Background Pressure Field

Add a 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 on 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 a Frequency Domain study type, the frequency of the background pressure field is the same as for the dependent variable p.

	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.

Select a : (the default), , , or . 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 both the total, background, and scattered acoustic fields select at the bottom of the settings window. This requires an additional input of the ρ (SI unit: kg/m3) for the defined background pressure field. Selecting this option will also define the velocity variables for the various fields.

The option defines the background pressure field pb of the type:

where p0 is the wave amplitude, k is the wave vector with amplitude ks = ω/c and wave direction vector ek, and x is the location on the boundary.

For enter values for the p0 (SI unit: Pa), the c (SI unit: m/s) of the fluid defining the field, either or , enter a ek (dimensionless), and a

(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 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 , the plane wave is expanded in its cylindrical harmonics and a general ek can be selected. This sets up a wave of the form:

where m is the specified in the Pressure Acoustics Equation Settings. To expand the solution, it is necessary to run a 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

The 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), ks = ω/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 , enter a p0 (SI unit: Pa), the c (SI unit: m/s) of the fluid defining the field, either or , enter a x0 (SI unit: m), a esa (the vector does not need to be normalized), and a

(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.

The 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, ks = ω/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 , enter a p0 (SI unit: Pa), the c (SI unit: m/s) of the fluid defining the field, either or , enter a x0 (SI unit: m), and a

(SI unit: rad).

In 2D axisymmetric models, the incident fields take a slightly different form due to the geometrical restrictions. Only enter the z0 (SI unit: m) since the source is always located on the z-axis in a 2D axisymmetric model.

	For both the cylindrical and the spherical wave options the source and/or source axis should be located outside the domain where the background pressure field feature is defined.

For the option, enter an expression for the pb (SI unit: Pa).