Background Pressure Field
Add a Background Pressure Field node to model a background/incident pressure wave to study the scattered pressure field ps, which is defined as the difference between the total acoustic pressure pt and the background pressure field pb:
This feature sets up the equations in a so-called scattered field formulation where the dependent variable is the scattered field p = ps. In a model where the background pressure field is not defined in all acoustic domains (or it is different), continuity is automatically applied in the total field pt on interior boundaries between domains.
The background pressure field has built-in options for plane waves, spherical waves, and cylindrical waves. It can also be defined by a user defined analytical expression, that is a function of space, or it can be given by the solution to another acoustics problem.
For exciting waveguide structures with a given wave type it is recommended to use the Port or Lumped Port conditions, instead of a background pressure field. If still used, the feature should be backed by a PML or radiation condition to model an infinite waveguide.
Background Pressure Field
Select a Background pressure field type: Plane wave (the default), Cylindrical Wave, Spherical Wave, or User defined. For 2D axisymmetric models, it is possible to expand the plane wave in their cylindrical harmonics.
To set up and calculate the intensity variables for the total, background, and scattered acoustic fields, select Calculate background and scattered field intensity at the bottom of the settings window. This requires an additional input of the Density ρ (SI unit: kg/m3) for the defined background pressure field. Selecting this option will also define the velocity variables for the various fields. Enabling this is useful for analyzing reflection problems, where the ratio between incident (background) and reflected (scattered) field power is of interest.
Plane Wave
The Plane wave option defines the background pressure field pb of the type:
where p0 is the wave amplitude, k is the wave vector with amplitude kω/c and wave direction vector ek, and x is the location on the boundary.
For Plane wave enter values for the Pressure amplitude p0 (SI unit: Pa), the Speed of sound c (SI unit: m/s) of the fluid defining the field, either From material or User defined, enter a Wave direction ek (dimensionless), and a Phase ϕ (SI unit: rad).
In 2D axisymmetric models, the incident fields take a slightly different form due to the geometrical restrictions. Only the z-component for the Wave direction ek can be entered. Per default, the wave can only travel in the axial direction since this is the only axisymmetric form of a plane wave.
By selecting Enable plane wave expansion, the plane wave is expanded in its cylindrical harmonics and a general Wave direction ek can be selected. This sets up a wave of the form:
where m is the Azimuthal mode number specified in the Pressure Acoustics Equation Settings. To expand the solution, it is necessary to run a Parametric Sweep over the mode number from 0 up to the desired resolution.
An example using the Enable plane wave expansion functionality can be found online in the Application Gallery. The model Plane Wave Scattering off a 2D Axisymmetric Object: Plane Wave Expansion Approach is found at www.comsol.com/model/51311
Cylindrical Wave
The Cylindrical Wave option defines the background pressure field pb as a predefined cylindrical wave:
where p0 is the amplitude given at the reference distance rref = 0.548/ks (the distance where the Hankel function is one), kω/c is the wave number, is the Hankel function of the second kind (representing an outgoing cylindrical wave), rs is the distance from the source axis, esa is the direction of the source axis, x0 is a point on the source axis, and x is the location on the boundary.
For Cylindrical Wave, enter a Pressure amplitude at reference distance p0 (SI unit: Pa), the Speed of Sound c (SI unit: m/s) of the fluid defining the field, either From material or User defined, enter a Source Location x0 (SI unit: m), a Source Axis esa (the vector does not need to be normalized), and a Phase ϕ (SI unit: rad).
In 2D axisymmetric models, the incident fields take a slightly different form due to the geometrical restrictions. Neither source location nor axis is needed as the source is always located on the z-axis.
Spherical Wave
The Spherical Wave option defines the background pressure field pb as a predefined spherical wave (only for 2D axisymmetric and 3D):
where p0 is the amplitude given at the reference distance of 1 m, kω/c is the wave number, rs is the distance from the source, x0 is the source location of the spherical wave, and x is the location on the boundary.
For Spherical Wave, enter a Pressure amplitude at reference distance p0 (SI unit: Pa), the Speed of Sound c (SI unit: m/s) of the fluid defining the field, either From material or User defined, enter a Source Location x0 (SI unit: m), and a Phase ϕ (SI unit: rad).
In 2D axisymmetric models, the incident fields take a slightly different form due to the geometrical restrictions. Only enter the Source Location, z coordinate z0 (SI unit: m) since the source is always located on the z-axis in a 2D axisymmetric model.
User Defined
For the User defined option, enter an expression for the Background pressure field pb (SI unit: Pa).
Acoustic Cloaking: Application Library path Acoustics_Module/Tutorials,_Pressure_Acoustics/acoustic_cloaking
Acoustic Scattering off an Ellipsoid: Application Library path Acoustics_Module/Tutorials,_Pressure_Acoustics/acoustic_scattering