COMSOL

1. Download Comsol Multiphysics 5.3
2. Download Comsol Multiphysics 5.3 Free

^®

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software version 5.3 update 3 contains performance and stability improvements to COMSOL Multiphysics^®, COMSOL Server™, and COMSOL Client. The update applies to COMSOL^® software version 5.3 (Build: 223), version 5.3 update 1 (Build: 248), and version 5.3 update 2 (Build: 260). The update includes all performance and stability improvements from 5.3 update 1 and update 2 and can be applied directly to an installation of version 5.3. If you have to install version 5.3, then an installation of this version will now include all the performance and stability improvements from update 1 and update 2.

If you have a version older than version 5.3 and a valid license that is on subscription, then perform a full installation of version 5.3 from the Product Download page, which will include all previous updates.

How to Apply the Software Update

Updating COMSOL Multiphysics^®

The easiest way to install the update for COMSOL Multiphysics^® is to start the program and then select Check for Product Updates. If using the Windows^® operating system, this is located in the File menu under Help. If using the Linux^® or macOS operating systems, this is located in the Help menu.

For more information on how to install the update and for offline installation, see the Additional Instructions tab below.

In order to check that the update installation was successful, first start the COMSOL Multiphysics^® software and select the About COMSOL Multiphysics menu option. If using the Windows^® operating system, this is located in the File menu under Help. If using the Linux^® and macOS operating systems, this is located in the Help menu. The listed version should be COMSOL Multiphysics^® 5.3 (Build: 316).

Updating COMSOL Server™

To update COMSOL Server™ if using the Windows^® operating system, run the Update program from the COMSOL Launchers folder in the Start menu.

Note that the COMSOL Server™ service process needs to be stopped before applying the update. For more information on how to install the update, installing on other operating systems, and offline installation, see the Additional Instructions tab below.

To check that the installation was successful, first make sure that COMSOL Server™ is running, then navigate to COMSOL Server™ in a web browser and follow the About COMSOL Server™ link in the lower-right corner. The new version should be COMSOL Server™ 5.3 (Build: 316).

Updating COMSOL Client for Use with COMSOL Server™

To update COMSOL Client for the Windows^® operating system, download the new version from Client Download and install. The previous 5.3 installation will be overwritten. Your installation of COMSOL Client must have the same version number as the COMSOL Server™ installation that you connect to.

The following instructions apply only if you are not using the method based on the Check for Product Updates menu item, as described above.

Updating COMSOL Multiphysics^®

1

Check the Version Number

1. Start COMSOL Multiphysics^®.
2. Open the About COMSOL Multiphysics dialog box. If using the Windows^® operating system, the dialog box can be found in the File menu under Help. If using either the Linux^® or macOS operating systems, the dialog box can be found under the Help menu.
3. Check that the version number is 5.3 (Build: 223, 248, or 260). This corresponds to the version that has not yet been updated.

2

Install the Update

Before you proceed with the installation, make sure to exit any running COMSOL Multiphysics^® processes or any software you have running that correlates to a LiveLink™ product you would like to update (Excel^®, MATLAB^®, or a CAD software).

1. Start the COMSOL^® software update installer:
   • Windows^® operating systems: Run the Update program from the COMSOL Launchers folder in the Start menu, or directly from the COMSOL 5.3 installation folder. The COMSOL Launchers folder can be found in the installation folder, for example, C:Program FilesCOMSOLCOMSOL53MultiphysicsCOMSOL Launchers.
   • Linux^® operating systems: Run the update script from the COMSOL 5.3 installation directory, for example, /usr/local/comsol53/multiphysics.
   • macOS operating systems: Run the COMSOL Update application from the COMSOL 5.3 installation directory, for example, /Applications/COMSOL53/Multiphysics.
2. The next step will be taken in the installer program's Options page and depends on whether or not you have a live internet connection or if you plan to download the update file for offline installation:
   • If you have an internet connection: Keep the Direct download setting.
   • If you have an internet connection via a proxy server: Select Download via proxy server and enter your proxy configuration settings.
   • If you do not have an internet connection on the target computer or if you want to apply the update several times on multiple computers: Download the following file to a folder on your computer DOWNLOAD UPDATE (276 MB) In the installer program, select Manual download and click Browse. Navigate to the downloaded file and click Open.
3. Click Next to get to the Release Notes page for reviewing the update details.
4. Click Next to get to the Install page and review the software components affected by the update.
5. In the Install page, click Install to start the installation of the update.

3

Check the Installation

1. Start COMSOL Multiphysics^®.
2. Open the About COMSOL Multiphysics dialog box. If using the Windows^® operating system, this is located in the File menu under Help. If using the Linux^® and macOS operating systems, this is located in the Help menu.
3. Check that the version number is 5.3 (Build: 316). If not, the installation did not succeed.

Updating COMSOL Server™

1

Check the Version Number

1. Navigate to the running version of COMSOL Server™ in a web browser.
2. Click the About COMSOL Server link in the lower-right corner.
3. Check that the version number is 5.3 (Build: 223, 248, or 260). This corresponds to the version that has not yet been updated.

Download Comsol Multiphysics 5.3

2

Stop COMSOL Server™

Before you proceed with the installation, make sure to stop any running COMSOL Server™ processes.

1. In Windows^®: Stop the server by either typing close, if COMSOL Server™ is running in a command window, or by running the Stop COMSOL Server shortcut from the COMSOL Launchers folder in the start menu, if COMSOL Server™ is installed as a Windows^® service.
2. In Linux^®: If you configured COMSOL Server™ using the systemd service, stop it by typing systemctl stop comsolserver53; otherwise, kill the COMSOL Server™ process.
3. In macOS: Kill the COMSOL Server™ process.

3

Install the Update

Before you proceed with the installation, make sure to stop any running COMSOL Server™ processes, as described above.

1. Start the COMSOL^® software update installer:
   • Windows^® operating systems: Run the Update program from the COMSOL Launchers folder in the Start menu, or directly from the COMSOL 5.3 installation folder. The COMSOL Launchers folder can be found in the installation folder, for example, C:Program FilesCOMSOLCOMSOL53ServerCOMSOL Launchers.
   • Linux^® operating systems: Run the update script from the COMSOL 5.3 installation directory, for example, /usr/local/comsol53/server.
   • macOS operating systems: Run the COMSOL Update application from the COMSOL 5.3 installation directory, for example, /Applications/COMSOL53/Server.
2. The next step will be taken in the installer program's Options page and depends on whether or not you have a live internet connection or if you plan to download the update file for offline installation:
   • If you have an internet connection: Keep the Direct download setting.
   • If you have an internet connection via a proxy server: Select Download via proxy server and enter your proxy configuration settings.
   • If you do not have an internet connection on the target computer or if you want to apply the update several times on multiple computers: Download the following file to a folder on your computer DOWNLOAD UPDATE (276 MB) In the installer program, select Manual download and click Browse. Navigate to the downloaded file and click Open.
3. Click Next to get to the Release Notes page for reviewing the update details.
4. Click Next to get to the Install page and review the software components affected by the update.
5. In the Install page, click Install to start the installation of the update.

4

Start COMSOL Server™ Again

• In Windows^®: Start COMSOL Server™ by using the COMSOL Server shortcut in the start menu. Alternatively, if COMSOL Server™ was installed as a Windows^® service, start it by using the Start COMSOL Server shortcut.
• In Linux^®: If you configured COMSOL Server™ using the systemd service, start it by typing systemctl start comsolserver53; otherwise, type <installation directory='>/bin/comsol server to start COMSOL Server™.
• In macOS: Type <installation directory='>/bin/comsol server to start COMSOL Server™.

5

Check the Installation

1. Navigate to the running version of COMSOL Server™ in a web browser.
2. Click the About COMSOL Server link in the lower-right corner
3. Check that the version number is 5.3 (Build: 316). (If not, the installation did not succeed.)

To manually install the different products, please follow the steps below.

Manual Update of COMSOL Multiphysics^®

1

Check the Version Number

1. Start COMSOL Multiphysics^®.
2. Open the About COMSOL Multiphysics dialog box. If using the Windows^® operating system, the dialog box can be found in the File menu under Help. If using either the Linux^® or macOS operating systems, the dialog box can be found under the Help menu.
3. Check that the version number is 5.3 (Build: 223, 248, or 260). This corresponds to the version that has not yet been updated.

2

Download the Update Files

Click on the appropriate link below to download the update. In some browsers, such as Internet Explorer® browser, a dialog box will then open where you can click Run directly after the download has occurred. Before clicking Run, make sure that you have closed all COMSOL sessions. In other browsers, such as Chrome™ browser, you have to select the downloaded file and run it.

• Windows - comsol_5.3.0.316_win.exe
• Linux - comsol_5.3.0.316_linux.tar.gz
• macOS - comsol_5.3.0.316_mac.dmg

Additional Product-Specific Update Files

If you have a license for any of the products listed in the table below, please also download the corresponding update:

Product	Update(s)
CAD Import Module	Windows - comsol_5.3.0.316_cad_win.exe Linux - comsol_5.3.0.316_cad_linux.tar.gz macOS - comsol_5.3.0.316_cad_mac.dmg
LiveLink™ for Excel®	Windows - comsol_5.3.0.316_llexcel_win.exe
LiveLink™ for Inventor®	Windows - comsol_5.3.0.316_llinv_win.exe
LiveLink™ for MATLAB®	Windows - comsol_5.3.0.316_mli_win.exe Linux - comsol_5.3.0.316_mli_linux.tar.gz macOS - comsol_5.3.0.316_mli_mac.dmg
LiveLink™ for SOLIDWORKS®	Windows - comsol_5.3.0.316_llsw_win.exe

3

Installation

Before you proceed with the installation, make sure you have closed any COMSOL sessions or stopped any running COMSOL processes or any software you have running that correlates to a LiveLink™ product you would like to update (Excel^®, MATLAB^®, or a CAD software).

Windows^® Operating Systems

Run the downloaded .exe file to extract the update to the COMSOL 5.3 installation directory, for example C:Program FilesCOMSOLCOMSOL53Multiphysics.

Linux^® Operating Systems

Copy the downloaded .tar.gz file to the COMSOL 5.3 installation directory:

Adobe illustrator cs6 portable free download for mac. cp comsol_5.3.0.316_linux.tar.gz [installdir]

where [installdir] is the root of the installation, for example

/usr/local/comsol53/multiphysics.

Unpack the installation with the commands:

cd [installdir]tar xvzf comsol_5.3.0.316_linux.tar.gz

macOS Operating Systems

Double-click the downloaded .dmg file to mount the disk image. In the Finder, open the mounted disk and double-click the COMSOL installer icon. Select your COMSOL installation folder, usually called comsol53/Multiphysics.

4

Check the Installation

1. Start COMSOL Multiphysics^®.
2. Open the About COMSOL Multiphysics dialog box. If using the Windows^® operating system, this is located in the File menu under Help. If using the Linux^® and macOS operating systems, this is located in the Help menu.
3. Check that the version number is 5.3 (Build: 316). If not, the installation did not succeed.

Manual Update of COMSOL Server™

1

Check the Version Number

1. Navigate to the running version of COMSOL Server™ in a web browser.
2. Click the About COMSOL Server link in the lower-right corner.
3. Check that the version number is 5.3 (Build: 223, 248, or 260). This corresponds to the version that has not yet been updated.

2

Stop COMSOL Server™

Before you proceed with the installation, make sure to stop any running COMSOL Server™ processes.

1. In Windows^®: Stop the server by either typing close, if COMSOL Server™ is running in a command window, or by running the Stop COMSOL Server shortcut from the COMSOL Launchers folder in the start menu, if COMSOL Server™ is installed as a Windows^® service.
2. In Linux^®: If you configured COMSOL Server™ using the systemd service, stop it by typing systemctl stop comsolserver53; otherwise, kill the COMSOL Server™ process.
3. In macOS: Kill the COMSOL Server™ process.

3

Download the Update Files

In some browsers, such as Internet Explorer® browser, a dialog box will then open where you can click Run directly after the download has occurred. Before clicking Run, make sure that you have closed all COMSOL sessions. In other browsers, such as Chrome™ browser, you have to select the downloaded file and run it.

• Windows - comsol_5.3.0.316_win_server.exe
• Linux - comsol_5.3.0.316_linux_server.tar.gz
• macOS - comsol_5.3.0.316_mac_server.dmg

Additional Product-Specific Update Files

If you have a license for any of the products listed in the table below, please also download the corresponding update:

Product	Update(s)
CAD Import Module	Windows - comsol_5.3.0.316_cad_win_server.exe Linux - comsol_5.3.0.316_cad_linux_server.tar.gz macOS - comsol_5.3.0.316_cad_mac_server.dmg
LiveLink™ for MATLAB®	Windows - comsol_5.3.0.316_mli_win_server.exe Linux - comsol_5.3.0.316_mli_linux_server.tar.gz macOS - comsol_5.3.0.316_mli_mac_server.dmg

4

Installation

Before you proceed with the installation, make sure you have closed any COMSOL sessions or stopped any running COMSOL processes.

Windows^® Operating Systems

Run the downloaded .exe file to extract the update to the COMSOL 5.3 installation directory, for example C:Program FilesCOMSOLCOMSOL53Server.

Linux^® Operating Systems

Copy the downloaded .tar.gz file to the COMSOL 5.3 installation directory:

cp comsol_5.3.0.316_linux_server.tar.gz [installdir]

where [installdir] is the root of the installation, for example

/usr/local/comsol53/server.

Unpack the installation with the commands:

cd [installdir]tar xvzf comsol_5.3.0.316_linux_server.tar.gz

macOS Operating Systems

Download Comsol Multiphysics 5.3 Free

Double-click the downloaded .dmg file to mount the disk image. In the Finder, open the mounted disk and double-click the COMSOL installer icon. Select your COMSOL installation folder, usually called COMSOL53/Server.

5

Start COMSOL Server™ Again

• In Windows^®: Start COMSOL Server™ by using the COMSOL Server shortcut in the start menu. Alternatively, if COMSOL Server™ was installed as a Windows^® service, start it by using the Start COMSOL Server shortcut.
• In Linux^®: If you configured COMSOL Server™ using the systemd service, start it by typing systemctl start comsolserver53; otherwise, type <installation directory='>/bin/comsol server to start COMSOL Server™.
• In macOS: Type <installation directory='>/bin/comsol server to start COMSOL Server™.

6

Check the Installation

1. Navigate to the running version of COMSOL Server™ in a web browser.
2. Click the About COMSOL Server link in the lower-right corner
3. Check that the version number is 5.3 (Build: 316). (If not, the installation did not succeed.)

Autodesk, the Autodesk logo, AutoCAD, Inventor, and Revit are registered trademarks or trademarks of Autodesk, Inc., and/or its subsidiaries and/or affiliates in the USA and/or other countries. Chrome is a trademark of Google Inc. Linux is a registered trademark of Linus Torvalds in the U.S. and other countries. macOS is a trademark of Apple Inc., registered in the U.S. and other countries. Microsoft, Internet Explorer, Excel, and Windows are either registered trademarks or trademarks of Microsoft Corporation in the United States and/or other countries. MATLAB is a registered trademark of The MathWorks, Inc. PTC, Creo, and Creo Parametric are trademarks or registered trademarks of PTC Inc. or its subsidiaries in the U.S. and in other countries. Solid Edge is a trademark or registered trademark of Siemens Product Lifecycle Management Software Inc. or its subsidiaries in the United States and in other countries. SOLIDWORKS is a registered trademark of Dassault Systèmes SolidWorks Corp.

All COMSOL^® software products undergo stability improvements that are introduced as updates. The following list contains the most important improvements in COMSOL^® version 5.3 update 3 (including those of update 1 and 2).

COMSOL Multiphysics

• Improved the responsiveness of the online context-sensitive help.
• Fixed a character-encoding error for the Simplified Chinese help desk page.
• Fixed a problem that would cause an unnecessary mesh rebuild when opening an old model; this problem only affected models using Mesh Parts under Global Definitions.
• Fixed an issue pertaining to importing a mesh to the Geometry node in the model tree or when remeshing a Deformed Geometry, where the existence of isolated edges and vertices could lead to a corrupt geometry and render the COMSOL Multiphysics^® software unstable.
• Added two new built-in methods for returning information associated with a model tree View node in the API; the view.geom() method returns either the geometry sequence or null for views not associated with a geometry, while the view.getSDim() method returns the space dimension.
• Changed the default constraint method for periodic conditions from the Elemental type to Nodal; this change makes the default constraint method consistent with earlier versions.
• Improved the terminology in the COMSOL Desktop^® user interface for the Spanish and French languages.
• Improved the performance of initialization of solutions and made other miscellaneous performance improvements.
• Added an error message for when unmeshed domains are included in the selection of the Geometrical Optics or Ray Acoustics interfaces; ordinarily, unmeshed domains and voids should be excluded from the physics interface selection in these cases.
• Fixed a problem that prevented opening MPH-files stored on a Samba^® disk when running on macOS operating system software.
• Added functionality so that the iterative solver suggestion now works for acoustic-structure interaction in the time domain.
• Fixed a problem related to accessing locally installed help files when running COMSOL Multiphysics^® connected to a remote COMSOL Multiphysics^® server session.
• Improved the performance of certain variables used in the interfaces based on the boundary element method for the case where these were evaluated inside component coupling operators.
• Fixed a problem with the COMSOL Multiphysics^® server so that it now works properly on Linux^® clusters.¹
• The predefined iterative solver suggestion for acoustic-piezoelectric interaction models now works in the time domain.¹
• Improved the stability of the Application Library Update in various ways, including instant integration of added or modified model documentation.²
• Fixed app layout issues and corrected an error that could be triggered as the result of an undefined variable.²
• Fixed a problem when using the Stabilized Convection-Diffusion Equation interface in combination with a unit system set to None.²
• The KdV Equation and Solitons model in the Equation Based folder in the COMSOL Multiphysics Application Library has been improved with a better time resolution.²
• Corrected an error that caused the SCGS smoother with Vanka variables to work incorrectly in cluster simulations.²
• Fixed a problem that would occur when saving MPH-files that were temporarily locked by other programs such as file synchronization software like Google Drive™ online storage service or Dropbox^® storage.²

COMSOL Server™

• Fixed several stability issues.

AC/DC Module

• Improved the performance of some of the demo applications in the Application Libraries.
• Improved the performance of certain variables used in the interfaces based on the boundary element method for the case where these were evaluated inside component coupling operators.

Acoustics Module

• Corrected the formulation of the time-domain PML for pressure acoustics in order to eliminate unwanted reflections for 2D axisymmetric models.
• Improved the dynamic help of the Acoustics Module.²
• Fix of an error in the expression for the compressibility in the Johnson-Champoux-Allard-Lafarge option for the Poroacoustics feature.²

Application Builder

• Fixed an issue with running External Class nodes through Batch jobs.²

CAD Import Module

• Fixed an issue pertaining to performing Defeaturing and Repair where the error message 'Error when serializing reference to: GeomObject' would appear when attempting to run a Study a second time.
• Fixed a problem with using the File Import for CATIA^® V5 product where importing certain CATIA^® V5 files incorrectly gave the error 'File version is not supported' in version 5.3.

CFD Module

• Updated the Two-Phase Flow multiphysics coupling node in the model tree so that the temperature input field is always visible.

Chemical Reaction Engineering Module

• Updated the step-by-step modeling instructions for the Zone Electrophoresis model.

ECAD Module

• Fixed a problem with importing ODB++ files where certain text objects were not automatically identified and ignored.
• Fixed a problem when importing GDS files that contain mirrored arrays.²

Electrodeposition Module

• Improved the step-by-step modeling instructions for the Rotating Cylinder Hull Cell model.

Geomechanics Module

• Fixed an error in the isotropic hardening option when used together with an elliptic cap in the soil plasticity material models.

Heat Transfer Module

• Corrected the expressions used for the postprocessing variables nteflux and nteeflux for models based on the Thermoelectric Effect interface.
• Enabled Thermal Expansion for models with an Isothermal Domain.
• Fixed a problem with the definitions of the Td and Tu variables, available on boundaries, which would occur in some configurations where an Isothermal Domain interface and a Thin Layer were combined.
• Improved the equation display for the Moist Air version of the Moisture Transport interface.
• Fixed the inverted legend on natural convection sketches.²
• Fixed the definition of energy balance postprocessing variables for models that have a diffuse surface boundary condition on internal boundaries.²
• Fixed a problem with missing entities in selections loaded from assembly components.²

LiveLink™ for Inventor^®

• Fixed a problem where selections would sometimes not work subsequent to adding a feature node in the Model Builder of the One Window interface.

LiveLink™ for MATLAB^®

• Fixed a problem pertaining to using mphstart and mphlaunch when there was a space in the installation path of COMSOL Multiphysics^®.
• Fixed a problem pertaining to mphnavigator that would occur when clicking 'Copy set' and simultaneously selecting a parameter node in the model tree.

Nonlinear Structural Mechanics Module

• Fixed a circular dependency error that would sometimes occur when combining viscoelasticity with a user-defined hyperelastic material.
• Corrected an error where a variable name could be undefined in the Navarro-Herring creep model.²

Plasma Module

• Fixed an undefined variable error that could occur with the Symmetry boundary condition in the Heavy Species interface.
• Added the correct weak contributions for the Flux condition in the Heavy Species Transport interface on boundaries with a nonzero normal velocity.

Ray Optics Module

• Corrected the description of the gopminop1 component coupling, which contained an error.
• Fixed a problem with the Illuminated Surface feature so that the initialization of ray intensity now works in 2D axisymmetric models.¹
• Fixed a problem with the Inlet feature for the Geometrical Optics interface so that ray direction initialization now works in 2D axisymmetric models.¹

Structural Mechanics Module

• Corrected an error where, in certain cases, the strain variable computed in a Spring Foundation node had the wrong sign.
• Updated the heat source term for the Thermoelasticity interface so that it is now nonzero only when the Structural transient behavior setting is set to Include inertial terms.
• Corrected an error that made it impossible to use a Point Mass condition in the 2D version of the Beam interface; this error occurred in cases where the Study property Include geometric nonlinearity was enabled.
• Fixed an error in the External Stress node in the Shell interface where the added stress could become incorrect if the Global coordinate system option was selected and another coordinate system was simultaneously used in the Shell Local System node in the model tree.
• Fixed a problem where the computed moment was incorrect in cases where Evaluate reaction forces had been selected for a Rigid Connector in the Solid Mechanics interface; the result was previously scaled by the area of the boundaries to which the Rigid Connector was attached.
• Fixed a problem in the Beam interface that made it impossible to use variables or expressions in the input fields for Section Orientation.
• Fixed a problem that would occur when the Solid Mechanics interface was used together with the Optimization Module interfaces in certain cases, causing an excessive number of constraints to be generated.
• Corrected an error that made it impossible to combine the features External Stress Relation and Contact.²
• Fixed a problem that would occur when exporting beam section properties.²
• Fixed a problem that would occur when 2D models contained more than one Rigid Connector feature having a Mass and Moment of Inertia attribute.²

¹ New in update 2
² New in update 3

Autodesk, the Autodesk logo, AutoCAD, Inventor, and Revit are registered trademarks or trademarks of Autodesk, Inc., and/or its subsidiaries and/or affiliates in the USA and/or other countries. Chrome and Google Drive are trademarks of Google Inc. Dropbox is a registered trademark of Dropbox, Inc. Linux is a registered trademark of Linus Torvalds in the U.S. and other countries. macOS is a trademark of Apple Inc., registered in the U.S. and other countries. Microsoft, Internet Explorer, Excel, and Windows are either registered trademarks or trademarks of Microsoft Corporation in the United States and/or other countries. MATLAB is a registered trademark of The MathWorks, Inc. PTC, Creo, and Creo Parametric are trademarks or registered trademarks of PTC Inc. or its subsidiaries in the U.S. and in other countries. Solid Edge is a trademark or registered trademark of Siemens Product Lifecycle Management Software Inc. or its subsidiaries in the United States and in other countries. SOLIDWORKS is a registered trademark of Dassault Systèmes SolidWorks Corp.

Particle Tracing Module Updates

For users of the Particle Tracing Module, COMSOL Multiphysics^® version 5.3 includes many new features, highlighted by the Periodic Condition and Rotating Frame features for particle tracing in sectors and rotating machinery, respectively. Additionally, you can define random initial positions for particle releases and visualize particle paths as ribbons. Browse all of the new features and functionality in the Particle Tracing Module below.

Particle Tracing Periodic Condition

You can use the new Periodic Condition feature to model particle tracing in periodic structures or in geometries with sector symmetries. When a particle reaches a surface with the Periodic Condition, it is immediately mapped to a destination point on a second surface. After the particle is mapped to the destination surface, its velocity can either be kept the same, rotated (for sector symmetry), or set to a new value by a user-defined expression.

Particles, colored by their unique particle index, traveling through a domain with sector symmetry.

Rotating Frames

The Rotating Frame feature in particle tracing is now available for rotating frames of reference. When you specify the center of rotation, direction of rotation, and angular velocity magnitude of the frame, the centrifugal, Coriolis, and Euler forces that are exerted on the particles are automatically applied. Particle tracing in rotating frames allows for easier modeling of particle motion in rotating machinery, such as mixers and turbomolecular pumps, because the particle trajectories can be computed in a frame of reference that is attached to the moving geometry.

By adding this feature to a model, release-based features will include an option to specify whether the initial particle velocity is defined with respect to the rotating frame or with respect to the inertial (nonrotating) frame. This latter additional feature is activated in the Advanced Settings section by selecting the Subtract moving frame velocity from initial particle velocity check box.

Particles are released at rest with respect to the rotating frame of reference; that is, they have a nonzero initial velocity with respect to a nonrotating (inertial) frame. Due to the fictitious centrifugal and Coriolis forces, the particles spiral out toward the boundary.

Particles are released at rest with respect to the nonrotating (inertial) frame of reference; that is, the frame velocity is subtracted from the initial velocity in the rotating (noninertial) frame. As a result, the balance of centrifugal and Coriolis forces causes the particles to orbit the center of rotation at constant speed.

Application Library path for an example showing the Rotating Frame feature:
Particle_Tracing_Module/Tutorials/turbomolecular_pump

Random Initial Positions

You can now release particles at random initial positions on selected domains, boundaries, and edges. Unique positions are chosen for each release time. This is available in the Release, Inlet, and Release from Edge features.

Particles are released at random positions on an Inlet boundary and are carried through a cylindrical pipe. The color expression is proportional to the release time.

Ribbons on Particle Trajectories

You can now visualize particle trajectories as ribbons. Unlike with lines and tubes, plotting the particle trajectories as ribbons gives you the flexibility to specify an orientation as well as a path for the particle motion. For curved trajectories, it is useful to use built-in expressions for the normal and binormal directions to better visualize the particle motion.

Motion of a charged particle in a uniform magnetic field. The ribbon has been oriented so that it is parallel with the binormal direction for the curved trajectory.'>

Motion of a charged particle in a uniform magnetic field. The ribbon has been oriented so that it is parallel with the binormal direction for the curved trajectory.

Motion of a charged particle in a uniform magnetic field. The ribbon has been oriented so that it is parallel with the binormal direction for the curved trajectory.

Coordinate System Selection for Inlets

When releasing particles at a boundary using the Inlet feature, you can initialize the particle velocity or momentum using any coordinate system that has been defined for the model component.

Lambertian Velocity Distribution

The particle release features now include an option to release particles with a Lambertian velocity distribution in 3D. Particles are released with initial directions based on Lambert's cosine law, also known as Knudsen's cosine law in molecular dynamics.

Lambert's cosine law states that the probability that a particle will be released through a differential solid angle element dω with polar angle θ is proportional to cos θ. By comparison, in the isotropic hemispherical distribution, the particle is equally likely to be released through any differential solid angle in the hemisphere.

Nonuniform Magnitudes in Velocity Distributions

For the spherical, hemispherical, conical, and Lambertian velocity distributions, it is now possible to release particles with a distribution of speeds as well as directions.

By default, every particle that is released from the same point in a velocity distribution will have the same magnitude. However, by expressing the initial speed in terms of the unique particle index, you can apply a different initial speed to each particle without changing the distribution of particle directions. This makes it easier to include distributions of particle speed or energy, as well as direction.

Particles with uniform speed (left) or a pseudorandom distribution of different speeds (right). The distribution of particle velocity directions has been left unchanged; it is an isotropic circle for both releases.'>

Particles with uniform speed (left) or a pseudorandom distribution of different speeds (right). The distribution of particle velocity directions has been left unchanged; it is an isotropic circle for both releases.

Particles with uniform speed (left) or a pseudorandom distribution of different speeds (right). The distribution of particle velocity directions has been left unchanged; it is an isotropic circle for both releases.

Lift Force

A dedicated Lift Force feature is now available for the Particle Tracing for Fluid Flow interface. Lift forces are relevant when particles move in a nonuniform fluid velocity field. The drag force acts in parallel with the fluid velocity with respect to the particle, whereas the lift force typically acts normal to it.

Two different formulations of the lift force are available: Saffman and Wall induced. The Saffman formulation for lift force is applicable to inertial particles in a shear flow that are an appreciable distance away from boundaries. The specialized Wall induced formulation is available for neutrally buoyant particles in channels.

Anisotropic Turbulent Dispersion

When applying a random turbulent dispersion term to the drag force on particles in a fluid using the continuous random walk model, the turbulent dispersion can now be either isotropic (the default) or anisotropic. If anisotropic turbulence is used, the turbulent dispersion terms are computed using specific expressions for the streamwise, spanwise, and wall normal directions. Anisotropic turbulence can provide a more realistic depiction of particle motion in a turbulent flow when the particles are close to walls.

Thermionic Emission of Electrons

A dedicated Thermionic Emission feature is now available to model the release of electrons from a hot metal cathode and is available in the Charged Particle Tracing interface. The total current density released from the boundary is computed using Richardson's law, where the effective Richardson constant, work function of the metal, and temperature can be specified.

Application Library path for an example showing the Thermionic Emission feature:
Particle_Tracing_Module/Charged_Particle_Tracing/planar_diode

Drag Correction Factor for Particles Close to Walls

A new drag correction factor adjusts the drag force that particles experience as they approach walls. Most common drag laws, such as the Stokes drag law, are formulated under the assumption that the particle is extremely small relative to the geometry size. These wall corrections improve the accuracy when the ratio of the particle radius to the distance to the nearest wall is not negligibly small. Simply select the Include wall corrections check box to enable these corrections.

Settings window for the Drag Force feature with the Include wall corrections option selected so as to account for nearby walls.'>

Settings window for the Drag Force feature with the Include wall corrections option selected so as to account for nearby walls.

Settings window for the Drag Force feature with the Include wall corrections option selected so as to account for nearby walls.

Symmetry Condition for Particle Tracing

The specialized Symmetry boundary condition is now available in the Charged Particle Tracing and Particle Tracing for Fluid Flow interfaces, and reduces the size of your model and computational resources required to solve it. It is a useful and special case of the Wall boundary condition that always imposes model particles to be specularly reflected at the boundary. This means that for every particle that would leave the modeling domain through a symmetry plane, an identical particle would simultaneously enter the modeling domain at the same location and same time.

Extra Time Steps in Trajectory Plots

When plotting particle trajectories, it is now easier than ever to plot additional time steps that correspond to particle-wall interaction times. The number of these extra time steps can now be controlled directly from the Settings window for the Particle Trajectories plot. Built-in options are available to specify the maximum number of extra time steps directly or as a multiple of the number of stored solution times.

New Options for Inlet Pairs

When releasing particles from an inlet pair defined on an assembly, you can now choose to release the particles from only the source boundary, the destination boundary, or both. This is most noticeable when using a mesh-based release of particles, since the mesh on either side of the identity pair can be different.

Mesh-based release of particles from the source boundary (left), the destination boundary (middle), or both source and destination (right). In each rectangle, the source boundary is on the side of the lighter-colored mesh.'>

Mesh-based release of particles from the source boundary (left), the destination boundary (middle), or both source and destination (right). In each rectangle, the source boundary is on the side of the lighter-colored mesh.

Mesh-based release of particles from the source boundary (left), the destination boundary (middle), or both source and destination (right). In each rectangle, the source boundary is on the side of the lighter-colored mesh.

Alternative Way to Assign Weights in Bidirectionally Coupled Space Charge Models

When using the Bidirectionally Coupled Particle Tracing study step to model electric particle-field interactions, it is now possible to assign different weights to the space charge density computed during different iterations of the solver loop. There are built-in options to make these weights remain constant (the default) or increase them in an arithmetic or geometric sequence. This can lead to faster convergence of bidirectionally coupled models in which the electric field and the trajectories of charged particles strongly influence each other.

The weights for the space charge density in each iteration of the Bidirectionally Coupled Particle Tracing study can be uniform, an arithmetic sequence (shown above), or a geometric sequence.'>

The weights for the space charge density in each iteration of the Bidirectionally Coupled Particle Tracing study can be uniform, an arithmetic sequence (shown above), or a geometric sequence.

The weights for the space charge density in each iteration of the Bidirectionally Coupled Particle Tracing study can be uniform, an arithmetic sequence (shown above), or a geometric sequence.

Convergence-Based Termination Criteria for Bidirectionally Coupled Models

For models that use the Bidirectionally Coupled Particle Tracing study step to iterate between stationary and time-dependent solutions, it is now possible to terminate the solver loop based on a convergence criterion instead of a fixed number of iterations. For example, when modeling bidirectionally coupled particle-field interactions, you can terminate the study when the relative error in the electron or ion current is sufficiently small. This allows you to state the level of accuracy you want, without having to expend computational resources to complete a fixed number of iterations after this criterion is satisfied.

New Component Couplings on Particles

New component couplings are automatically created for each instance of a particle tracing interface, and the behavior of the old component couplings has changed. The old component couplings, for example, pt.ptop1(expr), now automatically exclude both particles that have not yet been released and particles that have disappeared. The degrees of freedom of such particles are usually not-a-number (NaN), so it is convenient to automatically exclude them when evaluating sums and averages over the totality of particles.

The following table lists the component couplings that are automatically created for the Mathematical Particle Tracing interface.

Name	Description
`pt.ptop1(expr)`	Sum of expression `expr` over active, stuck, and frozen particles
`pt.ptop_all1(expr)`	Sum of expression `expr` over all particles
`pt.ptaveop1(expr)`	Average of expression `expr` over active, stuck, and frozen particles
`pt.ptaveop_all1(expr)`	Average of expression `expr` over all particles
`pt.ptmaxop1(expr)`	Maximum of expression `expr` over active, stuck, and frozen particles
`pt.ptmaxop_all1(expr)`	Maximum of expression `expr` over all particles
`pt.ptminop1(expr)`	Minimum of expression `expr` over active, stuck, and frozen particles
`pt.ptminop_all1(expr)`	Minimum of expression `expr` over all particles
`pt.ptmaxop1(expr, evalExpr)`	Evaluate `evalExpr` at the maximum of expression `expr` over active, stuck, and frozen particles
`pt.ptmaxop_all1(expr, evalExpr)`	Evaluate `evalExpr` at the maximum of expression `expr` over all particles
`pt.ptminop1(expr, evalExpr)`	Evaluate `evalExpr` at the minimum of expression `expr` over active, stuck, and frozen particles
`pt.ptminop_all1(expr, evalExpr)`	Evaluate `evalExpr` at the minimum of expression `expr` over all particles

Additional Statistics Based on Particle Status

When the Store particle status data check box is selected, the following new variables will be defined.

(Note: The expressions are written for an instance of the Mathematical Particle Tracing interface with tag pt. Physics interface tags will naturally be different for different physics interfaces.)

Tag	Name	Description
pt.fac	`pt.ptop1(pt.fs1)`	Fraction of particles active at final time
pt.ffr	`pt.ptop1(pt.fs2)`	Fraction of particles frozen at final time
pt.fst	`pt.ptop1(pt.fs3)`	Fraction of particles stuck at final time
pt.fds	`pt.ptop1(pt.fs4)`	Fraction of particles disappeared at final time
pt.fse	`pt.ptop1(!primary&&pt.fs>0)/pt.Ms`	Fraction of secondary particles released at final time

New Tutorial: Inertial Focusing Benchmark

For more than 50 years, it has been known that neutrally buoyant particles in a flow channel tend to converge to specific locations in the channel cross section. For a cylindrical pipe, or two parallel planes carrying a Poiseuille flow, the equilibrium position is about 0.6 times the pipe radius, or a distance from the parallel walls of about 0.2 times the channel width, respectively. This is sometimes called the Segre-Silberberg effect, while a ring of particles with a radius of 0.6 times the pipe radius is sometimes called the Segre-Silberberg annulus.

In this benchmark model, we reproduce the case of a flow channel bounded by two parallel walls. Wall-dependent lift and drag forces are exerted on the neutrally buoyant particles as they are carried along the channel by a parabolic fluid velocity profile. As particles are carried through the channel, the inertial lift force causes them to reach equilibrium positions at distances from the center of 0.3D, where D is the distance between the walls. These equilibrium positions are consistent with the Segre-Silberberg effect.

Particle trajectories in a rectangular channel. The color expression is the y-component of the particle velocity. Note that the channel is scaled for easier viewing, but actually has a 1000-to-1 aspect ratio.

Application Library path:
Particle_Tracing_Module/Fluid_Flow/inertial_focusing

New Tutorial: Thermionic Emission in a Planar Diode

When electrons are emitted from a heated cathode in a plane parallel vacuum diode, they contribute to the space charge density in the diode, which in turn affects the electric potential distribution. If the potential difference between the cathode and the anode is not sufficiently large, a potential minimum forms between them, repelling electrons of insufficient energy back toward the cathode. Such a diode is said to be operating in the space charge limited regime.

In this benchmark model, the dedicated Thermionic Emission feature is used to release thermal electrons from a cathode of a specified temperature and work function. The electron trajectories are bidirectionally coupled to the electric potential calculation in the diode using the specialized Electric Particle Field Interaction multiphysics coupling and Bidirectionally Coupled Particle Tracing study step. The electric potential distribution and the anode current compare favorably to the results of the analytical Langmuir-Fry model.

Electric potential close to the cathode in a planar diode, as compared to reference data. When self-consistent particle-field interactions are included in the model, a potential barrier forms next to the cathode. '>

Electric potential close to the cathode in a planar diode, as compared to reference data. When self-consistent particle-field interactions are included in the model, a potential barrier forms next to the cathode.

Electric potential close to the cathode in a planar diode, as compared to reference data. When self-consistent particle-field interactions are included in the model, a potential barrier forms next to the cathode.

Application Library path:
Particle_Tracing_Module/Charged_Particle_Tracing/planar_diode

New Tutorial: Einzel Lens

An Einzel lens is an electrostatic device used for focusing charged particle beams. It may be found in cathode ray tubes, ion beam and electron beam experiments, and in ion propulsion systems. This particular model consists of three axially aligned cylinders. The outer cylinders are grounded, while the cylinder in the middle is held at a fixed voltage. The 3D electrostatic field is computed with the Electrostatics interface and the particle trajectories are computed using the Charged Particle Tracing interface.

Application Library path:
Particle_Tracing_Module/Charged_Particle_Tracing/einzel_lens

New Tutorial: Turbomolecular Pump

The Free Molecular Flow interface (available in the Molecular Flow Module) is an efficient tool for modeling extremely rarefied gases when the gas molecules move much faster than any geometric entities in the domain. For turbomolecular pumps, in which the blades move at speeds comparable to the thermal speed of the gas molecules, a Monte Carlo approach is needed.

In this example, the trajectories of gas molecules are computed in the empty space between two rotating blades of a turbomolecular pump. The model uses the new Rotating Frame feature that applies centrifugal and Coriolis forces to the particles, allowing the trajectories to be computed in a noninertial frame of reference that moves with the rotating blades. The effect of the blade velocity on the compression factor is shown using a Parametric Sweep.

Note: The model in the example also requires the Molecular Flow Module.

Screenshot of the Turbomolecular Pump tutorial model. As the blade velocity increases, molecules have a higher probability of being transmitted forward through the pump and a lower probability to be transmitted backward, as shown by the increasing compression ratio.'>

Screenshot of the Turbomolecular Pump tutorial model. As the blade velocity increases, molecules have a higher probability of being transmitted forward through the pump and a lower probability to be transmitted backward, as shown by the increasing compression ratio.

Screenshot of the Turbomolecular Pump tutorial model. As the blade velocity increases, molecules have a higher probability of being transmitted forward through the pump and a lower probability to be transmitted backward, as shown by the increasing compression ratio.

Application Library path:
Particle_Tracing_Module/Tutorials/turbomolecular_pump