## Acoustics Module Updates

For users of the Acoustics Module, COMSOL Multiphysics^{®} version 6.0 brings a new *Piezoelectric Waves, Time Explicit* multiphysics interface, physics-controlled mesh functionality for pressure acoustics, and flow-induced noise. Read about these updates and more below.

### Piezoelectric Waves, Time Explicit Multiphysics Interface

With the *Piezoelectric Waves, Time Explicit* multiphysics interface, you get access to new capabilities for modeling wave propagation phenomena in piezoelectric media in the time domain. Both the direct and inverse piezoelectric effects can be modeled and the piezoelectric coupling can be formulated using the strain-charge or stress-charge forms. The new interface couples the *Elastic Waves, Time Explicit* interface with the *Electrostatics* interface using the new *Piezoelectric Effect, Time Explicit* multiphysics coupling.

The interface is based on the discontinuous Galerkin (dG or dG-FEM) method and uses a time-explicit solver. The electrostatics part of the equation system is solved at every time step through an algebraic system of equations solved with the classical finite element method (FEM). This ensures a very computationally efficient hybrid method that can solve very large models with many millions of degrees of freedom (DOFs). The method is well suited for distributed computing on cluster architectures. You can see this new interface in the updated Ultrasonic Flowmeter with Piezoelectric Transducers and Angle Beam Nondestructive Testing tutorial models.

*Piezoelectric Waves, Time Explicit*multiphysics interface in an angle beam nondestructive testing (NDT) setup.

### Physics-Controlled Mesh for Pressure Acoustics

Physics-controlled mesh functionality is now available for the *Pressure Acoustics, Frequency Domain* and *Pressure Acoustics, Transient* interfaces. The mesh that is generated follows best practices with regards to resolving the waves ensuring an adequate number of mesh elements. Furthermore, perfectly matched layers (PMLs) are meshed with a structured mesh, periodic conditions use copy mesh operations, and a single boundary layer mesh is used for *Exterior Field* calculations.

For the frequency domain, the maximum frequency is automatically picked up from the study. For the time domain, the maximum frequency is taken from the physics settings, ensuring a consistent spatial resolution for the mesh and temporal resolution for the solver time steps. For all other acoustics interfaces, and for *Solid Mechanics*, only PMLs and Periodic Conditions are handled. All tutorial models where the new physics-controlled meshing is applicable have been updated.

*Pressure Acoustics, Frequency Domain*. The domain mesh, structured mesh in PMLs, and boundary layer mesh are automatically generated.

### Introducing Flow-Induced Noise

A hybrid computational aeroacoustic (CAA) method is introduced for modeling flow-induced noise. It is based on a one-way coupling between the turbulent flow sources and the acoustic equations. The method assumes that no back-coupling exists from the acoustic field to the flow field. The computational method is based on the FEM discretization of Lighthill’s acoustic analogy (wave equation). This formulation of the equations ensures that solid boundaries, which can be fixed or vibrating, are implicitly taken into account. Two flow-induced noise options are available: the Lighthill analogy and the simpler aeroacoustic wave equation (AWE) analogy.

The new functionality relies on coupling a large eddy simulation (LES) fluid flow model, solved using the CFD Module, to the *Aeroacoustic Flow Source* domain feature in *Pressure Acoustics, Frequency Domain*. The coupling is achieved by using the *Aeroacoustic Flow Source Coupling* multiphysics coupling and the dedicated *Transient Mapping* study.

*Aeroacoustic Flow Source*feature in

*Pressure Acoustics, Frequency Domain*, the

*Aeroacoustic Flow Source Coupling*multiphysics, the

*Transient Mapping, FFT*study step, and the

*Frequency Domain*study. The model is a simulation of a tandem cylinder benchmark problem.

### Two New High-Frequency Pressure Acoustics Physics Interfaces

Two new physics interfaces are available that rely on a high-frequency assumption and are based on the Kirchhoff–Helmholtz integral. The first one, the *Pressure Acoustics, Asymptotic Scattering* interface, is dedicated for modeling scattering, while the other one, the *Pressure Acoustics, Kirchhoff-Helmholtz*, is primarily for modeling radiation.

#### Pressure Acoustics, Asymptotic Scattering

The *Pressure Acoustics, Asymptotic Scattering* interface is used to model scattering at high frequencies. The acoustic field is assumed to be locally plane such that the scattered field can be expressed analytically. The scattering object surface can be treated as perfectly reflecting or having absorbing properties by defining a surface normal impedance, a reflection coefficient, or an absorption coefficient. The latter two can depend on the angle of incidence. The interface can model scattering of spherical and plane waves. The interface has built-in functionality to compute the visibility factor using both a simple angle consideration and a more advanced hemicube method. You can view this feature in the Submarine High-Frequency Asymptotic Scattering tutorial model.

#### Pressure Acoustics, Kirchhoff–Helmholtz

The *Pressure Acoustics, Kirchhoff-Helmholtz* interface is used to model radiation at high frequencies. The acoustic field is assumed to be locally plane. This technique is also often referred to as high-frequency BEM or simply HFB. The method is often used for computing the radiated acoustic field from vibrating structures at high frequencies, without the need to model the surrounding fluid. The method is valid as long as the acoustic wavelength in the fluid is smaller than the structure and the structural modes. For a flat vibrating surface, the method reduces to computing the Rayleigh integral. A user-defined option gives access to the full Kirchhoff–Helmholtz integral formulation for defining both the pressure and its normal gradient.

*Pressure Acoustics, Asymptotic Scattering*interface used for modeling high-frequency scattering off a submarine hull. The hull is 60 m long and the frequency studied here is 2 kHz. The solution and rendering time is only a couple of minutes.

### New Domain Decomposition Method for Pressure Acoustics

It is now possible to solve large-scale pressure acoustics (Helmholtz problems) with the *Domain Decomposition (Schwarz)* method. This method is using the *Shifted Laplace* method together with the same absorbing boundary conditions for the internal overlapping boundaries as is used for the nonoverlapping Schur method. The advantage with this method is that multigrid can be used as a domain solver and a coarse grid is not needed for the domain decomposition method.

### Lumped Speaker Boundary and Interior Lumped Speaker Boundary

For many electroacoustics applications, speakers can be efficiently modeled by combining a lumped Thiele–Small representation and the finite element method. The electromagnetic components of the motor are modeled with an *Electric Circuit* interface while the acoustics portion is solved with the *Pressure Acoustics, Frequency Domain* interface. The approach assumes that the speaker diaphragm vibrations can be described by piston motion and is of particular interest for microspeakers. The *Interior Lumped Speaker Boundary* includes the effects of the air on both sides of the diaphragm. The *Lumped Speaker Boundary* has options to include the compliance of a back volume through an impedance. View these new features in the Lumped Loudspeaker Driver and Headphone on an Artificial Ear tutorial models.

*Interior Lumped Speaker Boundary*in the Headphone on Artificial Ear tutorial model. The speaker surface is seamlessly coupled to the

*Electric Circuit*that contains the lumped electroacoustic representation.

### Sector Symmetry Options for Exterior Field Calculation

The *Exterior Field Calculation* feature has been extended with new options to handle models with sector symmetry. Two options extend the existing *Symmetry planes* functionality: the *Sector symmetry* option and the *Sector symmetry with one symmetry plane* option. The latter is of particular interest when modeling loudspeaker drivers placed in an infinite baffle. The analysis of the exterior field can also be extended with an azimuthal mode number for advanced sector symmetric models.

*Exterior Field Calculation*feature used on a 60-degree loudspeaker sector. The new option

*Sector symmetry with one symmetry plane*allows for the combined simulation with an infinite baffle geometry with sector symmetry.

### Optimization with New Exterior Field Variables

In 3D, new exterior field variables are available for use in gradient-based optimization problems, such as shape optimization or topology optimization. The optimization objective can now be defined as a variable evaluated in the exterior field, defining, for example, values on a radiation pattern or an off-axis response. The variable exists only for the *Symmetry planes* option in the *Exterior Field Calculation* feature. The new variables are defined with _opt appended to the existing exterior field variables: The operator for the pressure is `pext_opt(x,y,z)`

and for the sound pressure level it is `Lp_pext_opt(x,y,z)`

. You can see this new update in the Shape Optimization of a Rectangular Loudspeaker Horn in 3D tutorial model.

*Objective Function*expression in this optimization problem.

### Magnetomechanics Multiphysics Interface

Two new physics interfaces for analysis of coupled magnetic and mechanical effects have been added: *Magnetomechanics* and *Magnetomechanics, No Currents*. Typical applications are when a magnetic field induces deformations in a solid or, conversely, when a moving structure changes the magnetic field. For example, this is the physical explanation for transformer humming. The new interfaces rely on the new *Magnetomechanical Forces* multiphysics coupling. This coupling is of particular interest when modeling certain types of acoustic transducers like a balanced armature transducer. This new functionality also requires the AC/DC Module and can be viewed in the Balanced Armature Receiver a Miniature Loudspeaker tutorial model.

*Magnetomechanical Forces*multiphysics coupling.

### Perfectly Matched Boundary (PMB) Radiation Condition

The new *Perfectly Matched Boundary* feature is a PML that is applied to the open boundary in the form of a radiation condition, without the need to define a domain, for example as a layer in the geometry model. The condition automatically applies a PML formulation using the extra dimension functionality of COMSOL Multiphysics^{®}. This also simplifies the requirements on the radiating boundary as it can, in principle, have any convex shape. Different options are available for controlling the attenuation direction. The new boundary condition is available for the *Pressure Acoustics, Frequency Domain* interface in all relevant space dimensions. You can view this new feature in the following tutorial models:

### Linearized Euler, Boundary Mode Physics Interface

The *Linearized Euler, Boundary Mode* interface is used to compute and identify propagating and nonpropagating modes in waveguides and ducts in the presence of a stationary background mean flow that is well approximated by an ideal gas flow. The interface performs an eigenmode analysis on a boundary, inlet, or cross section of the waveguide.

*Linearized Euler, Boundary Mode*interface.

### Linearized Navier–Stokes, Boundary Mode Physics Interface

The *Linearized Navier-Stokes, Boundary Mode* interface is used to compute and identify propagating and nonpropagating modes in waveguides and ducts in the presence of any stationary isothermal or nonisothermal background mean flow. It performs an eigenmode analysis on a boundary, inlet, or cross section of the waveguide. The interface considers all thermal and viscous loss effects and the interaction with the background flow. This includes the acoustic boundary layer losses, if necessary.

### Out-of-Plane and Boundary Mode Analysis for Linearized Euler and Linearized Navier–Stokes

In both the *Linearized Euler* and the *Linearized Navier-Stokes* interfaces, it is now possible to add optional out-of-plane and circumferential wave numbers in 2D and 2D axisymmetry, respectively. In the same space dimensions, you can now use the mode analysis study to set up so-called 2.5D simulations for these types of physics interfaces.

### Compute Displacement Postprocessing Feature in Elastic Waves, Time Explicit

A new postprocessing feature called *Compute Displacement* has been added to the *Elastic Waves, Time Explicit* physics interface. The feature allows for optimally computing the displacement at points, along edges, on boundaries, or in domains, by solving a set of auxiliary ODEs. The new features are added as subfeatures to a material model such as the *Elastic Waves, Time Explicit Model* or the *Piezoelectric Material* model. The feature does not affect the results but is solely used for postprocessing and generates field variables that can be used to visualize and postprocess displacements. Since the feature adds and solves additional equations, using it requires additional computational resources. You can see this new functionality in the Isotropic-Anisotropic Sample: Elastic Wave Propagation tutorial model.

### Minimum and Maximum Pressure Postprocessing Feature in Nonlinear Pressure Acoustics, Time Explicit

A new postprocessing feature called *Compute Minimum and Maximum Pressure* has been added to the *Nonlinear Pressure Acoustics, Time Explicit* interface. The feature computes the maximum and minimum pressure over time and space in a domain or on a boundary. Two variables are automatically created, nate.p_min and nate.p_max, that can be used in postprocessing to, for example, evaluate the size of a focal zone. View this feature in the High-Intensity Focused Ultrasound (HIFU) Propagation Through a Tissue Phantom tutorial model.

### Pair Multiphysics Couplings for Vibroacoustic Simulations

Two new multiphysics couplings have been added to the Acoustics Module for coupling acoustic and solid domains in an assembly. This is implemented as pair conditions and allows the use of nonconforming meshes at the interface between two domains in an assembly. The first type of multiphysics coupling, *Pair Acoustic-Structure Boundary*, is used in an assembly for coupling the *Pressure Acoustics, Frequency Domain* or the *Pressure Acoustics, Transient* interface to the *Solid Mechanics* interface. The second type of multiphysics coupling, *Pair Thermoviscous Acoustic-Structure Boundary*, is used in an assembly for coupling the *Thermoviscous Acoustics, Frequency Domain* or the *Thermoviscous Acoustics, Transient* interface to the *Solid Mechanics* interface. This coupling uses the penalty formulation for more efficient computations in the time domain. You can see these new couplings in the Modeling Piezoelectric Devices as Both Transmitters and Receivers tutorial model.

*Pair Acoustic-Structure Boundary*used in a piezoelectric tutorial model. Notice the nonconforming mesh at the piezo–fluid interface.

### Important Updates to Thermoviscous Acoustics

For thermoacoustics modeling, there are multiple new and improved features.

- For ports, a new
*Plane wave*option is available for handling slip and adiabatic cases or, alternatively, models that are not waveguides. The names of the waveguide modes, available in the previous software version, have been updated to*Numeric (0,0)-mode*and*Circular (0,0)-mode*. - The default discretization used in all thermoviscous interfaces has been changed from Lagrange to serendipity elements. This results in important performance gains when solving models that use structured meshes.
- There are improved solver settings when solving models with
*Nonlinear Thermoviscous Acoustics Contributions*. The settings are especially important for highly nonlinear problems. To use these new settings in a COMSOL Multiphysics^{®}version 5.6 model, you need to reset the solvers to their default settings. - The coupling between thermoviscous acoustics and structural mechanics, in the case of curved surfaces, has been improved by the use of the Nodal constraint type.
- In the
*Boundary Layers*mesh feature, a new*Thickness specification*option*All layers*has been added. This allows for easier setup of a mesh that spans the entire thermoviscous acoustic boundary layer. - In cases where the
*Density approximation*is set to*Second order*in the*Nonlinear Thermoviscous Acoustics Contributions*feature, material properties are now automatically evaluated if the air material (moist or dry) is specified using a*Thermodynamic System*feature. - In the
*Thermoviscous Acoustics, Frequency Domain*interface, it is now possible to add an optional circumferential wave number for 2D axisymmetric models. This allows for advanced 2.5D analysis of complex propagation patterns.

The following models demonstrate these features:

*Plane*wave port option used in a thermoviscous acoustics analysis to compute the transfer impedance of a perforate.

### Ray Acoustics News

#### Release with Directivity

In the *Ray Acoustics* interface, the new *Source with Directivity* node can now be used to release a distribution of rays with initial intensity or power based on a user-defined spatial directivity function. This is of particular interest when defining loudspeaker sources in ray acoustics simulations.

#### Release from Exterior Field Calculation

You can use the new *Release from Exterior Field Calculation* node to launch rays with an intensity and phase distribution based on an *Exterior Field Calculation* feature from a previous study. This facilitates multiscale acoustics simulation combining a mesh-based solution to the near field with a ray-tracing simulation over much larger distances. View this feature in the Ultrasonic Car Parking Sensor tutorial model.

#### Transformations when Loading Ray Coordinates from a File

When using the *Release from Data File* node to load the ray release positions from a file, you can now apply a transformation to the initial coordinates. You can use any combination of dilation (scaling), rotation, and translation. If the initial ray direction is also loaded from a file, then you can optionally apply the same rotation to both the position and direction.

*Release from Data File*feature is used to move, rotate, and scale the distribution of rays released from a speaker.

#### New Attenuation Models

In version 6.0 of the software, there are four different ways to define the attenuation coefficient that controls how the ray intensity power decreases as rays propagate through the simulation domain. You can specify either the pressure amplitude attenuation coefficient or the intensity amplitude attenuation coefficient in nepers per meter. Alternatively, you can enter the amplitude attenuation coefficient in decibels per unit length or in decibels per wavelength. All of these definitions of the attenuation coefficient are also available for modeling attenuation in the void region outside the geometry.

#### Simplified Names for Nonlocal Couplings

The *Ray Acoustics* interface defines couplings to compute the sum, average, maximum, or minimum of an expression over the rays in a model. In version 6.0, the names of these couplings have been simplified for easier use.

The following table lists the old and new coupling names.

Coupling Description | Old Name | New Name |
---|---|---|

Sum over rays | rac.racop1(expr) | rac.sum(expr) |

Sum over all rays | rac.racop_all1(expr) | rac.sum_all(expr) |

Average over rays | rac.racaveop1(expr) | rac.ave(expr) |

Average over all rays | rac.racaveop_all1(expr) | rac.ave_all(expr) |

Maximum over rays | rac.racmaxop1(expr) | rac.max(expr) |

Maximum over all rays | rac.racmaxop_all1(expr) | rac.max_all(expr) |

Minimum over rays | rac.racminop1(expr) | rac.min(expr) |

Minimum over all rays | rac.racminop_all1(expr) | rac.min_all(expr) |

Evaluate at maximum over rays | rac.racmaxop1(expr, evalExpr) | rac.max(expr, evalExpr) |

Evaluate at maximum over all rays | rac.racmaxop_all1(expr, evalExpr) | rac.max_all(expr, evalExpr) |

Evaluate at minimum over rays | rac.racminop1(expr, evalExpr) | rac.min(expr, evalExpr) |

Evaluate at minimum over all rays | rac.racminop_all1(expr, evalExpr) | rac.min_all(expr, evalExpr) |

The old names will still work in version 6.0 as well, so it is not necessary to update any existing models.

### Axial Symmetry with Twist

In the *Solid Mechanics* interface, in 2D axisymmetry, it is now possible to include circumferential deformations. This can be enabled by selecting the *Include circumferential displacement* check box in the *Axial Symmetry Approximation* section in the physics interface. With this option, it is possible to model, for example, torsion of axisymmetric structures in a computationally efficient manner.

### New Damping Models

New damping models have been added for the mechanical material models:

- The
*Wave attenuation*model is essentially a viscous model, but with parameters given by measured data for the attenuation of elastic waves in the material. It is available in the*Linear Elastic Material*in*Solid Mechanics*. - The
*Maximum loss factor*model is mainly intended for time-domain analysis of materials for which a loss factor representation provides a good description in frequency domain. This damping model is available for all material models that support viscous damping. - In the
*Piezoelectric Material*feature, there is, in addition to the mechanical damping*Maximum loss factor*, also a new frequency-domain damping model for dielectric loss:*Complex Permittivity*. - For
*Charge-Conservation, Piezoelectric*, you can now add two new dispersion models:*Debye*and*Multipole Debye*.

### Postprocessing News for Acoustics

For postprocessing and visualization, the new version includes the following news:

- New
*Discrete Fourier transform (DFT)*and*Moving average*options have been added for the*Impulse Response*plot feature used with the*Ray Acoustics*interface. - A new
*Information*section is available for plots when*Plot Information Section*is enabled in*Show More Options*. The new section displays the plot time, which can be important in*Ray Acoustic*models or models that use the new Kirchhoff–Helmholtz-based high-frequency interfaces. - In the
*Octave Band*plot, the*Quantity plotted*can now be selected as*Continuous power spectral density, Band power*, or*Band average power spectral density*. - A warning message has been added in the
*Energy Decay*subfeature when the behavior of the level decay deviates from normal. - A new
*Thermal Wave*color table is available and used as the new default for the temperature variation plot in the*Thermoviscous Acoustics*and*Linearized Navier-Stokes*interfaces. - New
*Wave*and*Wave Light*color tables have been added and are used as the default for all plots that represent the acoustic pressure. - Faster generation of large surface plots. This is apparent, for example, in the Propagation of Seismic Waves Through Earth tutorial model.
- The preview of the
*Receiver*dataset is now much faster.

*Thermal Wave*color table is used to represent the acoustic temperature fluctuations in a nonlinear thermoviscous acoustic simulation.

### Other Important Enhancements and Updates in the Acoustics Module

- The formulation for damping for the dG-FEM-based time-explicit interfaces has been improved. The new formulation is more stable, more accurate, and higher performing.
- Handling of lumped circular approximations in thermoviscous acoustics models has been improved. This applies to narrow region acoustics and interior perforated plates.
- The robustness of the mapping performed by the
*Mapping*study, in combination with the*Background Fluid Flow Coupling*multiphysics feature, has been improved. This is particularly noticeable for models with an imported geometry and for models that have a CFD boundary layer mesh on curved boundaries. - The
*Compressible Potential Flow*physics interface is now applicable in PML domains, which simplifies the setup of the background flow for the subsequent analysis in the*Linearized Potential Flow*interface.

### New and Updated Tutorial Models

COMSOL Multiphysics^{®} version 6.0 brings several new and updated tutorial models to the Acoustics Module.

#### Topology Optimization of a Magnetic Circuit

Application Library Title:

*magnetic_circuit_topology_optimization*

Download from the Application Gallery

#### Loudspeaker Spider Optimization

Application Library Title:

*loudspeaker_spider_optimization*

Download from the Application Gallery

#### Tweeter Dome and Waveguide Shape Optimization

Application Library Title:

*tweeter_shape_optimization*

Download from the Application Gallery

#### Helmholtz Resonator with Porous Layer

#### Eigenmodes in the Presence of Flow Using Linearized Navier–Stokes: Annulus Geometry with Shear Flow

#### Nonlinear Transfer Impedance of a Tapered Orifice

#### Submarine High-Frequency Asymptotic Scattering

Application Library Title:

*submarine_asymptotic_scattering*

Download from the Application Gallery

#### Chamber Music Hall

Application Library Title:

*chamber_music_hall*

Download from the Application Gallery

#### Schroeder Diffuser in 2D

Application Library Title:

*diffuser_schroeder_2D*

Download from the Application Gallery

#### Angle Beam Nondestructive Testing

Application Library Title:

*angle_beam_ndt*

Download from the Application Gallery

#### Ultrasonic Flowmeter with Piezoelectric Transducers

*Piezoelectric Waves, Time Explicit*functionality.

Application Library Title:

*flow_meter_piezoelectric_transducers*

Download from the Application Gallery

#### Shape Optimization of Rectangular Loudspeaker Horn in 3D

*Transformation*feature, and optimization with the exterior field variable.

Application Library Title:

*rectangular_horn_shape_optimization*

Download from the Application Gallery