lines (along with a regular line plot, deformed)
(again, this is much larger than you would use if plotted on a cut line solution.
you were trying to really visualize the physics).
Now our plot is looking pretty good. Let’s add CONTOUR PLOTS
a color range to the arrow plot so that what’s Let’s add a contour plot on the back wall of the
happening to the velocity is a little clearer. channel. Contour plots are helpful for telling
immediately if a device is approaching its limits
Right-click Arrow Volume 1 and choose Color or is in danger of failure (for instance, showing
Expression. Click Replace Expression, choose the exact temperature during a phase transition
Conjugate Heat Transfer (Laminar Flow) > or indicating that a mechanical structure is
Velocity magnitude (nitf.U), and then click Plot. approaching its yield stress level).
If you remember, we mentioned duplicating

solutions earlier. To create a contour plot, we’ll
need to add a new solution so that the contours
don’t appear everywhere in the model.
Expand the Data Sets node, right-click Solution

1, and choose Duplicate. A new solution (Solution
2) will appear in the Data Sets list. Right-click
Solution 2 and choose Add Selection.
Now our arrow plot shows the changing velocity
of the air flow as it enters and exits the channel. This feature is similar to hiding geometric
Check the Color legend box under the Coloring entities, which we did in the View node earlier
and Style tab to see a reference for the fastest so that we could see inside the model. Selections
and slowest flow regions (red being the fastest, in a solution allow you to choose which areas
blue the slowest). of the model you want to see, meaning that
anything unselected will not be used for plotting
This example showed an arrow volume plot. In results when the solution is used as the data set.
a similar fashion, arrow surface and arrow line
plots can be used to visualize vector quantities Set the geometric entity level to Boundary, and
select only the back wall of the channel.
HINT
In a case where we only want to see one layer of arrows in the z-direction, it’s
sometimes more helpful to change the entry method. Instead of Number of
points, change this to Coordinates. This allows you to limit the points used
in the z-direction to only one point and specify its location on the z-axis. For
example, try entering 5[mm] in the coordinates field and see what happens.

3D PLOTS
Now right-click 3D Plot Group 1 and choose Keep in mind that for this plot, we have two plots
Contour. This will add a contour plot. Make sure overlapping (the original surface and the contours).
to choose Solution 2 for the data set in the plot In this case, they don’t interfere with each other
settings. because they have the same color scheme; however,
in other cases this can be a problem. (See if you can
Change the expression to T (type it into the manipulate your results so that the surface plot no
field). Click Plot. Now we have a contour plot longer contains the back wall.)
showing the wall temperature changing over the
distance of the channel. It’s a little easier to see what’s going on now;
the contour layers show the evolution of the
temperature gradient on the back wall, which
is at its hottest right next to the heat sink. The HINT
contours are very smooth already (try refining
your mesh to get the smoothest results), but let’s Try clicking anywhere
add the lines back in so that we can get a really on the surface to see a
clear idea of what the temperature gradient is. table with values showing
the temperature data at
Duplicate the contour surface you just created, the positions clicked.
and set it to display lines instead of filled levels. Alternatively, check the
Play around with the colors and settings to Level labels box in the
Instead of lines, we can also blend the contours create an image similar to the following: contour plot settings under
so that the space between each level is filled in. the Coloring and Style
Check out the options available in the Levels tab tab to see data for each
and the Coloring and Style tab in the Contour contour level.
settings window:
See if you can create this plot using your new

knowledge of hidden entities and using multiple
surfaces:
Change the contour type from Lines to Filled,

as shown, and disable the arrow plot by right-
clicking its node and choosing Disable. Here’s
what we get:
DIFFERING VISUALS
Your results may not look exactly like the images shown here, since we
obtained these results using a refined mesh and a high-power computer.
We’ve also added a line plot to show some of the data set edges.

3D PLOTS
SLICE PLOTS Reset your temperature plot so that it contains

We’ve added surface, arrow, and contour plots. only the surface showing the overall temperature
Now it’s time for something a little different. with the heat sink and channel in the same
plot, without the contours. Now right-click the
The velocity plot that we deleted earlier node and choose Streamline. For the expression,
contained what is called a slice plot. Slice choose Replace Expression > Conjugate Heat
plots show cross-sectional surfaces used for Transfer (Heat Transfer in Solids) > Velocity field
visualizing the change in a variable over a (nitf.ux, nitf.uy, nitf.uz).
distance. For instance, for this model we
might add a slice plot to show the temperature Under the Streamline Positioning tab, change
changing as the slices move farther and farther the positioning to Magnitude controlled. Under
from the heat sink, or the velocity of the air as it the Coloring and Style tab, change the line type
flows through the channel. to Ribbon. Click Plot, and you’ll see a series of
lines showing the velocity vector field of the air
Let’s create a velocity slice plot. Rather than flowing past the heat sink. Go ahead and change
adding this into the plots we just finished, we’ll the ribbon width and positioning distances until
start a new plot group to avoid crowding up the you’re happy with the streamline arrangement.
visual. Right-click the Results node and add a
new 3D plot group. Right-click the new node Our first attempt is a little hard on the eyes—
and choose Slice. everything is red. Right-click the Streamline 1
node and add a color expression. In addition
Temperature is automatically chosen for the plot to making the plot more visually appealing, the
expression. If we plot it, we’ll see a series of slice color will now represent the velocity magnitude.
plots showing the initial temperature at the inlet Navigate to Replace Expression > Conjugate Heat
as comparatively low, increasing near the heat Transfer (Laminar Flow) and choose Velocity
sink, and decreasing again near the outlet. magnitude (nitf.U). Click Plot.
Let’s plot the velocity magnitude instead, as we

did with the arrow plots. The expression we
want is Conjugate Heat Transfer (Laminar Flow)
> Velocity magnitude (nitf.U).
SLICE POSITIONING
Now we have a slice plot showing the fluid
The slice plots shown here
velocity for different cross-sections of the air
use yz-planes that shift in
inside the channel.
the x-direction. However,
you can change these by
changing the settings under
the Plane Data tab. Try
ISOSURFACES
creating this plot using the
plane positioning tools: Isosurface plots show results quantities as a
set of colored surfaces on which the result is
constant. They might be used to show scalar
fields such as temperature, chemical species
concentration, electric potential, or pressure.
Let’s take a look at an example where we want
to know the acoustic pressure levels inside a
STREAMLINES speaker.
Streamline plots depict vector quantities
For more tips about
by showing curves that flow tangent to an If you have the Acoustics Module installed, open
positioning slice plots, turn
instantaneous vector field. They are often used the COMSOL Model Libraries and navigate to
to page 36 in the Tips and
to show fluid movement. For the heat sink Acoustics Module > Industrial Models > Vented
Tricks section.
model, for instance, we might add streamlines to Loudspeaker Enclosure to follow along.
visualize the air flow through the channel.

2D PLOTS
This model studies how the sensitivity of a 2D PLOTS

loudspeaker driver is affected by its enclosure.
The speaker driver is set in a vented enclosure Now, for a change of pace, let’s explore a few plot
and contains a magnet, voice coil, cone, and types in 2D. All of the plot types we showed on
other hardware components. The simulated air the 3D heat sink model can be used in 2D, and
domain is surrounded by a spherical perfectly the plots we’ll show here can also be used in 3D.
matched layer (PML) that absorbs outgoing
waves, minimizing reflections in order to The model we’ll use for this demonstration
model an infinite domain. The model solves is a pyramidal absorber used for microwave
for the sound pressure distributions at different absorption in an anechoic chamber. If you have
frequencies, local stresses and strains in moving the RF Module installed, this model is under File >
parts, and deformations in the structures. Model Libraries > RF Module > Passive Devices.
Under the Results node, click on the plot group

named Acoustic Pressure. It contains, among ANECHOIC CHAMBERS
other plots, an isosurface node.
An anechoic chamber is designed to absorb noise or electromagnetic waves and
is insulated from external sources of such waves. The walls are lined with an
absorbent material that is arranged and shaped to absorb as much radiation (in
this case) from as many directions as possible. Anechoic chambers are often used
for testing radar devices, antennas, or electromagnetic interference.
The pyramidal absorber is actually a 3D model,

but we’ll create some useful 2D plots for
visualization purposes. The geometry includes
one pyramidal unit cell surrounded by:
• A rectangular air domain

• Perfectly matched layers (PML) at
the top of the air domain, creating a
boundary that avoids internal reflections
back into the simulation domain
• A perfect electric conductor (PEC)
layer below the pyramid block,
representing a conductive coating on
the wall of the chamber
Your isosurface plot may look slightly different

than the one shown here, since the color range
has been modified.
These isosurfaces show constant pressure

surfaces inside the enclosure and outside of
the speaker cone. We can see the sound waves
moving outward from the speaker.

2D PLOTS
CUT PLANES Like a secret shortcut, this button is a doorway

Creating surface, arrow, and contour plots in to exactly what we need. The lines created by
2D works the same way as in 3D. However, if we a cut plane intersecting with the geometry are
start with a 3D geometry and want to create a displayed in green.
2D plot, we need a planar face to plot on. We’ll
create one by defining a cut plane—similar to We’ll orient the plane using the settings for this
the cut point we used in the pulley model. A cut new data set, Cut Plane 1, now found under the
plane creates a plane from a cross-section of a Results node:
3D model, and allows you to plot results on it as
if it were a 2D solution.
REDUCING DIMENSION
In the same way that we’ll use a cut plane with the pyramidal absorber model to
create a 2D plot, it is also possible to use a cut line or cut point to create 1D plots.
These create a data set at a chosen point (over a parameter such as time) or along a
line.
Right-click Results, add a 2D plot group, and

add a surface to the plot group. The variable
automatically entered in the expression field is
the electric field norm—which is what we want
to plot. But if you try to plot the surface, you’ll
see nothing but empty white.
Take a look at the top of the Surface settings

window. Next to the Plot button, a new icon has
appeared: If you click Plot, the cut plane will appear in red
overlaid on the model geometry in the Graphics
window. The vector normal to the plane will
appear as a blue arrow.
We want to visualize the electric field on

Since we haven’t defined a plane yet, COMSOL different areas of the pyramid. In the settings,
is anticipating that we will need to. Click on the change the Plane entry method field to Point
new button to create a cut plane. and normal instead of Three points. The new
plane should be set to contain point (0,0,0) and
normal vector (1,0,0). This will create a vertical
slice through the center of the pyramid.
Go back to the Surface node in 2D Plot Group 3,

make sure that the data set is set to Cut Plane 1,
and click Plot.

2D PLOTS
Now we have results: We’ll demonstrate this with the pyramidal

absorber model by creating a parametric
extrusion. A parametric extrusion extends a data
set by using a parameter (in this case, elevation
angle) as a dimension in the plot.
Right-click the Data Sets node and add a

parametric extrusion by choosing More Data
Sets > Parametric Extrusion 2D:
This surface plot is based on a chosen elevation

angle of θ = 1.48353 (85 degrees), which is
the largest elevation angle (that is, the angle
of incidence of the wave) that applies to this
pyramidal unit cell.
By changing the Parameter value (theta) field

under the Data tab, we can plot the results for
different elevation angles (click Plot each time
you change the value):
This will plot a chosen solution over selected

values of θ. COMSOL has automatically chosen
Cut Plane 1 as the solution to use:
ORIENTATION
A parametric extrusion
will create horizontal layers
regardless of the original
orientation of the cut plane.
PERIODIC ARRAYS Click Plot, and you’ll see that a series of slices (the
From these plots, we can see how the electric extrusion) has appeared in the Graphics window.
field changes with the elevation angle. But to see
this, we had to click Plot each time we changed On each slice, we’ll plot the electric field for a
the parameter value, and could only visualize different value of θ. Add a 3D plot group to the
one surface at a time. What if we want to create Results node and choose Parametric Extrusion
a side-by-side comparison? A periodic array 2D 1 as the data set. Then add a surface to this
offers a way to visualize results with different plot group, and click Plot (the electric field norm
parameter values. is automatically entered in the expression field).

2D PLOTS
It's crowded! To really get a feel for what’s going Adjust the y-minimum and y-maximum
on in the pyramidal unit cell, let’s go back to coordinates to be -150, 150.
Parametric Extrusion 2D 1 and reduce the
number of values we’re looking at. Add a surface to 2D Plot Group 5 and change
the data set to Cut Plane 1. For this first surface,
choose theta to be 1.22173 (70 degrees). Click
HINT Plot, and the familiar surface appears.
If you experiment with plotting a different variable and would like to return to the Duplicate Surface 1. Remove the title by setting
electric field plot, navigate to Replace Expression > Electromagnetic Waves, Frequency Title type to None under the Title tab. (This
Domain > Electric > Electric field norm (emw.normE) or simply type emw.normE into avoids titles being added for every surface
the expression field to plot it again. created in the plot group.) This time, set the
parameter value to be 0. Click Plot.
In the Parametric Extrusion 2D settings, set The second surface plotted right on top of the
the Parameter selection (theta) value to From first one, causing our earlier results to vanish.
list. Hold the CTRL key when you click to We need to add a deformation so that we can see
select multiple values. Scroll through the list these results side by side.
and choose the following values: 1.134464,
1.308997, and 1.48353 (equivalent to 65, 75, and Right-click the new surface node and choose
85 degrees, respectively). We’ll be looking at the Deformation. We want to shift the second plot
higher elevation angles, where the electric field by the width of the unit cell, which is 50mm.
changes the most. Under the Settings tab, check Change the y-component to -50, set the scale
the Level scale factor box and enter 150. factor to 1, and click Plot.
Now return to 3D Plot Group 4 and click Plot.
We’ve made a parametric extrusion! The

different slices show the electric field on the
You can see that the unit cell is 50mm wide by
pyramidal unit cell for the values of θ.
checking its width on the y-axis, or you can see
this by browsing through the Geometry node
HINT Now we’ll arrange each of the slices we want to
to see the original dimensions the model was
see in a 2D plot, so that we can really see them
created with.
You can also adjust the side by side. Add a 2D plot group to the Results
view by clicking the Zoom node. From 2D Plot Group 5, navigate to its
This looks great! We’ll add a few more surfaces
Extents button on the view (View 2D 5). Expand View 2D 5 and click
to complete the array.
Graphics window toolbar. on the Axis node.
This will cause the Graphics
window to snap to a fitted These settings control the range on the x- and REFERENCE
view of the plot. y-axes that are shown in the Graphics window.
For this array, we’ll need a little more room. If you need a refresher on how to navigate from
a plot group to its view, check page 9.

2D PLOTS
Duplicate Surface 2 three times. Use the

following settings: REPEATING PATTERNS
To create good visuals

with a repeating pattern,
try changing all of the
parameter values in a
periodic array like this
one to the same entry.
For example, the image
Go to the 2D Plot Group 5 node, uncheck Plot This model studies the transverse electric (TE) shown below has all of the
data set edges under the Plot Settings tab, and and transverse magnetic (TM) modes in a horn surfaces set to θ = 1.396236
click Plot. antenna. The combination of TE and TM modes (75 degrees):
generated by the corrugated inner surface of
the horn provides linear polarization on the
aperture of the antenna. The simulation results
show the electric field and radiation patterns
around the antenna.
We can now see the evolution of the electric field

using the values we selected earlier.
REVOLUTIONS AND MIRRORING

In certain cases, it isn’t necessary to model the The geometry of the model, as you can see
entire geometry of an object. In cases where below, was created in two dimensions.
the geometry is axisymmetric, an axisymmetric
model can be used. This involves modeling
only half of a cross-section, which simplifies
geometric and boundary conditions and
decreases computational time.
But once the model is solved, it can be helpful

to visualize the entire object. Since we really
picture things in terms of three-dimensional
space, this helps us orient our perspective of the
results.
Let’s take the example of an axisymmetric

antenna. If you have the RF Module installed,
navigate to File > Model Libraries > RF Module >
Antennas and open the corrugated circular horn
antenna model.

2D PLOTS
Several of the data sets use 2D revolutions This plot group shows the electric field translated
to give a better idea of what’s happening in into Cartesian coordinates (the model is created
the 3D device. Under the Data Sets node, in cylindrical coordinates). The norm is plotted
browse through the solutions. Solution 1 and on the circular revolutions we saw earlier
Revolution 2D 1 include the entire geometry. representing the antenna aperture and feed
The revolutions for Solutions 2 and 3 include openings. The arrow plots are shifted upward
only the waveguide feed and the aperture, and downward to be more visible, and show the
respectively, so their plots look like flat circles direction and strength of the electric field.
representing each opening. These will be
important later.
Solution 4 relies on the geometry of the horn

itself. Take a look at Revolution 2D Horn, shown
below.
The Axis Data and Revolution Layers tabs

contain the information that determines how
far the revolution is and around which axis. Create a new data set, Solution 5. Add a
In the default revolution, the solution revolves selection that includes domains 3, 4, and 6
250 degrees around the z-axis. Change the start (the horn, feed, and aperture). Then right-click
and revolution angles and click Plot to see the Data Sets and choose Revolution 2D 1. Choose
changes in the revolution: Solution 5 as the data set and use a start angle
of -90 degrees and a revolution angle of 225
degrees. The plot should look like this:
Start Angle: 0 Start Angle: -45

Revolution Angle: 360 Revolution Angle: 200

1D PLOTS
Now add a new 3D plot group to the Results 1D PLOTS

node and choose None for the data set. Add a
surface plot that uses the Revolution 2D 6 data Using 1D plots is a little different than using 2D
set that you just created. It will automatically or 3D plots. Most often, a 1D plot is used in a
plot the electric field norm: case where it is more helpful to visualize data
using a line graph than a surface, or where the
model geometry doesn’t lend itself to 2D plots.
We’ll take a quick look at 1D plot styles. Open

the shallow water equations model from File
> Model Libraries > COMSOL Multiphysics >
Equation-Based Models. This model simulates a
wave settling over a bed with an uneven surface
(such as a lake or pond bottom) when the water
is shallow. The wave shape is modeled as a
function of time.
Expand 1D Plot Group 1 under the Results

node. Click on Line Graph 1 and take a look at
the settings. Go ahead and experiment with the
fields in the Coloring and Style tab.
For more interesting visuals, you might try using
surfaces that rely on the Revolution 2D Aperture There are a few plot features that are unique
and Revolution 2D Horn data sets. In the image to 1D plots. For instance, the line style and
below, the surface plot on the aperture is shifted coloring take on a different meaning in 1D
upward 0.001 meters. than in 2D and 3D plots, because the line shape
usually indicates a change in the variable,
something accomplished by the surface color
gradient in a 2D or 3D plot.
The thickness of the line plot may be increased

or decreased using the Coloring and Style
options:
HINT
For certain geometries it is also helpful to mirror

the plot data—for instance, in a model of a pipe
where only half of the geometry was modeled. A
mirror data set can be added by right-clicking the
Data Sets node and choosing Mirror 2D or Mirror
3D, depending on whether your geometry is in two
or three dimensions.

1D PLOTS
The figure below shows Line Graphs 1 and 2 The plot below shows Line Graphs 1 and 2,
from 1D Plot Group 1, with Line Graph 1 at a where Line Graph 1 has 12 plus-sign-shaped
width of 3 and Line Graph 2 at a line width of 2. markers and Line Graph 2 has 14 asterisk-
shaped markers.
You can add indicators for evenly-spaced data

points at intervals along a line plot by changing Another feature that applies only to 1D plot
the Marker field and choosing settings for style groups is the labeling tools. Expressions for the
and number of markers: x- and y-axes can be changed in their respective
tabs, and the text in the box legend can be
changed under the Legends tab.
To change the location of the legend box, go to

the plot group node (e.g., 1D Plot Group 1) and
expand the Legend tab. The position can be set
to top, middle, and bottom heights in the left,
right, and middle sections of the grid.
CYCLING COLORS
The Cycle setting for line color causes the line plots to cycle through the available
colors (in this case only blue and green); this makes it easy to differentiate between
many different line plots overlaid in the same plot group.

1D PLOTS
Below are examples of a few more combinations 10*log10(emw.nPoav). This plots the near-field
for the two line graphs in this plot group, radiation pattern using a log scale.
including different colors, styles, and markers.
These use color expressions as well: Click on Polar Plot Group 5 and change
the Parameter selection (freq) field to Form
list. In the selection list, select the following
frequencies: 2e8, 5e8, 10e8, 1.3e9, 1.5e9. Use the
scroll bar and hold down the CTRL key to select
multiple values.
Click Plot. The resulting polar plot shows the

near-field radiation pattern for the specific
operating frequencies we selected, showing
the radiation range as well as how it changes
depending on the frequency. This model is
axisymmetric, so we are only visualizing half of
the pattern:
POLAR PLOTS
Polar plots are a specific type of 1D plot.
Polar plot groups create graphs using polar
coordinates, with radius r and angle Θ.
These are particularly useful for visualizing
electromagnetic and acoustic applications, such
as the distribution of sound emanating from a
megaphone or the range of an antenna. Polar
plots show quantities based on direction and
distance from a specific point of reference.
To demonstrate this, we’ll use a radio-frequency

There we go! We’ve created 3D, 2D, and 1D plots
application. If you have the RF Module installed,
and covered quite a range of the plot options the
navigate to File > Model Libraries > RF Module >
COMSOL® software offers for postprocessing.
Antennas and open the conical antenna model.
Hopefully you feel relatively comfortable with
This simulation studies the antenna impedance
the concept of each plot type we’ve discussed so
and the electric field radiation pattern around
far. If it seems like a lot, don’t worry; we’ll revisit
the antenna as it changes with frequency.
some of these as we explore other techniques.
Now let’s dive into some other visualization tools.
Take a look at Polar Plot Group 5. The line plot
it contains uses the expression

USING POSTPROCESSING FOR RESULTS INTERPRETATION
USING POSTPROCESSING FOR RESULTS

INTERPRETATION
Now that we’ve discussed the best ways to arrange This new plot shows something that the old
a model, let’s briefly explore how postprocessing surface didn’t: the energy transfer on the pillars
can help a designer or engineer make good of the heat sink nearest to the channel inlet
decisions about a design. Beyond creating (rotated toward the front in the previous image)
good, clear graphics, the techniques described is happening at a much higher rate than the
in this guide are meant to illuminate ways that transfer near the channel outlet. In fact, there
postprocessing can support interpretation of the are some pillars that don’t seem to have much
physics happening in a simulation. heat transferring at all; for design purposes, it’s
possible that these could be removed from the
Let’s return for a moment to the heat sink. device to save money and material.
When we plotted the first surface showing the
temperature in the heat sink and channel, the At a second look, it also seems that the tops
heat sink was nearly all white—which made of the pillars aren’t experiencing much heat
sense, because it would certainly be the hottest transfer either; could the pillars be made shorter
part of the geometry. But what if we didn’t want to save material? These are the sorts of questions
to plot the temperature relative to everything that a postprocessing plot can help us answer.
around it? What if we want to see how hot
different areas of the heat sink are relative to one If we want to see the entire geometry again, we
another? can easily combine this plot with the plot we
used earlier in the temperature surface, and
Create a 3D plot group for the heat sink that create an even more interesting visual:
contains the following:
• The line and surface plots we just
• A line plot that includes only the edges created
of the heat sink (it’s easiest to clear the • A surface plot for the channel
selection list and then use the Select temperature (containing only the back
Box tool to add these). wall and floor)
• A surface plot that includes only the heat • A line plot for the air domain (with all
sink, not the channel around it; plot the the lines of the channel plotted)
energy flux magnitude by typing
nitf.tefluxMag into the Expression field
or by adding it from Replace Expression
> Conjugate Heat Transfer (Heat Transfer
in Solids) > Domain Fluxes.
REFERENCE
For instructions on creating surface and line
plots, head to pages 8 in the Plot Type chapter.

DATA , TABLES, AND MESH
EXPORTING RESULTS
One of the final capabilities of the COMSOL® Add the expressions you want, then click Export.
software that we’ll touch on here is exporting Navigate to the folder you saved the text file in,
your results. This can take the form of reports, open it, and you’ll have your data there. It’s best to
plots, tables, graphics, or even animations. view the report in a text editor:
DATA, TABLES, AND MESH

HINT
Right-click the Export node in any model (we’ll The physical quantity you
use the heat sink for this demonstration) and export will dictate the
choose Data. In the settings for the new Data 1 precision needed. With
node, there are fields to select the data set you such high temperatures,
want to export from, a table in which to add two decimal places would
the expressions (we’ve chosen to export the be enough, but if we were
temperature of the heat sink and the air velocity exporting, for example, data
at different coordinates), and output settings such for the displacement in a
as the filename and format: MEMS device—with distances
measured at the micron
level—then six decimal places
You can also export tables, mesh, plots, and would be more appropriate.
images from the Export node. The level of precision can be
adjusted to full precision under
Tables can be exported using several file types, the Advanced tab in the Data
including spreadsheets in Microsoft Excel®: settings window.

DATA , TABLES, AND MESH
A mesh can be exported as a new COMSOL If you only want to export the exact image
Multiphysics® software binary file, which can be shown in the Graphics window, the easiest way
then imported into other models: to do this is to click the Image Snapshot button
in the Graphics window toolbar. From there,
you can choose what to include as well as set the
size and file type:
Images can be exported from plot groups. The

settings allow you to choose the plot you want to
export, the view that will be shown, and which
labels will be included from the layout in the
Graphics window (such as color legends, axis
orientation, and title): Setting the size to Current exports the exact
image shown on the screen.
The rendering settings for image exported from

the Graphics window can be adjusted from
the menu under File > Preferences. Under the
Graphics and Plot Windows section, you can
change the visualization options for graphics
generation.

REPORTS
REPORTS The export options allow you to generate a

report in HTML or Microsoft® Word software.
Exporting reports is a great way to compile all Click the Preview All button at the top of the
the information in your simulation, making settings, and you’ll the see the geometry, mesh,
it easy to hand it to a colleague or introduce solutions, and plots you created cycle through
someone else to using your model. the Graphics window. Once it’s finished, it will
show you a preview of the report document.
Right-click the Reports node, and you’ll see
options for creating brief reports, intermediate
reports, and complete reports, as well as an
option for creating a report with your own
custom settings.
• Complete reports contain all the

information about the model, including
details of the physics interfaces and the
underlying equations. This is great for
troubleshooting.
• Intermediate reports include the physics
settings and variables used in the model,
as well as information about the study,
results, and plots.
• Brief reports give an overview of the
model, including the plots and results,
but without details of the variables or Click Write to create the report.
physics.
• Custom reports allow you to choose
what is included in the report.
Choose Section from the dropdown list shown

above to create a node where you can add content
to the report. Right-clicking the new Section node
will reveal options for adding information about
the geometry, mesh, solver, study, and results.

SHORTCUTS
TIPS & TRICKS

Shortcuts
In addition to the plot techniques we’ve
explored, there are a few very useful shortcuts
HINT
that we haven’t mentioned yet. Many of these are
found at the top of the Graphics window. Nodes can be manually renamed by right-clicking
the node, choosing Rename, and typing the desired
In addition to the buttons for changing the title. This is a good way to organize data sets
zoom and view orientation, the options in this and plot groups, especially when there are many
toolbar control selections, transparency, and solutions with selections or multiple plots in the
scene lighting. We’ve already used several of same group.
these shortcuts, such as Zoom Extents. Here’s a
rundown of the others:
• Zoom Box: allows you to click and • Transparency: turns the model
drag the mouse to create a rectangular geometry transparent
box, highlighting an area of the
geometry to zoom in on • Image Snapshot: opens a dialog box to
export the current view in the Graphics
• Zoom Selected: zooms in on the area of window as an image
a selected geometric component
• Print: opens a dialog box to print the
• Go to Default 3D View: orients the current view
model in the default 3D view
• XY, YZ, and ZX Views: changes the
view to the xy-, yz-, or zx-plane
Rearranging the COMSOL
Desktop® Environment
• Selection and Hiding tools: similar
to the Hide Geometric Entities The COMSOL Desktop® Environment is very
feature available for View nodes, these flexible and easy to rearrange. Plotting in
selection tools can be used to select multiple windows is done under the Window
or hide entities when in a subnode Settings tab in a plot group node. Windows can
of a Component; they create a Hide also be renamed using these settings.
Geometric Objects node, which does not
apply to the Results node
• Scene Light: turns the scene lighting
completely on or off

SHOWING MESHES ON SURFACE PLOTS
Windows can be shifted to different areas of the

desktop and reorganized using the drag-and-
REFINING THE MESH
drop method, which makes it easy to view and
compare multiple plots together. For cases where the mesh
needs to be refined in certain
regions for higher accuracy,
The COMSOL® software has
a feature that will refine it for
you, called Adaptive Mesh
Refinement.
Release the mouse over the beige and white

box indicating the new location of the window
(shaded) to drop it.
Showing Meshes on Surface

Plots
Check the Wireframe box under the Coloring
Showing the mesh on a model is helpful for
and Style tab, and click Plot.
knowing how fine the resolution is on certain
areas when you’re investigating results, for
instance, to see if it needs to be refined for
higher accuracy in regions where there is a
strong gradient.
Let’s return to the original temperature surface

that we first plotted on the heat sink. Add a
second surface to the plot group, and set the
color settings to uniform black. In this case, it
doesn’t matter what the expression is, because
Now we can see that the mesh is finest around
we’re only plotting elements, not results.
the heat sink and pillars, and less refined on the
channel walls. If we were to disable the temperature
surface, we would see only the wireframe lines. Like
other plot types, wireframe surfaces can be plotted
on different data sets, and their coloring and style
settings may be adjusted to your liking.

SLIDING AND INTER AC TIVE POSITIONING
SLIDING AND INTERACTIVE

POSITIONING
For certain plot types, it can be more helpful to
use the mouse to position your results than to
use coordinates or settings. In some cases, there
is an option for interactive positioning.
Open the slice plot you created earlier that

shows the velocity of the air flow in the heat
sink channel. Under the Plane Data tab, check
the Interactive box. This feature lets you shift the
slices in the plot by dragging the slider bar (the
distance is shown in the Shift field).
In the Graphics window, the slices will move as

you move the bar, sometimes even vanishing
from the visible boundaries of the geometry
when the shifted distance is large enough.

CONCLUDING REMARKS
CONCLUDING REMARKS
We’ve covered the basics of what you need to
know to do some very savvy postprocessing,
including a few of the more advanced tricks used
to add a finishing flourish. To recap:
• Start with data sets and evaluations

to understand the physics happening
in your device; these are great for SUBSTRATE INTEGRATED
calculating maxima, minima, and WAVEGUIDE (SIW)
values at specific locations in your Model of leaky waves from a
model. You can also show an entire slot array on the top surface of
object in 3D (if you’ve only modeled a surface integrated waveguide
a portion of it) using data sets with (SIW) designed using the RF
mirroring and revolutions. Module. SIWs are used in
• Think about how you could best display antenna applications where
the information you’re working with. leaky waves can be directed
Who are you showing it to? Where is in a predetermined direction
it going to be seen? Choose a plot type by changing the operating
that fits the physics you want to depict frequency. Results show the far-
and your audience… field radiation pattern.
• …and start plotting! We’ve shown
how to use surface, arrow, line, slice,
contour, streamline, and isosurface
plots, as well as some of the fancier
techniques such as showing a mesh on
top of another surface.
• Export your work so that you can share
it with colleagues, collaborators, and
customers.
Postprocessing can help you understand and
interpret your simulation, make informed design
choices, and convey your results to others.
Experiment with some of the techniques here
and see what you can do! We hope this guide will
assist you in making your simulations—and your
vision—come alive.
31
HEAT EXCHANGER
Model of an air-filled shell and
tube heat exchanger with water
flowing in the inner tubes. Simu-
lation results reveal flow velocity,
temperature distribution, and
pressure within the vessel.

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COMSOL HANDBOOK SERIES

CUT POINTS AND EVALUATIONS

ESSENTIALS OF POSTPROCESSING AND VISUALIZATION IN COMSOL MULTIPHYSICS 2

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

SUPPORT KNOWLEDGE BASE

The postprocessing and visualization tools in

We have put together this material based on

ESSENTIALS OF POSTPROCESSING AND VISUALIZATION IN COMSOL MULTIPHYSICS 1

DATA SETS, DERIVED VALUES, AND TABLES

To demonstrate the use of data sets, derived

Each of these plots shows the stress in the pulley

2 COMSOL HANDBOOK SERIES

Go to the Cut Point 2D 1 node and click Plot.

In this model, the point (0,0) is at the center of

ESSENTIALS OF POSTPROCESSING AND VISUALIZATION IN COMSOL MULTIPHYSICS 3

DERIVED VALUES We can also add multiple variables to this table.

This allows us to evaluate the maximum of a

4 COMSOL HANDBOOK SERIES

In the geometry shown in the Graphics window, GLOBAL EVALUATIONS

Expand Component 1 and the Definitions node.

Choose the points you want to select by clicking

Their names are added to the selection list when

Under Geometric entity level, select Point. Click

Go to the Integration 2 node, again set the

Now we need to create the variable that we want

ESSENTIALS OF POSTPROCESSING AND VISUALIZATION IN COMSOL MULTIPHYSICS 5

Now let’s go back to the Results

6 COMSOL HANDBOOK SERIES

A final note: tables are very useful for checking

Right-click Results and choose 1D Plot Group.

Results show the table and graph indicating how

ESSENTIALS OF POSTPROCESSING AND VISUALIZATION IN COMSOL MULTIPHYSICS 7

CHOOSING A PLOT TYPE

8 COMSOL HANDBOOK SERIES

If you don’t remember the location of the expression

INVISIBILITY CLOAKS: HIDING ENTITIES

Back in the View 1 node, right-click the node

ENTITIES VS. OBJECTS

Now select the three faces of the channel that

ESSENTIALS OF POSTPROCESSING AND VISUALIZATION IN COMSOL MULTIPHYSICS 9

Also select boundary 121, the channel inlet. This

For a simple geometry like this, it is easy enough

You can define your selection and give it a name.

Under the Results node, the new group will

Go back to 3D Plot Group 1. We can see the

For models where you will select the same set

10 COMSOL HANDBOOK SERIES

LINE PLOTS These results were created using a Cut Line 3D

Line plots can also be used to show results

The results below show a plot running along the

Take a look at the Arrow Positioning tab. There

ESSENTIALS OF POSTPROCESSING AND VISUALIZATION IN COMSOL MULTIPHYSICS 11

If you remember, we mentioned duplicating

Expand the Data Sets node, right-click Solution

12 COMSOL HANDBOOK SERIES

See if you can create this plot using your new

Change the contour type from Lines to Filled,

ESSENTIALS OF POSTPROCESSING AND VISUALIZATION IN COMSOL MULTIPHYSICS 13

SLICE PLOTS Reset your temperature plot so that it contains