The Acoustics Module is designed specifically for those who work with devices that produce, measure, and utilize acoustic waves. Application areas include speakers, microphones, hearing aids, and sonar devices, to name a few. Noise control can be addressed in muffler design, sound barriers, buildings, and room acoustics applications.

Straightforward user interfaces provide tools for modeling acoustic pressure wave propagation in air, water, and other fluids. Dedicated modeling tools for thermoviscous acoustics enable highly accurate simulation of miniaturized speakers and microphones in handheld devices. You can also model vibrations and elastic waves in solids, piezoelectric materials, and poroelastic structures.

Multiphysics interfaces for acoustic-solid, acoustic-shell, and piezo-acoustics couplings bring your acoustic simulations to a new level of predictive power. Aeroacoustic problems can be modeled using one of several linearized equation approaches. Room and outdoor acoustics problems can be modeled using ray tracing or acoustic diffusion methods.

By using realistic simulations in 1D, 2D, 2D axisymmetry, or 3D, you can optimize existing products and design new products more quickly. Simulations also help designers, researchers, and engineers to gain insight into problems that are difficult to handle experimentally. By testing a design before manufacturing it, companies save both time and money.

The Acoustics Module consists of a set of physics interfaces – user interfaces with associated modeling and simulation tools – that enable you to simulate the propagation of sound in fluids and solids. Within the Acoustics Module, these are organized into pressure acoustics, acoustic-structure interaction, aeroacoustics, thermoviscous acoustics, ultrasound, and geometrical acoustics.

Acoustic simulations performed using the physics interfaces for pressure acoustics can easily model classic problems such as scattering, diffraction, emission, radiation, and the transmission of sound. These problems are relevant to muffler design; loudspeaker construction; sound insulation for absorbers and diffusers; the evaluation of directional acoustic patterns, like directivity; noise radiation problems; and much more.

The physics interfaces for acoustic-structure interaction model problems involving the interaction between structural elastic waves and fluid-borne sound. For example, acoustic-structure interaction is considered in detailed muffler design, ultrasound piezo-actuators, sonar technology, and noise and vibration analyses of machinery. Using COMSOL Multiphysics, this capability enables you to analyze and design electroacoustic transducers, including loudspeakers, sensors, microphones, and receivers.

The Aeroacoustics physics interfaces are used to model the one-way interaction between an external flow and an acoustic field, (fluid-borne noise). Applications range from jet-engine noise analysis to wind sensor simulation.

The physics interfaces for geometrical acoustics include Ray tracing and the Acoustic diffusion equation interfaces. Both interfaces are applicable for modeling acoustics in rooms and buildings. Ray tracing is also used, for example, in ocean acoustics and atmosphere acoustics.

Thermoviscous acoustic applications are accurately modeled using the provided, appropriate physics interfaces. These are applications that include small geometrical dimensions where the thermal and viscous fluid properties need to be considered, for example, cell phones, hearing aids, MEMS applications, and transducer designs.

Completely integrated in the COMSOL Multiphysics^{®}environment, the Acoustics Module can be combined with other modules for a wider range of multiphysics simulations. Such is the case for the multiphysics interfaces for acoustic-shell interaction and thermoviscous acoustic-shell interaction, which are available when combining the Acoustics Module with theStructural Mechanics Module. Similarly, physics interfaces for pipe acoustics are available when combining the Acoustics Module with the Pipe Flow Module.

Multiphysics couplings and predefined multiphysics interfaces are set up in COMSOL Multiphysics by introducing a Multiphysics node. For example, coupling the physics describing pressure acoustics in a fluid domain to the physics describing structural mechanics in a surrounding solid is achieved in COMSOL Multiphysics by adding an Acoustics interface and a Solid Mechanics interface separately and then coupling them at the boundary using the relevant coupling under the multiphysics node. This functionality makes it possible to decouple or one-way couple the two contributing physics, as well as giving full control over all functionalities in the Acoustics and Solid Mechanics interfaces.

Among the many multiphysics couplings available are the Acoustic-Structure Boundary, the Aeroacoustic-Structure Boundary, and the Thermoviscous Acoustic-Structure Boundary multiphysics interfaces. These all couple a fluid domain to a structure that includes a solid, an external or internal shell, or a membrane. Also available are the Acoustic-Thermoviscous Acoustic Boundary, Acoustic-Porous Boundary, and Porous-Structure Boundary multiphysics interfaces, while the Piezoelectric Effect multiphysics interface connects a Solid Mechanics interface and an Electrostatics interface for modeling piezoelectric materials. All multiphysics models are fully coupled by default, while one-way coupling and dissociating the couplings can be achieved by manipulating the Multiphysics node.

The Acoustics Module adheres to the same workflow as any other add-on module in the COMSOL^{®} Product Suite. All modeling steps are accessed from the COMSOL Desktop^{®} and include defining the geometry, selecting materials, selecting a suitable physics interface, defining boundary and initial conditions, automatically creating the finite element mesh, solving, and visualizing the results. Acoustic simulations can be coupled with any other COMSOL Multiphysics^{®} add-on product in just about any way imaginable by a suite of preset multiphysics couplings, such as with the Structural Mechanics Module for acoustic-shell interaction, or by user-defined couplings. The Optimization Module can be combined with the Acoustics Module for optimizing geometric dimensions, acoustic transmission, and more.

For repetitive modeling tasks, LiveLink™ *for* MATLAB^{®} makes it possible to drive COMSOL^{®} simulations with MATLAB^{®} scripts or functions. Any operation available in COMSOL Desktop^{®} can alternatively be accessed through MATLAB^{®} commands. You can also include COMSOL^{®} commands in the MATLAB^{®}environment with your existing MATLAB^{®} code.

For acoustic simulations driven from spreadsheets, LiveLink™ *for*Excel^{®} offers a convenient alternative to modeling from COMSOL Desktop^{®} with synchronization of spreadsheet data with parameters defined in the COMSOL^{®} environment. TheCAD Import Module and LiveLink™ products for leading CAD systems makes it easy to perform acoustic simulations using CAD models. The LiveLink™ products make it possible to keep the parametric CAD model intact in its native environment but still control the geometric dimensions from within COMSOL Multiphysics^{®}. Linking your acoustics models to CAD products allows you to simultaneously perform parametric sweeps over several model parameters.

The equations within the Acoustics Module are solved using the finite element method with higher-order element discretization in combination with state-of-the-art solvers. The different formulations cover both frequency- and time-domain simulations. Your results are presented in the graphics window through preset plots of acoustic and displacement fields, sound pressure levels, stresses and strains, or as expressions of physical quantities that you can define freely, as well as derived tabulated quantities.

The Acoustics Module is shipped with an extensive Model Library with many examples of applications ranging from modeling sound insulation lining, loudspeakers, microphones, and mufflers. Many of these examples show how to simulate acoustic losses. The loss models of the Acoustics Module range from empirical equivalent-fluid models for fibrous materials, solving Biot's theory in the Poroelastic Waves interface, to a fully-fledged thermal and viscous loss model using the Thermoviscous Acoustics interface.

**Pressure Acoustics**

The Pressure Acoustics interfaces describe and solve sound fields through a scalar acoustic pressure field, which represents acoustic variations (or excess pressure) with respect to the ambient stationary pressure. They enable solving either in the frequency domain, where the Helmholtz equation is solved, or as a transient system, where the classical scalar wave equation is solved. A special physics interface for boundary mode acoustics is used to study propagating modes in waveguides and ducts, and is based on the fact that only a finite set of shapes, or modes, can propagate over longer distances.

A large variety of boundary conditions are available and include hard walls and impedance conditions, radiation, symmetry, and periodic conditions for modeling open boundaries as well as conditions for applying sources. The interfaces also contain several equivalent-fluid models, which mimic the behavior of sound propagation in more complex media. Several poroacoustics fluid models prescribe losses in porous or fibrous materials. Narrow region acoustics models add the thermoviscous losses associated with hard boundaries in narrow regions. Attenuation can be added as a user-defined relation, or it can be calculated for viscous and thermally conducting fluids. Perfectly matched layers (PMLs) are also available to truncate the computational domain by absorbing outgoing acoustic waves, thereby mimicking an infinitely extended domain.

When your calculations have been performed, a far-field feature can be used to determine the pressure and phase information at any distance outside the computational domain. Dedicated results and analysis capabilities are available for visualizing the far-field with polar plots in 2D and 3D.

**Acoustic-Structure Interaction**

Coupling fluid and structural domains is achieved by using the predefined multiphysics interfaces of the Acoustics Module, which automatically set up the relevant physics and multiphysics couplings. From one side of the fluid-solid boundary, the Acoustic-Structure Boundary interfaces handles the fluid pressure that acts on the solid domain and, from the other, the structural accelerated displacement that acts on the fluid domain. Multiphysics couplings encompass applications involving acoustic-solid, acoustic-shell, and acoustic-piezoelectric interactions – all within the frequency and time domains, and in 3D, 2D, and 2D axisymmetric geometric models. The couplings involving structural shells are available when combining the Acoustics Module with the Structural Mechanics Module, where you are also able to access more advanced structural modeling capabilities.

Elastic waves are an important application area for acousticians. With the Acoustics module you can use the Solid Mechanics interface to get a full structural-dynamics formulation that includes all the effects of shear waves and pressure waves in solids.

The Acoustic-Piezoelectric Interaction multiphysics interfaces not only simulate the acoustic-structure interaction with great accuracy, but also supports solving and modeling the electric field in the piezoelectric material. When combined with theAC/DC Module or the MEMS Module, you can also combine piezoelectric simulations with SPICE circuits. This capability is excellent when, for example, using lumped models to describe some of the electrical behavior of a transducer while using the full finite element description for the other physics.

The Pipe Acoustics interfaces (available together with the Pipe Flow Module) are used for 1D modeling of the propagation of sound waves in flexible pipe systems. The equations are formulated in a general way to include the effects of the pipe wall compliance with the possibility of a stationary background flow.

The Elastic Waves interface is a full structural-dynamics formulation that includes all the effects of shear waves and pressure waves. Using Biot’s theory, the Poroelastic Waves interface accurately models the propagation of sound in a porous material, including the two-way coupling between deformation of the solid matrix and the pressure waves in the saturating fluid through a dedicated multiphysics boundary condition that enables easy coupling of the porous domain and a fluid domain.

**Geometrical Acoustics**

The Geometrical Acoustics branch includes the Ray Acoustics and the Acoustic Diffusion Equation physics interfaces. The physics in both interfaces are valid in the high-frequency limit where the acoustic wavelength is smaller than the characteristic geometric features. This is at frequencies above the Schroeder frequency for rooms. Both interfaces are suited for modeling acoustics in rooms and buildings like concert halls. The Acoustic Diffusion Equation is restricted to indoor applications whereas the Ray Acoustics interface can be used, for example, in ocean acoustics and atmosphere acoustics. The acoustic properties at boundaries are included through different models for the absorption.

The Ray Acoustics physics interface is used to compute the trajectories, phase, and intensity of acoustic rays. Ray acoustics is valid in the high-frequency limit where the acoustic wavelength is smaller than the characteristic geometric features. The interface can be used to model acoustics in rooms, concert halls, schools, office buildings, and many outdoor environments. The properties of the media in which the rays propagate can change continuously within domains (graded media) or discontinuously at boundaries. At exterior boundaries, it is possible to assign a variety of wall conditions, including combinations of specular and diffuse reflection. Impedance and absorption can depend on the frequency, intensity, and direction of incident rays. Transmission and reflection are also modeled at material discontinuities. A background velocity may also be assigned to any medium.

The Acoustic Diffusion Equation interface solves a diffusion equation for the acoustic energy density. It is applicable for high-frequency acoustics where the acoustic fields are diffuse. The diffusion properties are dependent on both the room geometry and absorption properties of walls, room fittings (uses average volumetric absorption based on average cross-section and attenuation), and volumetric attenuation (viscous and thermal in large volumes only). The interface is well suited for quick assessment of sound pressure level distribution inside buildings and other large structures.

The Acoustic Diffusion Equation interface can be used to determine the reverberation times at different locations. This can be done either by performing a transient analysis and looking at the energy decay curve, or by performing an eigenvalue analysis. Inputs for all sources, absorption parameters, and transmission losses can be determined using one of the bands, provided in the module. Using these input types and a parametric sweep over the studied band, the user can easily plot and analyze the model results to express results in these bands.

**Aeroacoustics**

Ideally, computational aeroacoustic (CAA) simulations would involve solving the fully compressible Navier-Stokes equations in the time domain. The acoustic pressure waves would then form a subset of the fluid solution. This approach is often impractical for real-world applications due to the required computational accuracy necessary, the computational time, and memory resources. For solving many practical engineering problems, a decoupled two-step approach is used instead: first solve for the background mean fluid flow, then for the acoustic perturbations of the flow. This very important one-way interaction is also known as a fluid-borne noise/sound phenomenon.

The primary tools in the Acoustics Module for fluid-borne sound is the Linearized Euler and the Linearized Navier-Stokes physics interfaces, while the Linearized Potential Flow interfaces provides a more simplified approach.

The Linearized Euler interfaces are used to compute the acoustic variations to pressure, velocity, and density for a given background mean-flow. They solve for the linearized Euler equations, including the energy equation, with the assumptions that the background flow is an ideal gas (or is well-approximated by an ideal gas) and that there are no thermal or viscous losses. The Linearized Euler physics interfaces are available for time domain, frequency domain, and eigenfrequency analyses. Application examples for areoacoustics with the Linearized Euler equations include analyzing the propagation of noise from jet engines, modeling the attenuation properties of mufflers in the presence of non-isothermal flow, and the study of gas flow meters. These are all situations where a gas background flow influences the propagation of acoustic waves in the fluid.

The Linearized Navier-Stokes interfaces are used to compute the acoustic variations in pressure, velocity, and temperature in the presence of any stationary isothermal or non-isothermal background mean-flow. The interfaces are used for aeroacoustic simulations that can be described by the linearized Navier-Stokes equations. The equations include viscous losses and thermal conduction as well as the heat generated by viscous dissipation. The coupling between the acoustic field and the background flow does not include any predefined flow induced noise. Coupling the Linearized Navier-Stokes, Frequency Domain interface to structures, using the Aeroacoustic-Structure Boundary multiphysics coupling, enables detailed vibration analysis of structures in the presence of flow.

For simplified one-way interactions, the Linearized Potential Flow interfaces are available in both the frequency and transient domains, and utilize formulations based on a fluid-potential. Moreover, the Compressible Potential Flow interface is used to model the background mean flow of an inviscid, compressible fluid that has no vorticity as it is irrotational by nature. Finally, the Linearized Potential Flow, Boundary Mode interface is used to study boundary mode acoustic problems in a background flow field, typically used to specify sources at inlets.

**Thermoviscous Acoustics**

The Acoustics Module provides state-of-the-art modeling capabilities for thermoviscous acoustics (also known as viscothermal acoustics), which is critical for accurate simulation of acoustics in geometries with small dimensions. Close to walls, viscosity and thermal conduction become important as a viscous and thermal boundary layer are created, resulting in significant losses. This makes it necessary to include thermal conduction effects and viscous losses explicitly in the governing equations.

The physics interfaces for thermoviscous acoustics are used to solve for the full set of linearized compressible flow equations with zero background flow, that is, the linearized Navier-Stokes, continuity, and energy equations all together. Because a detailed description is needed to model thermoviscous acoustics, all the physics interfaces simultaneously solve for the acoustic pressure, the particle velocity vector, and the acoustic temperature variation.

In the Thermoviscous Acoustics interface, the governing equations are implemented as a time-harmonic formulation and solved in the frequency domain. Both mechanical and thermal boundary conditions are available. Coupling the thermoviscous acoustic domain to a pressure acoustic domain is also straightforward with a predefined multiphysics boundary condition. A Thermoviscous Acoustic-Structure Boundary multiphysics coupling is available, and makes it easy to solve for coupled vibro-acoustics. You can, for example, use it to model small electroacoustic transducers or damping in MEMS devices. It can also be used to analyze the interaction between shells and acoustics in small dimensions, for example, the damped vibrations of shells in hearing aids to prevent feedback problems.

The *Thermoviscous Acoustics*, *Boundary Mode*interface is used to compute and identify propagating and nonpropagating modes in waveguides and ducts. The interface performs a boundary mode analysis on a boundary, inlet, or cross section of a waveguide or duct of small dimensions, including the thermal and viscous loss effects that are important in the acoustic boundary layer near walls. The interface can be used when setting up sources in systems with small ducts, like hearing aids or mobile devices, for example.

**Ultrasound**

The *Ultrasound* interfaces are used to compute the transient propagation of acoustic waves over large distances, relative to the wavelengths. Acoustic disturbances with frequencies that are not audible for humans are classified as ultrasound. This implies that ultrasonic waves have a short wavelength. The interfaces under the Ultrasound branch are, however, are not restricted to high-frequency propagation, but can, in general, be applied to any acoustically large problem.

The *Convected Wave Equation*, *Time Explicit* interface is used to solve large transient linear acoustic problems containing many wavelengths in a stationary background flow. It is suited for time-dependent simulations with arbitrary time-dependent sources and fields. In general, the interface is suited for modeling the propagation of acoustic signals over large distances relative to the wavelength, for example, linear ultrasound problems. The interface includes absorbing layers that are used to set up effective nonreflecting like boundary conditions. The interface is based on the discontinuous Galerkin method and uses a time-explicit solver. The method is very memory lean. Application areas include ultrasound flow meters and other ultrasound sensors where time of flight is an important parameter. The applications are not restricted to ultrasound, but also include, for example, transient propagation of audio pulses in room acoustics or car cabins.