Characteristic Specific Impedance Models
For well-defined wave types in infinite domains, an impedance condition exists in every point whereby the pressure and normal velocity are related. Thus, these impedances can be imposed on a boundary to model an infinite, open domain in cases where the wave source inside the domain is either a direction (plane wave), a point (spherical wave) or a line (cylindrical wave). However, be aware that only the boundary-normal component of the velocity is used in the impedance boundary condition while the tangential component is ignored; in cases of nonnegligible tangential components it is recommended to instead use the options Plane Wave Radiation, Spherical Wave Radiation, and Cylindrical Wave Radiation.
Plane wave
The impedance is given by
,
see Ref. 6. This is given solely by material parameters and has no user input.
Spherical wave
This impedance corresponds to the wave from a point source. It is calculated from the expression (given in Ref. 6)
where x0 is the user-specified location of the point source generating the spherical waves, x is the position of the boundary, and rb is the distance between the two.
Cylindrical wave
This classic infinite-domain wave impedance from an acoustic line source with the user-specified direction and position x0 is presented in, for example, Ref. 6. The expression for the impedance is
where is the Hankel function of the second kind of order m given in terms of the Bessel functions of order m of the first and second kind, Jm(x) and Ym(x), respectively. Notice that the source axis vector esa is automatically normalized in this implementation.