The Incident Pressure Field node is a subnode to all nonreflecting boundary conditions (plane, cylindrical, spherical wave radiation, and matched boundary). From the
Physics toolbar, add to
Matched Boundary,
Plane Wave Radiation,
Spherical Wave Radiation, or
Cylindrical Wave Radiation nodes. In the frequency domain, four options exist for the
Pressure field type:
Plane wave,
Cylindrical wave,
Spherical wave, and
User defined.
The Incident Pressure Field has built-in functionality to perform a plane wave expansion. This allows modeling scattering problems involving 2D axisymmetry using a 2D axisymmetric, model even though a plane wave is not in general axisymmetric.
From the Incident pressure field type list, select
Plane wave (the default),
Cylindrical wave,
Spherical wave, or
User defined to define the incident pressure field type.
If the incident pressure field pi is a predefined plane wave, it is 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 Plane Wave, enter a
Pressure amplitude p0 (SI unit: Pa), the
Speed of Sound c (SI unit: m/s) of the medium defining the incident wave, the
Wave direction ek (SI unit: m), and a
Phase (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.
If the incident pressure field pi is a predefined cylindrical wave, it is of the type:
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 Cylindrical wave, enter a
Pressure amplitude at reference distance p0 (SI unit: Pa), the
Speed of sound c (SI unit: m/s) of the medium defining the incident wave, a
Source location x0 (SI unit: m), a
Source axis esa (the vector is automatically normalized), and a
Phase (SI unit: rad).
If the incident pressure field pi is a predefined spherical wave (only for 2D axisymmetric and 3D), it is of the type:
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 Spherical wave, enter a
Pressure amplitude at reference distance p0 (SI unit: Pa), the
Speed of sound c (SI unit: m/s) of the medium defining the incident wave, a
Source location x0 (SI unit: m), and a
Phase (SI unit: rad).
In 2D axisymmetric models, the incident fields take a slightly different form due to the geometrical restrictions. Only enter the z-coordinate for the
Source location z0 (SI unit: m) since the source is always located on the
z-axis in a 2D axisymmetric model.
If User defined is selected, enter the expression for the
Incident pressure field pi (SI unit: Pa) as a function of space.