*Released May 3rd, 2013*

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Breakthrough analysis tools expand the COMSOL Multiphysics® simulation platform. Five new add-on modules open new frontiers in multiphysics simulation.

## Multibody Dynamics Module

The Multibody Dynamics Module provides a powerful set of tools to efficiently optimize and design sophisticated multibody structural mechanics models using finite element analysis. As an add-on to the Structural Mechanics Module, it is used to simulate the dynamics of a mixed system of rigid and flexible bodies, each of which may undergo large translational and rotational displacements.

Engineers and researchers can design precise multibody structural mechanics models using a library with eight different types of joints to connect the different bodies. You can specify translational and rotational constraints, as well as locking, so as to restrict the relative motion of the bodies. The following joint types are included in the Multibody Dynamics Module:

- Prismatic (3D, 2D)
- Hinge (3D, 2D)
- Cylindrical (3D)
- Screw (3D)
- Planar (3D)
- Ball (3D)
- Slot (3D)
- Reduced Slot (3D, 2D)

Time-dependent, stationary, frequency-domain, and eigenfrequency multibody dynamics analyses can be performed. All bodies in a multibody structural mechanics model are flexible and have elastic properties by default, and can be made rigid by selectively tagging them with a Rigid Domain property. Boundaries or parts of boundaries of flexible bodies can also be made rigid. Nonlinear elastic properties are defined by combining your multibody dynamics design and analyses with the Nonlinear Structural Materials Module or the Geomechanics Module.

Joints can be assigned applied forces and moments as well as a prescribed motion as a function of time. Torsional springs with damping properties can also be assigned to the joints. By using these features you can analyze and postprocess:

- The velocities and relative displacement and rotation between two parts
- Joint moments and reaction forces
- Frames of reference for local and global coordinate-systems
- Flexible body stresses and deformations
- Fatigue analysis together with the Fatigue Module

## Wave Optics Module

The Wave Optics Module is useful for accurate component design and simulation, and provides a dedicated tool-set for electromagnetic wave propagation in nonlinear or linear optical media. It features the groundbreaking Beam Envelope Method for electromagnetic full-wave propagation, which is based on direct discretization of Maxwell’s equations. The electric field is expressed as the product of a slowly varying envelope function and a rapidly varying exponential phase function, without the traditional approximations. Optical systems with geometric dimensions much larger than the wavelength can be simulated accurately with the Wave Optics Module, whereas ray tracing approximations of light waves cannot. The Beam Envelope Method requires knowledge of the main-direction of propagation and complements the conventional electromagnetic full-wave propagation methods also featured in the Wave Optics Module.

Several 2D and 3D analysis methods are available, including frequency-domain, eigenfrequency, and time-domain electromagnetic simulation. The Wave Optics Module enables simulation of wave propagation through optical media including engineered metamaterials and gyromagnetic materials. It is made possible through built-in support for permeability, permittivity, and generic anisotropic refractive index tensors.

Other important features in the Wave Optics Module include port and scattering boundary conditions, Floquet-periodic structures with higher-order diffraction modes, S-parameter computations, complex-valued spatially varying material models, perfectly matched layers (PMLs), and the best solvers available. As a result, you can easily simulate optical fibers, bidirectional couplers, optical sensors, plasmonic devices, metamaterials, laser beam propagation, and nonlinear optical processes in photonics.

## Molecular Flow Module

The Molecular Flow Module is ideal for the design and simulation of low pressure gas systems that cannot be modeled with conventional fluid dynamics tools. Kinetic effects become important as the mean free path of the gas molecules becomes comparable to the length scale of the flow. For gases, the ratio of the molecular mean free path to the flow geometry size is given by the Knudsen number. There are four flow regimes depending on the value of the Knudsen number (Kn):

- Continuum flow (Kn<0.01)
- Slip flow (0.01<Kn<0.1)
- Transitional flow (0.1<Kn<10)
- Free molecular flow (Kn>10)

The Molecular Flow Module applies to the transitional flow and free molecular flow regimes, whereas the Microfluidics Module covers continuum and slip flows.

A fast angular coefficient method in the Molecular Flow Module enables fast computations of steady-state free molecular flow where only the surface of the CAD geometry is meshed. Transitional flow is solved using the discrete velocity method. The Molecular Flow Module covers isothermal and non-isothermal molecular flows including computing the heat flux contribution from the gas molecules.

Adsorption / desorption and deposition features can be used to design and optimize processes like chamber pump-down as well as film growth. Postprocessing of the number densities within the modeling domain is possible for free molecular flow and allows for applications such as estimating number density profiles along the path of ion beams. The Molecular Flow Module is very applicable for the design and simulation of vacuum systems for mass spectrometers, semiconductor processing, satellite technology, and particle accelerators, as well as very small channel applications like shale gas exploration and flow in nanoporous materials.

## Semiconductor Module

The Semiconductor Module permits device simulation of the fundamental physics of semiconductors through a user-friendly interface design. Charge-carrier transport methods form the basis of the module and are used to solve the drift-diffusion equations with non-isothermal or isothermal transport models. A Galerkin least-squares stabilized finite element method and the finite volume method with Scharfetter-Gummel upwinding are two numerical methods provided with the Semiconductor Module to enable semiconductor modeling.

The interface has dedicated features for modeling semiconducting and insulating materials, as well as boundary conditions for ohmic contacts, Schottky contacts and gates. In addition to the dedicated semiconductor user interfaces, the module also includes enhanced capabilities for simulating electrostatic behavior. In addition, an interface for electrical circuits with a SPICE import capability can be coupled to the device level simulations enabling mixed device and system level modeling.

The Semiconductor Module Model Library contains a suite of models with step-by-step instructions that demonstrate how to use the interface for simulating a range of practical devices. Device applications that can be analyzed using the Semiconductor Module include: PN junctions, bipolar transistors, metal-oxide-semiconductor field-effect transistors (MOSFETs), metal semiconductor field-effect transistors (MESFETs), thyristors, and Schottky diodes.

## Electrochemistry Module

The Electrochemistry Module augments your workflow in understanding, designing, and optimizing electrochemical systems through precise and efficient simulation. This includes modeling the electrochemical reactions, current density distributions, and material transport in applications such as electroanalysis, electrolysis, electrodialysis, electrochemical sensors, and bioelectrochemistry. This is the ideal design and verification tool for the researcher working in the lab or the industrial chemical engineer.

Specialized interfaces in the Electrochemistry Module allow for the straightforward definition of coulometry, potentiometry, voltammetry, amperometry, and electrochemical impedance spectroscopy studies. From here, simulation can be used together with experiment to calculate parameters such as exchange current densities and activation overpotentials.

The Electrochemistry Module also provides interfaces for modeling systems assuming primary, secondary, or tertiary current distributions using the Butler-Volmer and Nernst-Planck equations. Together with interfaces for surface and homogeneous chemical reactions, material transport in dilute and porous media, flow in free and porous media, electric currents, and heat transfer, the Electrochemistry Module covers an extensive range of applications involving electrochemical reactions. This includes pH, glucose and gas sensors, chlor-alkali and aluminum electrolytic cells, the production of hydrogen and oxygen through electrolysis, the desalination of seawater and treatment of waste electrolyte, and the study of electrobiochemical systems in bioengineering and biomedical applications.

## Mesh and Geometry

### 2D Modeling Work Planes from 3D CAD Cross Sections

You can now make quick what-if studies in 2D on cross-sections of 3D CAD models. Partition your 3D geometry model with a Work Plane and create a separate 2D model on the resulting Cross Section geometry. This modeling technique can be used to complement realistic, but heavy-to-compute, 3D simulations with one or more simulations on 2D planar intersections. Understanding of the process to be modeled, and certain parameters and solver settings can be fine-tuned prior to tackling the 3D simulation.

A further advantage is to exploit rotational symmetry to reduce simulation time: In a 3D geometry that is rotationally symmetric around an axis, you can easily apply a Work Plane from the axis to the geometry edge and then perform a 2D axisymmetric simulation. Related to this is a new utility for axisymmetric geometry models: the part of your 2D cross-sectional geometry that has negative radius coordinates is now automatically removed before meshing. Another example where the 2D Cross Section tool is useful is for a 3D geometry that was originally constructed in a CAD software by extruding, revolving, or embedding a sketch plane. You can now use the Cross Section feature to recover the original 2D sketch plane geometry.

### Increased Automation for Swept Meshing

The swept mesher now automatically analyzes the geometry model in order to minimize the number of source and destination surfaces that need to be manually defined. For certain types of geometry models, manual intervention is no longer required when creating a swept mesh.

### Visualization of Intersection in Work Plane

When drawing in a work plane, the intersections of all 3D objects with the work plane can be visualized as blue curves. (In version 4.3a, you could see either the projection of the 3D edges onto the work plane, or the 3D edges that lie in the work plane, but not the intersections.)

### Message About Number of Geometric Entities

When the Form Union and Form Assembly feature is built, a message containing the number of objects and entities will be printed in the Messages window. This can be used to detect errors in the geometry, for example, when an unwanted thin domain has been created due to a mismatch between objects.

### Named Selections in the Geometry Sequence

You can now add selection features in the geometry sequence: Explicit (former Object Selection), Ball, Box, Cylinder, Union, Intersection, Difference, Complement, and Adjacent. Use these to select domains, boundaries, edges, or vertices in geometry objects, or entire geometry objects. You can refer to the named selection in input selections in subsequent geometry features. Important applications include those where geometric entities are deleted. You can, for example, select a large number of faces using a Box Selection, and then delete them using Delete Entities. Another example is to select a loop of edges using an Explicit Selection with Group by continuous tangent selected, and then use this selection in a Cap Faces feature. You can also use the resulting selections in physics, meshing, selections under Definitions, etc. Geometry selections provide a very robust associative mapping technique for selections used in a parametric sweep when there are potentially large, topological changes.

### New Virtual Geometry Operations: Merge Edges and Collapse Faces

Using the Collapse Faces operation, you can collapse a small face into a vertex and a narrow face into one or more edges. By default the Collapse Faces operation tries to ignore the resulting merged vertex or edges. The operation has built-in heuristics to determine how to collapse the selected face. If the operation fails to determine how to collapse a face you get the error "Failed to determine how to collapse this face. Use the Merge Edges operation or the Collapse Edges operation instead." Then, you should use the Merge Edges operation if you want to collapse the face into one or more edges or the Collapse Edges operation if you want to collapse the face into a vertex.

**Collapse Faces**

Using the Collapse Faces operation, you can collapse a small face into a vertex and a narrow face into one or more edges. By default the Collapse Faces operation tries to ignore the resulting merged vertex or edges. The operation has built-in heuristics to determine how to collapse the selected face. If the operation fails to determine how to collapse a face you get the error "Failed to determine how to collapse this face. Use the Merge Edges operation or the Collapse Edges operation instead." Then, you should use the Merge Edges operation if you want to collapse the face into one or more edges or the Collapse Edges operation if you want to collapse the face into a vertex.

**Merge Edges**

The Merge Edges operation allows you to specify the edges to keep and remove, respectively, when collapsing a face. The selected edges to keep and remove must belong to the same face. The operation automatically determines the (short) edges to collapse, if any.

### New Geometry Operations for Solids, Surfaces, and More

You can use the new Boolean operation, Partition, to partition a geometry object using one or several tool objects. You can use this, for example, to create an interior boundary in a solid object, using a surface or work plane as a tool object. The Boolean operations, Union, Intersection, Difference, Compose, and Partition, now support all types of geometry objects: solids, surfaces, edges, and points. A typical application of this would be to trim surface objects either by intersecting it with a solid object or by subtracting it from an overlapping surface.

### Continue Meshing Functionality for the Swept, Boundary Layer, and Mapped Mesher

Continue meshing means that the mesher does not stop with an error if it encounters a problem when meshing a geometric entity. Instead, it continues meshing the remaining entities and returns the resulting mesh together with error and warning nodes containing information on the encountered problems. This makes it easier to understand the reason for a meshing failure and how to avoid it.

### Imported Meshes: Cylinder Selection, Minimal Boundary Partitioning, and 2D NASTRAN Import

- Cylinder selection has been added to the previous Ball, Box, and Logical Expression mesh selection tools. Using the Cylinder feature for an imported mesh, you can partition the mesh according to an element set defined by the coordinates of a cylinder.
- There is a new Minimal option for Boundary Partitioning of imported meshes. If you choose this option and import a mesh from a file, then the import operation does not introduce any additional boundary partitioning than what is already specified in the original file, and what is required by the topological criteria for geometric boundaries used by COMSOL.
- It is now possible to import a NASTRAN file defining a planar surface mesh located in the xy-plane, with arbitrary z coordinates, as a 2D mesh.

## Results

### Isosurface STL Export

You can now export the geometry shape information as a triangular surface mesh of a 3D volume, surface, slice, multislice, isosurface, or far field plot to an STL file. The resulting STL file is a surface mesh, and not a true CAD representation, that can be used with dedicated CAD software packages for redrawing the model using CAD solid and surface operations. The surface mesh can also be used for shell (but not solid volume) simulations in COMSOL.

### Additional Image Export Functionality

TIFF and GIF export are now supported in addition to BMP, JPEG, and PNG. The quality of exported JPEG images can be controlled with a new setting for the compression rate.

### Color Expressions for 1D Plots

Color expression attributes could previously only be added to 2D and 3D plots. Now it is possible to add color expressions to the following 1D plots: Line Graph, Point Graph, Global. This enables the simultaneous visualization of two quantities in the same 1D plot.

### Reversed Arc Length for Line Graphs

Reversed arc length can be the x-axis parameter in line graphs. This makes it easier to produce 1D plots with a consistent arc length direction for circular loops and curves consisting of multiple curve segments.

## Studies and Solvers

### Sensitivity Study Type

A new Study type allows for a wide range of sensitivity analyses of the relationship between variations in input to variations in output of a simulation. In the Sensitivity Study type you may select model parameters to use as sensitivity variables. For example, in a mechanical simulation you can use this to predict what effect changing a geometrical parameter of a part has on its overall stiffness.

This is convenient if your model is already parameterized, provided that the parameters are used only in places where COMSOL Multiphysics accepts an expression containing the dependent field variables. Sensitivity in geometric dimensions are handled through the Deformed Geometry user interface which deforms the background finite element mesh. This technique can also be used to determine the impact of post-manufacturing errors on the operation of a mechanical part since the Deformed Geometry operation can be applied to the original CAD model even when the original parameterization is lost. Two different sensitivity methods are available: Forward and Adjoint.

### Stop Condition Updates

The Stop Condition feature that triggers termination of a transient simulation has several important updates.

**Multiple Stop Expressions and Support for Boolean Expressions**

The Stop Condition feature now supports a table of multiple stop expressions. Each expression can be evaluated to stop either on Negative (<0) or True (>=1), allowing for boolean expressions. In addition, a user defined description can be entered that is an output to the solver log when the stop occurs.

**Stop on Events**

In Time Dependent Studies there is now support in the Stop Condition feature to stop on an Implicit Event. All Implicit Events in the model are shown in the table and the user selects the ones to trigger a stop.

**Output at Stop**

The user can now choose to have the solver steps before and after the stop added as solutions. For event stops, this means before and after reinitialization.

**Store Solution Before and After Events**

In the Output block of the Time-Dependent Solver, the user can now set the option to store additional solutions before and after events (regardless if they are set to stop or not). The solutions stored are the ones before and after reinitialization at the event.

### Memory Information in Log Window

After solving, the Log window now displays the maximum amount of Physical and Virtual Memory that was used during the solution.

### Saving Solutions at Intermediate Parameter Values

You can now specify the path for saving solutions at intermediate parameter values to file during parametric sweeps. For the Keep Solutions in Memory setting, select Only Last, and you will get a text field for typing a Filename.

### Go to Source for Physics and Variables Selection

In the tree view under Physics and Variables Selection in the study step node’s Settings window, there is now a Go to Source button that you can click to move to the corresponding node in the model tree. The geometry in the Graphics window also displays the selection for the nodes that you click in the study step node’s physics tree.

## COMSOL Multiphysics

### Coordinates Systems for Curved Geometric Shapes

A new tool for automatic coordinate system creation makes it easy to define anisotropic material properties that follow curved geometric shapes. The Curvilinear Coordinates interface lets you choose between three different methods representing different properties of the computed coordinate system: Diffusion Method, Elasticity Method, and Flow Method. Several methods are available since different engineering disciplines have different requirements and there is no one unique definition of a shape-following coordinate system. The new Curvilinear Coordinate Systems can be applied for any type of physics that emphasize anisotropic thermal conductivity in heat transfer, orthotropic materials for structural mechanics, and anisotropic media in electromagnetics.

### Documentation Updates

The COMSOL Multiphysics Reference Manual replaces the earlier COMSOL Multiphysics User's Guide and COMSOL Multiphysics Reference Guide and provides a single comprehensive resource for documenting the functionality of COMSOL Multiphysics.

The COMSOL Installation Guide replaces the earlier COMSOL Installation and Operations Guide and COMSOL Quick Installation Guide with more focus on how to install the COMSOL software. Information about COMSOL commands and its general operation is now available in the COMSOL Multiphysics Reference Manual.

### File Locking

With version 4.3b, only one user can open and edit an MPH-file at the same time. If you try to open an MPH-file that is already open in another COMSOL Desktop, that MPH-file is locked, and you can only open the MPH-file in a read-only mode. That means that you can edit the model but you cannot save it unless you save the MPH-file with another name. When an MPH-file is locked, COMSOL creates a separate lock file with the same filename as the MPH-file plus the extension .lock, stored in the same directory as the locked MPH-file. If a lock file remains after all COMSOL Desktop sessions have ended, you can reset the lock when opening the file by clicking Reset Lock and Open.

### Curvature Variables

Variables evaluating the principal curvatures and principal curvature directions are now available on all boundaries. Not only can you use these variables for postprocessing but you can also use them as part of mathematical expressions defining materials or boundary conditions. Applications are numerous and this functionality is important for any type of physics which involves dependencies on curvature.

### New Units

Three new units have been added for more convenient modeling:

- For force, the kilopond is introduced, with the COMSOL units, *kp* or *kpf*
- For pressure, inches of water is introduced, with COMSOL units, *inAq* and *inH2O*
- For dynamic viscosity, poise is introduced, with COMSOL unit, *P*. You can also use *cP* for centipoise, as well as other standard prefixes.

## CAD Import Module and LiveLink™ Products for CAD*

### CAD Import Module

If you have licensed the CAD Import Module, you can now export your geometry to the ACIS file (.sat or .sab) format in addition to all previous formats.

File import for the latest versions of several leading CAD packages are now supported:

- SolidWorks(R) 2013
- Autodesk Inventor(R) 2013
- Creo(TM) Parametric 2.0

### LiveLink™ *for* SolidWorks®

Synchronizing the geometry between SolidWorks® and COMSOL now also includes material selections. Selections that contain synchronized geometry objects (bodies) are created in COMSOL based on the material definitions from the CAD design. The selections are named after the material name in SolidWorks. Use these selections as input for geometry features requiring object selections, or for any model definitions, physics, or material settings requiring domain selections. The LiveLink node in the COMSOL Model Tree contains a table with a list of the synchronized selections.

### LiveLink™ *for* Solid Edge®

To allow the user to select which parameters should be synchronized between Solid Edge and COMSOL, a dialog box has been implemented in Solid Edge®. Selected parameters are automatically transferred to COMSOL during synchronization. This means that they appear in the table in the settings window of the LiveLink feature node, such that the user does not need to manually enter parameters in the Solid Edge geometry. Thus it is now much faster to set up a geometric parameter sweep or optimization when working with LiveLink™ *for* Solid Edge®.

### LiveLink™ *for* Inventor®: One Window Interface

The collaboration between COMSOL and Autodesk is growing with an extension of the functionality of LiveLink™ *for* Inventor® to provide a One Window Interface. Users of Autodesk Inventor are now able to perform their multiphysics analyses directly within the Inventor environment. All of the COMSOL modeling tools are available in the Autodesk Inventor User Interface, while changes in geometry are synchronously updated between the two packages.

### LiveLink™ *for* SpaceClaim®

It is now much easier and quicker to set up a geometric parameter sweep or optimization when working with LiveLink™ *for* SpaceClaim®. User-defined geometry dimensions created in SpaceClaim are automatically transferred to COMSOL during synchronization. You no longer need to manually enter parameters to control the SpaceClaim geometry.

## LiveLink™ *for* Excel®

### Work with Multiple Files, Excel® 2013, Interpolation Functions, and Tables

- You can open multiple COMSOL models from Excel® with the limitation of one model per Workbook.
- File locking is supported when opening a COMSOL model using the Open button on the Excel ribbon; if you attempt to open a file that is already opened, you can do so in read-only mode.
- Version 4.3b comes with support for Excel 2013, the Desktop Version, in addition to the previous Excel 2007 and Excel 2010 (Windows only).
- Excel files data can be now be used in interpolation functions.
- Excel files can now be exported from Tables.

### Material Export from Excel® to COMSOL

Material data in spreadsheets can now easily be exported from Excel® to COMSOL's Material Browser and saved in your own material library. The Material Export Settings allows you to specify the material name and material property data to include in your library. You also have the option to Append a material to an existing library.

## LiveLink™ *for* MATLAB®

LiveLink™ *for* MATLAB® includes three new functions: mphsolution, mphtable, and mphparticle.

- You can now retrieve information on the solution object using the function mphsolutioninfo for different inner and/or outer parameters.
- Data in columns and headers of a table contained in a COMSOL model can now be retrieved using the function mphtable at the MATLAB® command prompt.
- When using LiveLink™
*for*MATLAB® together with the Particle Tracing Module, you can now obtain information along particle trajectories for quantities such as particle position, particle velocities, or any Results expressions. The new function mphparticle only supports particle datasets created with the Particle Tracing Module.

## Disclaimer

COMSOL, COMSOL Multiphysics, Capture the Concept, COMSOL Desktop, and LiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see http://www.comsol.com/tm.

## CFD Module

### Frozen Rotor for CFD Rotating Machinery

The Frozen Rotor feature efficiently solves for the pseudo-steady flow field in rotating machinery for laminar and turbulent flows. This functionality is offered as a study type for the Rotating Machinery, Fluid Flow user interface and is equivalent to solving for the stationary Navier-Stokes equations where centrifugal and Coriolis forces have been added to the rotating domains.

The term "frozen" refers to the fact that the rotor will be frozen in position compared to its surrounding non-rotating parts, such that all components of the system are in fact stationary. If the non-rotating part of the geometry is rotationally invariant, or the model contains only one rotating domain, then the Frozen Rotor method will give a steady-state solution corresponding to the same model solved using the Rotating Machinery user interface. In other cases the method will give a more approximate solution, the quality of which depends on the position of the rotor, and how close the frozen and stationary components are to each other. Examples where the full Rotating Machinery solution can also be obtained with the Frozen Rotor feature include mixers without baffles and where the entire system rotates, such as centrifugal separation in a lab-on-a-chip.

Examples where the Frozen Rotor solution can be strongly dependent on the rotor position are turbines and mixers with baffles. In these cases, the Frozen Rotor method can be used to obtain a starting solution for a transient simulation to then be solved using the Rotating Machinery user interface. From here the Rotating Machinery method is used to reach pseudo-steady state, in a much quicker time than if it is used from the beginning. If the Rotating Machinery method starts with a zero velocity, it may require 10-50 rotations before pseudo-steady state is reached. Whereas, starting with a Frozen Rotor solution, pseudo-steady state is often reach within ten rotations or less, saving precious simulation time.

### Thin Screens for CFD

Using the Screen feature for thin permeable barriers makes it easy to model screen-like components such as wire-gauzes, grilles, and perforated plates. It is available for Single-Phase Flow, Non-Isothermal Flow, and Conjugate Heat Transfer, and supports both laminar and turbulent flow. For easy characterization of the flow properties through a screen, you can specify correlations for resistance and refraction coefficients.

### Swirl Flow in Mixture Model and Bubbly Flow

Swirl Flow is now handled by the homogenized two-phase flow user interfaces, Mixture Model and Bubbly Flow. A new Swirl Flow property checkbox adds an out-of-plane velocity component for a 2D-axisymmetry Study.

### SST Turbulence Model

The CFD Module now includes the Shear Stress Transport (SST) turbulence model, which is a two-equation low-Reynolds number Reynolds-averaged Navier–Stokes (RANS) turbulence model. Being a low-Reynolds turbulence model, it is characterized by the fact that it doesn't use wall functions. Historically, the SST turbulence model has mainly been used to simulate exterior flows, typically wings and wing-like geometries as well as turbines. However, the SST model is a popular tool for general engineering applications and has been applied successfully to many other situations.

A new benchmark model of a NACA 0012 wing profile is included in the Model Library of the CFD Module. The SST model requires a rather fine resolution at the walls and is not suitable for external flows where the geometries are not slender or internal flows with sudden expansions. The main advantage of the SST turbulence model is that it combines the best of two worlds: the popular k − ω and k − ε turbulence models. It is formally a mix between the k − ω model and the k − ε model, but the k − ε part is reformulated so that the model solves for the turbulent kinetic energy, k, while the k − ω part solves for the specific dissipation rate, ω. The underlying idea is that k − ω is better than k − ε close to walls, while k − ε behaves better in the free-stream. The model achieves this swapping between the models by introducing a blending function which has the effect that the model is equivalent to k − ω close to walls and equivalent to k − ε far from walls.

### New CFD Solver

Virtually all fluid flow user interfaces now default to a multigrid solver that uses a new Symmetrical Coupled Gauss-Seidel (SCGS) smoother and is available for linear P1+P1 elements. Performance improvement varies between models, but typically you can expect to reduce the total computational time by about 25%. The SCGS smoother is more robust than previously used smoothers. For challenging turbulent flow simulations, where previously direct solvers were needed, you can now in many cases use this new default solver and reduce memory requirements. The new SCGS smoother is fully functional in combination with the Laminar Inflow boundary condition and removes previous limitations related to mesh anisotropy.

### Automatically Included Stefan Velocity

The Stefan velocity is automatically accounted for in the Reacting Flow user interface. The Stefan velocity is acting in the normal velocity, and is always automatically added by the Wall feature. It is initialized as zero. When a Flux or Mass Fraction feature is added on the same boundary, a corresponding addition to the Stefan velocity is added. The fact that the Stefan velocity is added in the normal direction is seen in the equation display for the Wall feature. The definition and application of the Stefan velocity is automatic, except for the need to prescribe mass boundary conditions on a wall. This new feature makes it easy to add or remove one or several species on a wall when solving for Transport of Concentrated Species. The flux for the species without boundary condition will automatically be zero as a result of the Stefan velocity.

## Pipe Flow Module

### Two-Phase Flow in Pipes

Two-phase pipe flow for gas-liquid mixtures has been added to the Pipe Flow Module. It is based on homogenized modeling and solves for one fluid's velocity/pressure field and then adjusts either the friction factor or Reynolds number according to quality (mass fractions gas phase). A correction factor needs to be given and can be taken from literature. The two-phase flow interface is robust in its simplicity, as it does not incorporate phase transition, compressibility, or liquid holdup.

### Pipe Acoustics in the Frequency Domain

When combined with the Pipe Flow Module, the Acoustics Module features a new Pipe Acoustics user interface for modeling the propagation of sound waves in flexible pipe systems in the frequency domain. The new user interface comes with a library of different engineering end-impedance models. This 1D application along edges solves for the acoustic pressure and acoustic particle velocity averaged on the pipe cross-section. A stationary background flow can optionally be included. The interface is available in 3D on edges and points, and in 2D on boundaries and points. See also the news for the Acoustics Module.

## Microfluidics Module

### New Model Tutorial: Topology Optimization of a Tesla Microvalve

This new model tutorial performs a topological optimization for a Tesla microvalve. A Tesla microvalve inhibits backwards flow using friction forces rather than moving parts. The design can be optimized by distributing a specific amount of material within the modeling domain. The goal is to maximize the ratio of the pressure drop for the forwards and backwards flow across the device.

## Subsurface Flow Module

### Heat Transfer with Phase Change

The Apparent Heat Capacity Method makes the modeling of phase change easier. Previously, you had to account for the phase change in energy balances by using equation-based modeling. The implementation of this method simplifies your workflow by allowing specification of a few input quantities the:

- Material states before and after the transition
- Phase change temperature
- Transition temperature interval between phases
- Latent heat

The Apparent Heat Capacity Method modifies the four material properties of density, heat capacity, thermal conductivity, and the ratio of specific heats, by smoothing the discontinuous jump at the phase change temperature and adding a distributed latent heat contribution to the heat capacity at the phase change temperature. The tutorial models in the Model Library, which involved a phase change, have been updated to utilize and exemplify this feature.

### Heat Transfer in Porous Media

The Heat Transfer in Porous Media user interface has been reworked to also include a new domain feature makes modeling more convenient. This replaces the previous Heat Transfer in Fluids and Porous Matrix user interface.

## Heat Transfer Module

### Multi-Wavelength Heat Radiation

Common glass is transparent for light at visible wavelengths but opaque for infrared and ultraviolet light. When an incident light passes through it, it often changes wavelength when it reflects off a surface. If the reflected light is in the infrared spectrum, it will not escape the glass enclosure. This leads to the well-known greenhouse effect, heating up the enclosure.

With the new Multiple Spectral Bands interface, you can define up to 5 spectral bands with user-defined maximum and minimum wavelengths per interval. There is also a quick setting for Solar and Ambient radiation, which covers the common case of just two bands. You can define a blackbody ambient source that distributes its power across the different channels according to a Planck distribution parametrized with the ambient temperature. Emissivity surface properties are defined separately for each spectral band, as well as blackbody surface fractional or user-defined emissive power. Another useful radiation-based enhancement is support for transparent media with a non-unity refractive index.

### Heat Transfer with Phase Change

The Apparent Heat Capacity Method makes modeling phase change of materials easier. Previously, you had to account for phase change in energy balances by using equation-based modeling. The implementation of this method simplifies your workflow by allowing specification of a few input quantities:

- Materials before and after the transition
- Phase change temperature
- Transition temperature interval between phases
- Latent heat

The Apparent Heat Capacity Method modifies the four material properties of density, heat capacity, thermal conductivity, and the ratio of specific heats, by smoothing the discontinuous jump at the phase change temperature and adding a distributed latent heat contribution to the heat capacity at the phase change temperature. The tutorial models in the Model Library that have involved a phase change have been updated to utilize and exemplify this feature.

### Thermal Contact

The heat flux across a thin layer between two contacting surfaces is proportional to the temperature difference over the layer where the constant of proportionality is the thermal contact conductance. This term relies on the degree of contact: the greater the contact forces, the greater the conductance between these two surfaces. A new boundary condition in the Heat Transfer Module allows for the thermal contact conductance between two contacting surfaces to vary with contact pressure, by allowing for three contributions to the thermal conductance:

- Thermal Constriction Conductance: this relates to the actual contact occurring between two surfaces, which depends on the surface properties and the contact pressure. It represents the fact that when the pressure increases, the actual contact and conductance also increase.
- Gap Conductance: this describes thermal contact conductance affected by the presence of thin layers of fluids between surfaces, typically air. It is negligible when the contact pressure is significant, but can play an important role just prior to good contact as high pressures are being applied. Applying highly-conducting thermal grease between contacting surfaces is a common method to overcome unwanted Gap Conductance effects.
- Radiative Conductance: This assumes that the two surfaces can be represented in the contact region by two radiating, parallel plates. Radiative conductance is the contribution to thermal contact conductance caused by surface-to-surface radiation.

In many cases the contribution from Gap Conductance and Radiative Conductance can be neglected. Each of the three thermal contact conductance contributions can be evaluated based on either predefined correlation curves or coupled with structural mechanics contact from the Structural Mechanics or MEMS Modules. A friction heat source can also be represented, including a heat partition coefficient. The Thermal Contact feature can be applied to internal boundaries as well as to pairs in an assembly.

### New Models

The following models are new to the Heat Transfer Module Model Library:

**Condensation Detection in an Electronic Device:**

This example simulates the thermodynamical evolution of moist air in an electronic box with the aim of detecting whether condensation occurs when the external environment properties change. The model imports measured data for the air temperature, pressure, and water vapor concentration.

**Freeze Drying:**

This example models the process of ice sublimation in a vial under vacuum-chamber conditions, a test case for many freeze-drying setups.

**Tin Melting Front:**

This example demonstrates how to model phase transition by a moving boundary interface according to the so called Stefan problem. A square cavity containing both solid and liquid tin is submitted to a temperature difference between left and right boundaries.

**Shell and Tube Heat Exchanger:**

This model includes two separated fluids with different temperatures which flow through the heat exchanger, one flows through the tubes (tubeside) and one through the shell around the tubes (shellside).

**Electronic Enclosure Cooling:**

This study simulates the thermal behavior of a computer power supply unit (PSU).In this model, an extracting fan and a perforated grille cause an air flow in the enclosure to cool internal heating.

**Cross-Flow Heat Exchanger:**

This model solves the fluid flow and heat transfer in a micro heat exchanger made of stainless steel. These types of heat exchangers are found in lab-on-chip devices in biotechnology and microreactors, for example, for micro fuel cells.

**Plate Heat Exchanger:**

This tutorial illustrates one of the most common heat exchanger devices, which can be used to either cool or heat fluids and solids.

**Thermal Contact Resistance Between an Electronic Package and a Heat Sink:**

This example reproduces parts of the study of a publication on the thermal contact resistance at the interface between a heat sink and an electronic package. This model focuses on the heat transfer through the contact interface where four parameters influence the joint conductance: contact pressure, microhardness of the softer material, surface roughness, and surface roughness slope.

**Contact Switch:**

This model illustrates how to implement a multiphysics contact. It models the thermal and electrical behavior of two contacting parts of a switch. The electrical current and the heat cross from one part to the other only at the contact surface.

### Thermal Diffusivity Variables

Variables are now available for the mean thermal diffusivity, and for the thermal diffusivity tensor components, .

### Thermal Resistance Input for Thin Thermally Resistive Layers

In addition to the previously available Layer thickness and thermal conductivity, you can now also use a Thermal resistance option for Thin Thermally Resistive Layers.

### Heat Transfer in Porous Media

The Heat Transfer in Porous Media user interface has been reworked with a new domain feature. This replaces the previous Heat Transfer in Fluids and Porous Matrix user interface and makes modeling more convenient.

### Moist Air Conversion Functions

Three new functions have been added to convert relative humidity into vapor concentration or moisture content and to quickly get the saturation pressure:

- Relative humidity to vapor concentration: fc(RH,T,pA)
- Relative humidity to moisture content: fxvap.(RH,T,pA)
- Saturation pressure function: psat(T)

## Structural Mechanics Module

### Bolt Pre-Tension

The new Bolt Pre-Tension feature is used for modeling pre stressed bolts. It is available in the Solid Mechanics user interface where, for each physical bolt, a Bolt selection subfeature is available. You select a boundary that describes a cross-section through each bolt. Each bolt will generate results quantities for postprocessing: bolt force, bolt shear force, and pre deformation.

### Setting the Center of Rotation for Rigid Connector

The center of rotation for a rigid connector can be defined as the centroid of an arbitrary combination of geometrical entities, which does not need to be part of the selection for the Rigid Connector itself. For example, this makes it easy to create an arbitrary point on a rigid connector surface, or in a rigid domain, and use that as the center of rotation. This functionality is available only in the Solid Mechanics user interface.

### Beam Cross Section User Interface

A new Beam Cross-Section user interface automatically computes beam properties based on a general beam cross-section model created as a 2D geometry object.

The following beam cross-section data can be computed:

- Area
- Center of gravity
- Moments of inertia
- Principal axis directions
- Torsional rigidity
- Torsional section modulus
- Distribution of stresses from bending, torsion and shear
- Shear center
- Shear area
- Warping constant
- Warping section modulus

It is also possible to evaluate the stress distribution in the cross section, given a set of section forces: axial force, bending moments, shear forces, and twisting moments. When coupled with beam elements in 3D this provides a high-fidelity method for stress evaluation in critical cross-sections of a beam.

## Fatigue Module

### Rainflow Analysis with the Palmgren-Miner Rule

A new fatigue feature called Cumulative Damage evaluates fatigue caused by a variable or random amplitude load. An irregular structural response is first processed with the Rainflow counting algorithm. Three options for stress evaluation are available: principle stress and von Mises stress with a sign determined by principle stress or hydrostatic stress. The damage is calculated using the Palmgren-Miner rule and takes into account the influence of the R-value which can be provided through the limiting S-N curve. The load cycle can be specified in two ways, either as the solution history or via the generalized loads. The first method processes solution by solution and can take into account non-elastic effects. In the second method, the load is created as the superposition of a few basic load cases. This allows for evaluation of large load histories such as the processing of 10000 load steps. A new Matrix Histogram plot is used to visualize the results of the Rainflow cycle count

### More Analysis Types: Shell, Plate, and Multibody Dynamics

The Fatigue Module can now be used together with the Shell, Plate, and Multibody Dynamics user interfaces in addition to the previously available support for Solid Mechanics, Thermal Stress, Joule Heating and Thermal Expansion, or Piezoelectric Devices.

## Nonlinear Structural Materials Module

### Three New Hyperelastic Material Models

Three new hyperelastic material models are added: Gent, Gao, and Storakers, for simulation of rubber-like materials.

## Acoustics Module

### Pipe Acoustics in the Frequency Domain

When combined with the Pipe Flow Module, the Acoustics Module features a new Pipe Acoustics user interface for modeling the propagation of sound waves in flexible pipe systems in the frequency domain. The new user interface comes with a library of different engineering end-impedance models. This 1D application along edges solves for the acoustic pressure and acoustic particle velocity averaged on the pipe cross-section. A stationary background flow can optionally be included. The interface is available in 3D on edges and points, and in 2D on boundaries and points.

### Additional Material Inputs for Thermoacoustics

The material input for the Thermoacoustic interface has been updated to include options for entering the compressibility and the coefficient of thermal expansion. This enables modeling the propagation of compressible waves (sound waves) in any fluid with user-defined inputs and non-standard constitutive relations. Several options exist for entering these coefficients.

### New Model Tutorials

Several new model tutorials are available, including:

- Lumped Loudspeaker Driver
- Focused Ultrasound Induced Heating in Tissue Phantom
- Vibrating Micromirror with Viscous and Thermal Damping
- Vibrating Particle in Water with Thermoacoustic Material Parameters

## AC/DC Module

### Boundary Coils

Coils with very thin cross-sections can now be modeled as boundaries. This avoids the need to mesh the thickness of thin coils resulting in excessive mesh count and memory usage. Both single-turn and multi-turn coil models are available for both 2D and 3D. The Single-turn coils feature includes lateral skin effect and is a tailored application of the previously available Electric Currents, Shell user interface.

### New Magnetics Solver

New solver technology in the AC/DC Module speeds up magnetics simulations. A new preconditioner called Auxiliary Space Maxwell Solver (AMS) is now available as an iterative solver option. AMS is applicable to stationary or time-dependent magnetics simulations where vector finite elements are used. It is used together with the Geometric Multigrid Solver (GMG) with AMS as a Coarse-level solver in the multigrid hierarchy; this is also the new default setting. The speedup is around 20% for smaller models but the new GMG+AMS combination scales beneficially compared to previous solvers for larger models with millions of degrees of freedom.

### New Boundary Conditions for Oxide Layers, Conductive Magnetic Shields, and Cracks in Metallic Components

The Magnetic and Electric Fields user interface allows for several new combinations of magnetic and electric boundary conditions: Magnetic Shielding with Electric Shielding, Electric Insulation and Contact Impedance, as well as Magnetic Continuity with Electric Insulation and Contact Impedance. This makes it possible to model oxide layers, electrically conductive magnetic shields, and cracks in metallic structures.

### Coils: Updates to Coil Group Functionality and New RLC Coil Group

Coil Group is now a setting in the Single-Turn Coil feature and is no longer available as a separate feature. Similarly, the Coil Group setting is available for Multi-Turn Coils and the new Boundary Coils. A new subfeature allows grouping domains into a single turn with parallel and series connections of different domains.

A new RLC Coil Group can be used to approximate a 3D coil with a 2D coil model where, due to capacitive coupling or other phenomena, there is relatively significant current flow in the in-plane directions. The feature includes, in the current balance, the in-plane current flow driven by the potential difference between each turn, e.g. capacitive coupling. To ease the modeling of coils with many turns, the geometry model is automatically analyzed to create an intuitive domain number ordering.

### Magnetic Field Formulation for Materials with Highly Nonlinear Resistivity

A new user interface for materials with highly nonlinear resistivity uses a formulation of Maxwell's equations expressed directly in the magnetic H-field. Important applications include simulation of superconductive materials. To help with this, a new ”E-J Characteristic” material property group has been added to the Materials definitions. This makes it possible to specify a material nonlinearity where the current density J is a function of the electric field E.

### RC Parameter Extraction: Floating Potential Group

For resistance and capacitance (RC) parameter extraction, the new Floating potential group dramatically simplifies setup of models with a large number of floating electrodes. Each group of connected boundaries is considered as a separated electrode with a separate floating potential. This is available for the Electrostatics (capacitance extraction), Electric Currents (resistance extraction), and Magnetic and Electric Fields user interfaces.

### Electrical Contact

The new Electrical Contact feature calculates the electric current between two surfaces in contact with a conductance that varies with surface properties combined with mechanical contact pressure. It represents the well-known fact that the higher the contact pressure, the better the contact. The current flux across a thin layer is proportional to the voltage difference over the layer where constant of proportionality is the electrical conductance. The electrical conductance can be evaluated based on either a predefined correlation curve, or it can be coupled with structural mechanics contacts from the Structural Mechanics Module or MEMS Module. The Electrical Contact feature can be applied to internal boundaries as well as to pairs in an assembly.

### New Models

Some of these models are available through the Model Library Update.

**Electrodynamic Bearing:** This model illustrates the working principle of a passive electrodynamic bearing. An electrically conducting rotor rotating in a magnetic field produced by a permanent magnet induces eddy currents on the conducting rotor.

**Homopolar Generator:** A homopolar generator is composed of an electrically conductive rotating disc placed in a uniform magnetic field that is perpendicular to the plane of rotation. This example models the flow of current through the copper conductor and the rotating disc.

**Static Field Modeling of a Halbach Rotor:** This model presents the static-field modeling of an outward-flux-focusing magnetic rotor using permanent magnets. This magnetic rotor is also known as a Halbach rotor.

**Axial Magnetic Bearing Using Permanent Magnets:** This model illustrates how to calculate design parameters like magnetic forces and stiffness for an axial permanent magnet bearing.

**Superconducting Wire:** This model has been recreated using the new Magnetic Field Formulation physics user interface.

## RF Module

### Periodic Structures for Electromagnetic Waves

Periodic ports are now also available in 3D for transmission and reflection of waves incident upon a periodic structure. The Periodic port automatically calculates all possible diffraction orders for a periodic structure with higher-order diffraction phenomena. For complete generality, you can specify a Reference point subfeature to characterize a general periodic structure such as a rectangular or hexagonal lattice. Incident waves are specified with elevation and azimuthal angle.

### Lumped Elements

Passive lumped ports are now available via the Lumped Element boundary condition which makes it easy to compute S-parameter matrices without generating unnecessary S-parameter entries. Three types of lumped elements are available: Uniform, Coaxial, and User defined. For frequency domain computations, Z, L, and C inputs are available; for the transient case, Z is available.

### Analytical Circular Port in 3D

The analytical Circular Port feature for 3D models provides predefined modes similar to what was previously available for the Rectangular Port feature. This feature is available for frequency domain studies only and includes TE and TM mode types.

## MEMS Module

### Thermal Expansion for Piezoelectric Devices

Thermal expansion is now available in the Piezoelectric Devices user interface. The temperature used can be either a given temperature constant or expression, or the temperature field variable for a full Heat Transfer simulation.

## Plasma Module

### Collisionless Heating

A collisionless heating feature has been added based on the Hagelaar model. The feature adds an additional heat source for the electrons to mimic the effect of collisionless heating. This feature is available for 2D axisymmetric models and it introduces an extra dependent variable for the out-of-plane electron drift velocity.

## Chemical Reaction Engineering Module

### Thin Impermeable Barrier

A new boundary condition, Thin Impermeable Barrier, is available on interior boundaries in several mass transport user interfaces. It makes it possible to define a wall condition between two fluid domains with a no-mass-flux condition on both sides. This is especially useful for representing thin walls as interior boundaries. You no longer need to define a solid domain with a no-mass-flux condition on both sides, which can result in a dense mesh. Thin Impermeable Barrier can also be combined with the Interior Wall or Rotating Interior Wall conditions. The Thin Impermeable Barrier boundary condition is available in the following user interfaces: Transport of Concentrated Species, Solute Transport (Subsurface Flow Module), Species Transport in Porous Media, Reacting Flow.

## Batteries & Fuel Cells Module

### New and Updated Models

The following models are new to the model library of the Batteries & Fuel Cells Module:

- Fuel Cell with Serpentine Flow Field
- Lithium-Ion Battery Model with Multiple Intercalating Electrode Materials
- Single Particle Model of a Lithium-Ion Battery

In addition, the Vanadium Redox Flow Battery model has been revised.

### Limiting Current Density and Edge Electrode

There is now a Limiting Current Density feature in the Electrode Kinetics section of the Porous Electrode Reaction and the Electrode Reaction nodes.

A new Edge Electrode feature can now be found in the Secondary Current Distribution user interface. Use the Edge Electrode with 3D models to simulate an electric current conduction in the tangential direction of an edge. The feature is the first of its kind in the COMSOL environment and is particularly suitable for geometries such as long pipes and thin wires where the electric potential variation within the electrode in the normal direction to the electrode surface is negligible. This assumption allows for the thin electrode domain to be replaced by a lumped one-dimensional partial differential equation formulation on the edge. In this way it is possible to reduce the problem size and avoid potential problems with mesh anisotropy in the thin layer. Edge Electrode Reactions can be added to the Edge Electrode feature to model electrode reactions. This functionality is available in all of the Batteries & Fuel Cells, as well as the Electrodeposition, Corrosion, and Electrochemistry Modules.

### Electroanalysis

The new Electroanalysis user interface provides equations, boundary conditions, and rate expression terms for modeling mass transport of diluted species in electrolytes using the diffusion-convection equation, by solving for electroactive species concentrations. This user interface is applicable for electrolyte solutions containing a large quantity of inert “supporting electrolytes” where Ohmic loss is assumed to be negligible. The user interface includes tailor-made functionality for modeling cyclic voltammetry problems. The Electroanalysis user interface is available in all of the Batteries & Fuel Cells, as well as the Electrodeposition, Corrosion, and Electrochemistry Modules.

### Easy Switching Between Primary and Secondary Current Distributions

Switching between Primary and Secondary Current Distributions in the Secondary Current Distribution user interface can now be done by simply changing the Current Distribution Type property in the Secondary Current Distribution user interface. Both the Primary Current Distribution and the Secondary Current Distribution entries in the Model Wizard now make use of the Secondary Current Distribution user interface but with different default values for the Current Distribution Type property. This functionality is available in all of the Batteries & Fuel Cells, as well as the Electrodeposition, Corrosion, and Electrochemistry Modules.

### Additional Intercalating Material

The user interfaces for Lithium Ion Battery and Battery with Binary Electrolyte now has a new Additional Intercalating Material feature.

## Corrosion Module

### Limiting Current Density and Edge Electrode

There is now a Limiting Current Density feature in the Electrode Kinetics section of the Porous Electrode Reaction and the Electrode Reaction nodes.

A new Edge Electrode feature can now be found in the Secondary Current Distribution user interface. Use the Edge Electrode with 3D models to simulate an electric current conduction in the tangential direction of an edge. The feature is the first of its kind in the COMSOL environment and is particularly suitable for geometries such as long pipes and thin wires where the electric potential variation within the electrode in the normal direction to the electrode surface is negligible. This assumption allows for the thin electrode domain to be replaced by a lumped one-dimensional partial differential equation formulation on the edge. In this way it is possible to reduce the problem size and avoid potential problems with mesh anisotropy in the thin layer. Edge Electrode Reactions can be added to the Edge Electrode feature to model electrode reactions. This functionality is available in all of the Batteries & Fuel Cells, as well as the Electrodeposition, Corrosion, and Electrochemistry Modules.

### Infinite Electrolyte and Electroanalysis

For simulating current distribution in electrolytes that are much larger than the modeling domains, there is now a new Infinite Electrolyte boundary condition in the Secondary Current Distribution and the Corrosion, Secondary user interfaces.

A new Electroanalysis user interface enables simulation of mass transport of diluted species in electrolytes using the diffusion-convection equation, by solving for electroactive species concentrations.

This functionality is available in all of the Electrodeposition, as well as the Batteries & Fuel Cells, Corrosion, and Electrochemistry Modules.

### New Models

The following models are new to the model library of the Corrosion Module:

**Isolator Thickness Effect:**this model demonstrates the effect of aluminum isolator thickness on galvanic corrosion using a parametric study.**Corrosion Protection of a Ship Hull:**this example shows a secondary current distribution around a ship hull using an impressed current cathodic protection (ICCP) system for protection of the shaft and propeller.**Localized Corrosion:**This example demonstrates galvanic corrosion between two different phases in a magnesium alloy for a representative cross-sectional microstructure configuration.

### Easy Switching Between Primary and Secondary Current Distributions

Switching between Primary and Secondary Current Distributions in the Secondary Current Distribution user interface can now be done by simply changing the Current Distribution Type property in the Secondary Current Distribution user interface. Both the Primary Current Distribution and the Secondary Current Distribution entries in the Model Wizard now make use of the Secondary Current Distribution user interface but with different default values for the Current Distribution Type property. This functionality is available in all of the Batteries & Fuel Cells, as well as the Electrodeposition, Corrosion, and Electrochemistry Modules.

## Electrodeposition Module

### Rotating Cylinder Hull Cell

The new Rotating Cylinder Hull (RCH) cell tutorial simulates non-uniform current, potential, and concentration distributions along the working electrode of the RCH cell. Primary, secondary, and tertiary current distributions are compared, demonstrating how complexity can be gradually incorporated in the model. The example is based on a published paper. The model is axisymmetric and compares primary, secondary, and tertiary current distributions.

### Easy Switching Between Primary and Secondary Current Distributions

Switching between Primary and Secondary Current Distributions in the Secondary Current Distribution user interface can now be done by simply changing the Current Distribution Type property in the Secondary Current Distribution user interface. Both the Primary Current Distribution and the Secondary Current Distribution entries in the Model Wizard now make use of the Secondary Current Distribution user interface but with different default values for the Current Distribution Type property. This functionality is available in all of the Batteries & Fuel Cells, as well as the Electrodeposition, Corrosion, and Electrochemistry Modules.

### Limiting Current Density and Edge Electrode

There is now a Limiting Current Density feature in the Electrode Kinetics section of the Porous Electrode Reaction and the Electrode Reaction nodes.

A new Edge Electrode feature can now be found in the Secondary Current Distribution user interface. Use the Edge Electrode with 3D models to simulate an electric current conduction in the tangential direction of an edge. The feature is the first of its kind in the COMSOL environment and is particularly suitable for geometries such as long pipes and thin wires where the electric potential variation within the electrode in the normal direction to the electrode surface is negligible. This assumption allows for the thin electrode domain to be replaced by a lumped one-dimensional partial differential equation formulation on the edge. In this way it is possible to reduce the problem size and avoid potential problems with mesh anisotropy in the thin layer. Edge Electrode Reactions can be added to the Edge Electrode feature to model electrode reactions. This functionality is available in all of the Batteries & Fuel Cells, as well as the Electrodeposition, Corrosion, and Electrochemistry Modules.

### Infinite Electrolyte and Electroanalysis

For simulating current distribution in electrolytes that are much larger than the modeling domains, there is now a new Infinite Electrolyte boundary condition in the Secondary Current Distribution and the Corrosion, Secondary user interfaces.

A new Electroanalysis user interface enables simulation of mass transport of diluted species in electrolytes using the diffusion-convection equation, by solving for electroactive species concentrations.

This functionality is available in all of the Electrodeposition, as well as the Batteries & Fuel Cells, Corrosion, and Electrochemistry Modules.

## Optimization Module

### Optimization Study

The Optimization study node now includes all available optimization methods, gradient based as well as gradient free. The available methods are:

**Gradient-Based Optimization Methods**

- SNOPT
- Levenberg-Marquardt

**Gradient-Free Optimization Methods**

- Nelder-Mead
- Monte Carlo
- Coordinate search

For the gradient-free optimization methods, you can now choose a method for multiple objectives: sum of objective (the default), minimum of objectives, or maximum of objectives.

### Updated and New Models

The following models in the Optimization Module Model Library now use the Optimization study node to set up the optimization:

- Tuning Fork Optimization
- Curve Fit Mooney-Rivlin
- Horn Shape Optimization (also requires the Acoustics Module)
- Optimal Cooling (also requires the Chemical Reaction Engineering Module)
- Pipeline Insulation (also requires the Pipe Flow Module)
- Bowtie Antenna (also requires the RF Module)

## Particle Tracing Module

### Velocity Reinitialization

The velocity of a particle can be changed arbitrarily if a certain logical expression is fulfilled. This can be used for general purpose Monte Carlo simulations and is available in all user interfaces of the Particle Tracing Module.

### Monte Carlo Elastic Collisions

A Monte Carlo elastic collision option is now available in the Elastic Collision Force feature in the Charged Particle Tracing user interface. The particle velocity changes by a discrete amount if a collision occurs with a suitably high probability. The collision probability is determined by the Collision cross section and Background number density. This modeling option is useful in particle motion where the background pressure is above vacuum, such as for ion funnels and ion mobility spectrometers.

### Changing Auxiliary Variables

It is now possible to change the value of an auxiliary dependent variable when it crosses or touches a boundary and also make this available in the Wall boundary condition. This value can be a function of any combinations of particle variables and other model variables. A simple application for this is to use it to count the number of times a particle strikes a wall.