## Acoustics Module Updates

For users of the Acoustics Module, COMSOL Multiphysics^{®} version 5.3a includes a physics interface for modeling boundary elements that also has the ability to combine with finite elements in the same model, impulse response plots for ray acoustics, and a new physics interface for modeling pressure acoustics with the discontinuous Galerkin formulation. Browse these and many more Acoustics Module updates and features below.

### New Boundary Elements Interface for Acoustics

The boundary element method (BEM) is now included in the Acoustics Module in the form of a new *Pressure Acoustics, Boundary Elements* interface. The new interface, available in 2D and 3D, is well suited for frequency-domain simulations solving the Helmholtz equation with constant-valued material properties. Additionally, it is implemented as a scattered field formulation with the option of adding a *Background Pressure Field* for modeling scattering problems.

*Spatial sensitivity generated by a linear array of nine tonpilz piezo transducers driven at 10 kHz. All nine tonpilz transducers are modeled with piezoelectric materials and solids. Acoustics in the exterior part is modeled with the*

Spatial sensitivity generated by a linear array of nine tonpilz piezo transducers driven at 10 kHz. All nine tonpilz transducers are modeled with piezoelectric materials and solids. Acoustics in the exterior part is modeled with the *Pressure Acoustics, Boundary Elements* interface. The different physics are coupled using the built-in *Acoustic-Structure Boundary* multiphysics coupling.

*Pressure Acoustics, Boundary Elements*interface. The different physics are coupled using the built-in

*Acoustic-Structure Boundary*multiphysics coupling.

*Interaction between the tonpilz sonar array and a scattering object. In this model, a "sound-hard" sphere is placed roughly 30 wavelengths away from the source. The image to the left shows the sound pressure level, while the image to the right shows the deformation of the array (there is constant phase shift applied for each row).*

Interaction between the tonpilz sonar array and a scattering object. In this model, a "sound-hard" sphere is placed roughly 30 wavelengths away from the source. The image to the left shows the sound pressure level, while the image to the right shows the deformation of the array (there is constant phase shift applied for each row).

Additionally, with COMSOL Multiphysics^{®} 5.3a, you can seamlessly couple the boundary elements interface with the physics interfaces that are based on the finite element method (FEM). This includes coupling to vibrating structures, via the *Acoustic-Structure Boundary* multiphysics coupling, and coupling to FEM acoustic domains, via the new Acoustic BEM-FEM Boundary multiphysics coupling. With this hybrid approach, you can use the best suited method, FEM or BEM, where needed. For example, the interior of a vibrating structure can be modeled with FEM, which allows for more general material properties, whereas the exterior domain is modeled with BEM, which is better suited for modeling large or infinite domains.

When using BEM, only the surfaces adjacent to the modeling domain of interest need to be meshed. This significantly reduces the need for creating large volumetric meshes, making the BEM-based interfaces especially useful for modeling radiation and scattering problems with complex CAD geometries.

Typical cases where using the new BEM-based interfaces is advantageous:

- Large fluid domains that would otherwise need an FEM-based volumetric mesh
- As a replacement of an FEM-based radiation condition or an FEM-based perfectly matched layer (PML)
- Models that include an infinite wall or an infinite sound soft boundary located far away from the radiating objects (measured in terms of wavelengths)
- Modeling the interaction of radiating and scattering objects located far away from each other where the space in between would otherwise need an FEM-based volumetric mesh

Note that BEM is computationally more demanding than FEM for the same number of degrees of freedom. However, significantly fewer degrees of freedom are typically needed with BEM in order to get the same accuracy as with FEM. BEM generates fully populated or dense system matrices that need dedicated numerical methods that are different from those of FEM. When solving acoustic models of small and medium size, the FEM-based *Pressure Acoustics, Frequency Domain* interface will typically be faster than solving the same problem with BEM.

All dedicated postprocessing tools previously used for the FEM-based interfaces work out-of-the-box with the BEM-based interfaces, including the *Directivity* plot and *Far Field* plots for the spatial response assessment.

*The user interface of the*

The user interface of the *Pressure Acoustics, Boundary Elements* interface with the results of the Spherical Scatterer: BEM Benchmark model shown.

*Pressure Acoustics, Boundary Elements*interface with the results of the Spherical Scatterer: BEM Benchmark model shown.

### Acoustic-Structure Interaction with Hybrid BEM-FEM

The picture below shows an example of a loudspeaker system where the BEM-FEM approach is useful. In this case, the elastic properties of the cabinet and driver are important, and porous materials are used inside the enclosure. The interior of the speaker can be modeled using FEM with either the *Poroacoustics* model in the *Pressure Acoustics, Frequency Domain* interface or the *Poroelastic Waves* interface. The vibrating structures can be modeled with solids, shells, or both, and the exterior acoustics domain can be modeled with BEM.

*Full vibroacoustics analysis of a loudspeaker including exterior and interior acoustics, cabinet, and driver. The model couples acoustics (BEM and FEM), structural shells, and solids, using six multiphysics couplings.*

Full vibroacoustics analysis of a loudspeaker including exterior and interior acoustics, cabinet, and driver. The model couples acoustics (BEM and FEM), structural shells, and solids, using six multiphysics couplings.

*The speaker cabinet deformation (left) and the sound pressure level inside the speaker and in the near field on the back wall and on the floor (right).*

The speaker cabinet deformation (left) and the sound pressure level inside the speaker and in the near field on the back wall and on the floor (right).

**Application Gallery links for examples using the Pressure Acoustic, Boundary Elements interface:**

Spherical Scatterer: BEM Benchmark

Tonpilz Transducer Array for SONAR Systems

Vibroacoustic Loudspeaker Simulation: Multiphysics with BEM-FEM

Bessel Panel

### Impulse Response Plots for Ray Acoustics

You can now postprocess the impulse response from a ray acoustics simulation with the new *Impulse Response* plot, which reconstructs and visualizes the impulse response based on receiver data. The new *Receiver* data set collects the ray information and serves the purpose of a virtual microphone, providing data for the *Impulse Response* plot.

The *Receiver* data set calculates the virtual intersection between rays and a sphere of finite size. The sphere size can be determined either from an expression (based on the number of rays, the room volume, and the source-to-receiver distance) or it can be entered manually. The data set determines ray arrival time, recorded intensity, and frequency, and it is used by the *Impulse Response* plot. This data set can also be exported for use in an external tool. There is an option to enter a user-defined directivity for the receiver. The receiver location can easily be changed and it is not necessary to solve the model again to change the recording location for the impulse response.

The *Impulse Response* plot interprets the ray data from the receiver using an octave, 1/3 octave, or 1/6 octave frequency resolution. The same resolution should be used for all sources and wall properties, for example, the absorption and scattering coefficients, source power, and so forth. The plot generates the impulse response with a default sampling of 44,100 Hz.

*The COMSOL Multiphysics*

The COMSOL Multiphysics^{®} GUI shown with the Small Concert Hall Acoustics model and the Settings window for the *Impulse Response* plot and the resulting impulse response.

^{®}GUI shown with the Small Concert Hall Acoustics model and the Settings window for the

*Impulse Response*plot and the resulting impulse response.

**Application Gallery link for example of an Impulse Response plot:**

Small Concert Hall Acoustics

### New Pressure Acoustics, Time Explicit Physics Interface

A new physics interface, *Pressure Acoustics, Time Explicit*, based on the discontinuous Galerkin (dG-FEM) formulation, employs a time-explicit method that is memory efficient, with low memory consumption. The interface can be used to solve large, transient, linear acoustic simulations that contain many wavelengths, and is well suited for time-dependent simulations with arbitrary time-dependent sources and fields. There is an additional *Background Acoustic Field* option for modeling scattering problems and you can use absorbing layers to set up effective nonreflecting-like boundary conditions. The exterior scattered far-field can be calculated by combining the *Far-Field Calculation* feature with a *Time to Frequency FFT* study step. The interface is available in 2D, 2D axisymmetric, and 3D. Important application areas for this new interface include transient propagation of audio pulses in room acoustics and scattering phenomena involving large objects relative to the wavelength.

The *Pressure Acoustics, Time Explicit* interface solves the linearized Euler equations assuming an adiabatic equation of state. The dependent variables are the acoustic pressure and the acoustic velocity perturbations. No attenuation mechanisms due to bulk losses are included in the interface. Losses at boundaries can be modeled with impedance conditions for losses of the resistive type.

*Build-up of the scattered field from an incident plane wave onto a submarine. This animation shows a simulation at 700 Hz. The same simulation at 2000 Hz has 70 million DOF and requires 25 GB of RAM to solve, which is significantly less than a corresponding FEM-based model would require.*

**Application Gallery link for example using the Pressure Acoustics, Time Explicit interface:**

Submarine Scattering: Time Domain Simulation and FFT

### Improved Stabilization for the Linearized Euler Interfaces

New and improved numerical stabilization methods have been added to the *Linearized Euler* interfaces. The new default stabilization scheme is the *Galerkin least squares (GLS) stabilization*, which significantly improves stability and convergence for simulations that have coarse meshes. The new stabilization also makes solutions much less sensitive to small changes in the mesh. If desired, you can turn off the stabilization or select one of the optional *Streamline upwind Petrov-Galerkin (SUPG) stabilization* or *Streamline diffusion (legacy method)* schemes. The new default settings are well suited for modeling most acoustic-flow interaction problems that are based on the *Linearized Euler* interfaces.

Another way of stabilizing the linearized Euler equations is to use the so-called *Gradient Term Suppression (GTS) stabilization*. With this method, equation terms, typically the reactive terms, are simply removed from the governing equations. The GTS stabilization for the interface has also been improved for this release, with new options that give better control over the terms removed. The user can now choose to remove reactive terms depending on their type; inducing gradients of the background density, pressure, or velocity, respectively. In addition, there is an option to remove all convective terms in the equations.

**Application Gallery link for an example using the improved Galerkin least squares (GLS) stabilization:**

Point Source in 2D Jet: Radiation and Refraction of Sound Waves Through a 2D Shear Layer

### Absorbing Layers for the Linearized Euler Interface in the Time Domain

Absorbing layers are now available in the *Linearized Euler, Transient* interface, making it simpler to define open boundaries in the time domain. The absorbing layers use a combination of three techniques to set up effective nonreflecting boundary conditions, scaling, artificial numerical viscosity, and a simple impedance condition. This method ensures minimal numerical reflections of the outgoing waves.

*In this benchmark model for the linearized Euler equations, the radiation and reflection of sound in a narrow jet are analyzed. Shown here, the transient propagation of acoustic waves and the growth of the Kelvin-Helmholtz instabilities as the absorbing layers are used for the time-domain simulation.*

**Application Gallery link for an example using absorbing layers with the Linearized Euler, Transient interface:**

Point Source in 2D Jet: Radiation and Refraction of Sound Waves Through a 2D Shear Layer

### Plane Wave Expansion for Pressure Acoustics in 2D Axisymmetric Models

There is now a built-in option to solve plane wave scattering problems in 2D axisymmetric models using a plane wave expansion approach. The option automatically expands the applied plane wave in a *Background Pressure Field* or *Incident Pressure Field* feature into its cylindrical harmonics in terms of the circumferential mode number. This allows solving large scattering problems involving axisymmetric structures in a computationally efficient manner.

**Application Gallery link for an example using the Plane Wave Expansion option:**

Plane Wave Scattering off a 2D Axisymmetric Object: Plane Wave Expansion Approach

### New Option for Background and Incident Pressure Fields for Transient Pressure Acoustics

The *Pressure Acoustics, Transient* and the *Pressure Acoustics, Time Explicit* interfaces now have a built-in option *Plane wave (monochromatic)* to define monochromatic plane waves as a background pressure field or an incident pressure field. The new option simplifies setting up this common wave form for transient simulations. If other types of transient fields are needed, the user-defined option allows the definition of any field based on an analytical expression or interpolation data. The new option also has a built-in ramp function that smoothly increases the amplitude of the wave over the first period, in order to ensure good numerical performance.

**Application Library path for an example using the Plane wave (monochromatic) option:**

*Acoustics_Module/Electroacoustic_Transducers/probe_tube_microphone*

### Updated Material Input for Linearized Navier-Stokes and Thermoviscous Acoustics

When working with either the *Linearized Navier-Stokes* or the *Thermoviscous Acoustics* physics interfaces, it is necessary to enter correct and valid material data. The models intrinsically include correct behavior of the compressibility depending on temperature and pressure fluctuations. This means that the effective speed of sound is always modeled correctly, even in very narrow gaps where conditions become isothermal. When defining the (isobaric) coefficient of thermal expansion and the isothermal compressibility, both material parameters now have an option to be defined in terms of the speed of sound and ratio of specific heats (using their thermodynamic definitions). This simplifies setting up models where these parameters are not explicitly known.

**Application Library path for an example using the From speed of sound option:**

*Acoustics_Module/Aeroacoustics_and_Noise/Helmholtz_resonator_with_flow*

### Linear Frequency Axis Option in Directivity Plots

The frequency scale style can now be changed from Logarithmic to Linear under the *Coloring and Style* section in *Directivity* plots.

*Directivity plot with logarithmic (left) and linear (right) frequency axis scales (data from the Lumped Loudspeaker Driver tutorial model).*

Directivity plot with logarithmic (left) and linear (right) frequency axis scales (data from the Lumped Loudspeaker Driver tutorial model).

### Improvements to Solvers and Solver Suggestions

The automatically generated solver suggestions are improved for several multiphysics applications involving acoustics interfaces. For example, when using the *Acoustic-Structure Boundary* or the *Thermoviscous Acoustic-Structure Boundary* multiphysics couplings, the generated solver suggestion now accounts for whether the acoustics interface is coupled to a solid or a shell/membrane interface. This ensures memory efficient and fast solvers for large models, if the solver suggestions are used.

The *Transient Solver Settings* section, available in all transient acoustic interfaces, is now more intuitive than before. When a transient acoustics interface is involved in a multiphysics model, the *Transient Solver Settings* defined for the acoustics interface are now automatically used when solving the coupled problem. As an example, this ensures the optimal solver configuration for vibroacoustic problems solved in the time domain.

A general speedup of linear solvers by reusing already computed data is now done by default. For example, MUMPS and PARDISO can employ a new *Reuse preordering* option in the solvers, relevant for most acoustic problems. See the Studies and Solvers section for more information.

*The suggested iterative solver is now enabled and used in the Vented Loudspeaker Enclosure model from the Application Library. The solution time and memory consumption are significantly reduced using the suggested solver.*

The suggested iterative solver is now enabled and used in the Vented Loudspeaker Enclosure model from the Application Library. The solution time and memory consumption are significantly reduced using the suggested solver.

**Application Library paths for examples using a new iterative solver suggestion:**

*Acoustics_Module/Vibrations_and_FSI/vibrating_micromirror*

*Acoustics_Module/Electroacoustic_Transducers/vented_loudspeaker_enclosure*

**Application Library path for an example using the automatic transient solver settings for a piezoacoustic model:**

*Acoustics_Module/Ultrasound/flow_meter_piezoelectric_transducers*

### Important Enhancements and Bug Fixes

- 25–30% speedup when solving time-explicit simulations employing the dG method, as compared to version 5.3 of COMSOL Multiphysics
^{®} - Cluster support for solving time-explicit simulations based on the dG method interfaces
- The
*Interior Wall*and*Interior Velocity*boundary conditions have been added to the*Convected Wave Equation*interface - A
*User defined*option has been added for the out-of-plane component in the background mean flow input for the*Convected Wave Equation*in 2D axisymmetric models

### Updated Tutorial Model: Bessel Panel

A Bessel panel is a way to arrange a number of loudspeakers so that the angular sound distribution resembles that of a single speaker. This model combines five Bessel panels in the same pattern to approximate a purely radial sound field. The speakers are driven with different signals, some of them in counter-phase. This results in an approximately homogeneous polar far-field distribution. The updated model now uses a BEM-FEM approach to solve the radiation from the idealized speaker panel.

*Spatial directivity of the Bessel panel depicted in 3D.*

Spatial directivity of the Bessel panel depicted in 3D.

**Application Library path:**

*Acoustics_Module/Tutorials/bessel_panel*

### Updated Tutorial Model: Lumped Loudspeaker Driver Using Lumped Mechanical System

This is a model of a moving-coil loudspeaker where a lumped parameter analogy represents the behavior of the electrical and mechanical speaker components. The Thiele-Small parameters (small-signal parameters) serve as input to the lumped model. In this model, the mechanical speaker components such as moving mass, suspension compliance, and suspension mechanical losses are modeled using the *Lumped Mechanical System* interface.

*Pressure field plotted as isosurfaces (above the speaker cone) and as a surface plot (below the speaker cone).*

Pressure field plotted as isosurfaces (above the speaker cone) and as a surface plot (below the speaker cone).

**Application Library path:**

*Acoustics_Module/Electroacoustic_Transducers/lumped_loudspeaker_driver_mechanical*

### New Tutorial Model: Vibroacoustic Loudspeaker Simulation, Multiphysics with BEM-FEM

This model shows a full vibroacoustic analysis of a loudspeaker including the driver, cabinet, and stand. It applies a nominal driving voltage to extract the resulting sound pressure level in the cabinet and in the outside room, as well as the deformation of the cabinet and driver, for a given frequency. The loudspeaker is located on a hard floor some distance from a wall located behind it. The example uses a hybrid BEM-FEM approach and couples the *Solid Mechanics, Shell*; *Pressure Acoustics, Frequency Domain*; and *Pressure Acoustics, Boundary Elements* physics interfaces. The model uses six built-in multiphysics couplings to connect the single-physics interfaces together.

*Sound pressure level of the radiated acoustic field from a loudspeaker modeled using a full vibroacoustics simulation. The exterior acoustics are modeled using the new*

Sound pressure level of the radiated acoustic field from a loudspeaker modeled using a full vibroacoustics simulation. The exterior acoustics are modeled using the new *Pressure Acrostics, Boundary Elements* interface, which is coupled to the FEM interfaces.

*Pressure Acrostics, Boundary Elements*interface, which is coupled to the FEM interfaces.

**Application Gallery link for example using the Pressure Acoustics, Boundary Elements interface:**

Vibroacoustic Loudspeaker Simulation: Multiphysics with BEM-FEM

### New Tutorial Model: Tonpilz Transducer Array for Sonar Systems

This tutorial models a linear array of nine tonpilz piezoelectric transducers in a 3x3 grid. The transducers are located in a box below the sea surface, and a voltage is applied, including a phase change across the three rows. The exterior acoustics is modeled using a *Pressure Acoustics, Boundary Elements* interface, which is coupled to the vibrating structures with an *Acoustic-Structure Boundary* multiphysics coupling. This sets up a hybrid BEM-FEM model for the full system.

*Pressure field generated by an array of piezoelectric tonpilz transducers at 10 kHz.*

Pressure field generated by an array of piezoelectric tonpilz transducers at 10 kHz.

**Application Gallery link for an example using the Pressure Acoustics, Boundary Elements interface:**

Tonpilz Transducer Array for Sonar Systems

### New Tutorial Model: Small Concert Hall Acoustics

This tutorial model analyzes the acoustics of a small concert hall using the *Ray Acoustics* physics interface and has been updated to include the new *Impulse Response* plot functionality. The model setup includes an omnidirectional sound source, wall boundary conditions for specular and diffuse scattering, sound pressure evaluation on a boundary, a *Receiver* data set, an *Impulse Response* plot, and an energy decay curve. The results are compared to a simple reverberation time estimate.

*Impulse response of the Small Concert Hall plotted using the*

Impulse response of the Small Concert Hall plotted using the *Receiver* data set and the Impulse Response plot in postprocessing.

*Receiver*data set and the Impulse Response plot in postprocessing.

**Application Gallery link:**

Small Concert Hall Acoustics

### New Tutorial Model: Submarine Scattering, Time-Domain Simulation and FFT

This model analyzes the scattering of a plane wave off a submarine hull to determine the scattered field and the spatial response. The model uses a *Pressure Acoustics, Time Explicit* interface to model this large acoustic model in the time domain. Then, an FFT study is used to transform the results into the frequency domain and the scattered field is analyzed with the *Far-Field Calculation* feature.

*Scattered pressure field after simulating 12 periods of a 700 Hz plane monochromatic background field. The submarine has a total length of 32 m.*

Scattered pressure field after simulating 12 periods of a 700 Hz plane monochromatic background field. The submarine has a total length of 32 m.

**Application Gallery link:**

Submarine Scattering: Time-Domain Simulation and FFT

### New Tutorial Model: Vibrating MEMS Micromirror with Viscous and Thermal Damping, Transient Behavior

Micromirrors are used in certain MEMS devices to control optical components. This example model, a vibrating micromirror surrounded by air, illustrates a mirror that is initially actuated for a short time and then exhibits damped vibrations. It uses the *Thermoviscous Acoustics, Transient*; the *Shell*; and the *Pressure Acoustics, Transient* interfaces to model the fluid-solid interaction in the time domain. Use of the *Thermoviscous Acoustics* interface provides full details of viscous and thermal damping of the mirror in relation to the surrounding air.

*Micromirror displacement and pressure distribution at a given time depicted in colors. The transient evolution of displacement of the mirror is depicted in the graph, showing the damped vibrations due to thermal and viscous losses.*

Micromirror displacement and pressure distribution at a given time depicted in colors. The transient evolution of displacement of the mirror is depicted in the graph, showing the damped vibrations due to thermal and viscous losses.

**Application Gallery link:**

Vibrating Micromirror with Viscous and Thermal Damping: Transient Behavior

### New Tutorial Model: Plane Wave Scattering off a 2D Axisymmetric Object, Plane Wave Expansion Approach

The problem of plane wave scattering off a cylinder-shaped object suggests the use of the 2D axisymmetric formulation. This can save the computation time and reduce the memory usage compared to the model in 3D space. This example demonstrates the use of the built-in plane wave expansion functionality to solve the problem. It also highlights the steps required during the study and the postprocessing.

*Scattered pressure field of a 2D axisymmetric geometry computed using plane wave decomposition.*

Scattered pressure field of a 2D axisymmetric geometry computed using plane wave decomposition.

**Application Gallery link:**

Plane Wave Scattering off a 2D Axisymmetric Object: Plane Wave Expansion Approach

### New Tutorial Model: Acoustic Liner with a Grazing Background Flow

This model demonstrates how to compute the acoustic properties of an acoustic liner with a grazing flow. The liner consists of eight resonators with thin slits and the background grazing flow is at Mach number 0.3. The sound pressure level above the liner is computed and can be compared to results from a published research paper. The model first computes the flow using the SST turbulence model available in the CFD Module. The acoustics are then computed using the *Linearized Navier-Stokes, Frequency Domain* interface of the Acoustics Module.

*Note that the CFD Module is needed to run this model.*

*The acoustic velocity fluctuations as a plane wave propagates above the first four resonators of a liner. The color plot shows the velocity amplitude and the arrows show the velocity vector. Near the holes at the surface of the liner, vorticity is generated by the flow-acoustics interaction.*

**Application Gallery link:**

Acoustic Liner with a Grazing Background Flow

### New Tutorial Model: Coriolis Flow Meter

A Coriolis flow meter, also known as a mass flow meter or an inertial flow meter, is used to measure the mass flow rate of a fluid traveling through it. It makes use of the fact that the fluid's inertia through an oscillating tube causes the tube to twist in proportion to the mass flow rate. Typically, the density and thereby the volumetric flow rate can also be assessed using the device.

This model shows how to simulate a generic Coriolis flow meter with a curved geometry. When the fluid passes through the elastic structure, a curved duct, it interacts with the movement of the duct when vibrating. The phase difference between the deformation of two points on the duct is caused by the Coriolis effect and can be used to evaluate the mass flow rate through the system.

This model uses the *Linearized Navier-Stokes, Frequency Domain* interface coupled to the *Solid Mechanics* interface using the built-in multiphysics coupling. The background mean flow is modeled using the *Turbulent Flow, SST* interface. In this way, fluid-structure interaction (FSI) can be modeled efficiently in the frequency domain.

*Movement of the Coriolis flow meter pipe for three mass flow rates. The flow meter is actuated at the natural frequency of the structure. The deformation amplitude and phase are exaggerated for visualization. As the flow rate increases, the phase difference upstream and downstream increases.*

**Application Gallery link:**

Coriolis Flow Meter: FSI Simulation in the Frequency Domain

### New Tutorial Model: Dispersion Curves for a Fluid-Filled Elastic Pipe

The dispersion curves for a fluid-filled pipe with elastic walls are computed and compared with the analytical results for a pure elastic and an acoustic waveguide, respectively. Results show good agreement and also provide insight into the dynamics of the fluid-filled pipe at low and midrange frequencies.

*Four different coupled vibroacoustic propagating modes in a fluid filled pipe.*

Four different coupled vibroacoustic propagating modes in a fluid filled pipe.

**Application Gallery link:**

Dispersion Curves for a Fluid-Filled Elastic Pipe