The Pressure Acoustics, Frequency Domain Interface

The interface (

), found under the branch (

) when adding a physics interface, is used to compute the pressure variations for the propagation of acoustic waves in fluids at quiescent background conditions. It is suited for all frequency-domain simulations with harmonic variations of the pressure field.

The physics interface can be used for linear acoustics described by a scalar pressure variable. It includes domain conditions to model losses in a homogenized way, so-called equivalent fluid models, for porous materials as well as losses in narrow regions (waveguides or slits). The plane wave attenuation behavior of the acoustic waves may also be entered as a user-defined quantity, or based on the losses in the atmosphere or ocean. Effective anisotropic material properties can be modeled with an effective anisotropic density formulation. Domain features also include background acoustic fields, as well as monopole and dipole domain sources.

The physics interface solves the Helmholtz equation in the frequency domain for given frequencies, or as an eigenfrequency or mode analysis study. The harmonic variation of all fields and sources is given by

using the +iω convention.

An acoustics model can be part of a larger multiphysics model that describes, for example, the interactions between structures and acoustic waves. This physics interface is suitable for modeling acoustics phenomena that do not involve fluid flow (convective effects).

The sound pressure p, which is solved for in pressure acoustics, represents the acoustic variations (or acoustic perturbations) to the ambient pressure. In the absence of flow, the ambient pressure pA is simply the static absolute pressure.

The governing equations and boundary conditions are formulated using the total pressure pt with a so-called scattered field formulation. In the presence of a Background Pressure Field defining a background pressure wave pb (this could, for example, be a plane wave), the total acoustic pressure pt is the sum of the pressure solved for p (which is then equal to the scattered pressure ps) and the background pressure wave: pt = p+pb. The equations then contain the information about both the scattered field and the background pressure field.

	For good modeling strategies, meshing, solvers, postprocessing information, acoustics specific plots, as well as tips and tricks, see the Modeling with the Pressure Acoustics Branch (FEM-Based Interfaces) section.

When the geometrical dimensions of the acoustic problems are reduced from 3D to 2D (planar symmetry or axisymmetric) or to 1D axisymmetric, it is possible to specify an out-of-plane wave number kz and an azimuthal mode number m (sometimes referred to as the circumferential mode number), when applicable. In this case, the wave number used in the equations keq contains both the ordinary wave number k as well as the out-of-plane wave number kz and azimuthal wave number km = m/r, when applicable.

The following table lists the names and SI units for the most important physical quantities in the Pressure Acoustics, Frequency Domain interface:

Table 2-1: Pressure Acoustics, Frequency Domain Interface Physical Quantities
Quantity	Symbol	SI Unit	Abbreviation
Pressure	p	Pascal	Pa
Total pressure	pt	Pascal	Pa
Background pressure	pb	Pascal	Pa
Scattered pressure	ps	Pascal	Pa
Density (quiescent)	ρ or ρc	kilogram/meter3	kg/m3
Frequency	f	Hertz	Hz
Wave number	k	1/meter	1/m
Dipole domain source	qd	newton/meter3	N/m3
Monopole domain source	Qm	1/second2	1/s2
Speed of sound	c or cc	meter/second	m/s
Specific acoustic impedance	Z or Zsp	pascal-second/meter	Pa·s/m
Acoustic impedance	Zac	pascal-second/meter3	Pa·s/m3
Normal acceleration	an	meter/second2	m/s2
Normal velocity	vn	meter/second	m/s
Source location	x0	meter	m
Wave direction	ek	(dimensionless)	1

In the following descriptions of the functionality in this physics interface, the subscript c in ρc and cc (the density and speed of sound, respectively) denotes that these can be complex-valued quantities in models with damping.

When this physics interface is added, these default nodes are also added to the — , , and .

Then, from the toolbar, add other nodes that implement, for example, boundary conditions and point conditions. You can also right-click to select physics features from the context menu.

	Physics Nodes — Equation Section in the COMSOL Multiphysics Reference Manual

The is the default physics interface name.

The is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the field. The first character must be a letter.

The default (for the first physics interface in the model) is acpr.

Expand the section to see the equations solved for with the specified. The default selection for is . The available studies are selected under .

•

For , the scaling and nonreflecting boundary settings are optimized for the numerical performance of the different solvers and study types.

Select to (selected per default). This shows the physics symbols, like for example, normals or symmetry planes in the Graphics window when applicable.

In this section you can add out-of-plane information defining an out-of-plane wave number kz or an azimuthal wave number km = m/r through the mode number m. Add if applicable:

•

For 1D axisymmetric components, the default kz (SI unit: rad/m) is 0 rad/m. The default m (dimensionless) is 0. The pressure has the form:

•

For 2D axisymmetric components, the default m (dimensionless) is 0. The pressure has the form:

•

For 2D components, the default kz (SI unit: rad/m) is 0 rad/m. The pressure has the form:

Note that when performing a mode analysis study in 2D (solving for the out-of-plane wave number) the property is not used as this is now the variable solved for.

For all component dimensions, and if required, click to expand the section, then select as the and enter the settings as described below.

The default Δ is 1/ω2 and is . These values correspond to the equations for a Frequency Domain study when the equations are study controlled.

To get the equations corresponding to an Eigenfrequency study, change the Δ to 1 and the to .

Select to enable the option (not selected per default). This option is used to compute the full scattering matrix when Port conditions are used. For more details see The Port Sweep Functionality subsection. The section only exists for 3D and 2D axisymmetry.

The zero level on the dB scale varies with the type of fluid. That value is a reference pressure that corresponds to 0 dB. This variable occurs in calculations of the sound pressure level Lp based on the root mean square (rms) pressure prms, such that

where pref is the reference pressure and the star (*) represents the complex conjugate. This is an expression valid for the case of harmonically time-varying acoustic pressure p.

Select a based on the fluid type:

•

to enter a reference pressure pref, SPL (SI unit: Pa). The default value is the same as for air, 20 μPa.

Enter a value or expression for the cref (SI unit m/s). The default is 343 m/s.

From the list select the element order and type (Lagrange or serendipity) for the , the default is .

	Choosing between Lagrange and Serendipity Shape Functions has influence on the number of DOFs solved for and on stability for a distorted mesh.

To see all settings in this section, click the button (

) and select in the dialog box.

This physics interface defines one dependent variable (field), the p. If required, edit the name, which changes both the field name and the dependent variable name. If the new field name coincides with the name of another pressure field in the model, the interfaces share degrees of freedom and dependent variable name. The new field name must not coincide with the name of a field of another type, or with a component name belonging to some other field.