in the homogeneous domain exterior to a closed surface, S,
can be explicitly expressed in terms of the values of
p and its normal derivative on
S:
Here the coordinate vector r parameterizes
S. The unit vector
n is the outward normal to the exterior infinite domain; thus,
n points
into the domain that
S encloses. The function
G (R, r) is a Green’s function satisfying
This essentially means that the Green’s function, seen as a function of r, is an outgoing traveling wave excited by a simple source at
R. In 3D, the Green’s function is therefore:
The default in the Exterior Field Calculation feature is to evaluate the full Helmholtz-Kirchhoff integral given in
Equation 2-19 and
Equation 2-20.
Taking the limit of Equation 2-19 when |
R | goes to infinity and ignoring the rapidly oscillating phase factor, the far field,
pfar is defined as
In this integral, r and
z are the radial and axial components of
r, while
R and
Z are the radial and axial components of
R.
To evaluate the pressure in the far-field limit according to the equations in this section, set the Type of integral option to the
Far-field integral approximation for r → ∞ option in the
Exterior Field Calculation section in the
Settings window for the feature. See
Exterior Field Calculation.