A low-order BEM has been developed by Morino and Kuo [2]
for solving the boundary integral
equation (6) in the case of fully wetted (non-cavitating) flow.
The hydrofoil surface is approximated with N flat panels on which constant
strength dipoles and sources are distributed.
The source strengths
are proportional to 
and are known
via equation (3).
The dipole strengths are
proportional to 
and are determined from applying equation (6)
at the mid-points of the panels.
The Kutta condition is numerically implemented by employing Morino's condition [2].
where 
and 
are the potentials at the upper
and lower trailing edge panels, respectively.
The discretized version of equation (6) may be written in the following matrix form:
where 
and 
are the vectors
with N components the
perturbation potentials and their normal derivatives on each panel,
respectively.
In the case a cavity is present, the low-order BEM was extended by
Kinnas and Fine [3]. In this case equation (6)
still applies. Now, the source strengths are only known on the wetted
part of the hydrofoil. However, by integrating equation (5)
over the cavity surface, on the cavity
can be expressed in terms of the arclength
and the cavitation number 
. The unknown sources on the cavity surface,
the unknown potentials on the wetted surface, and the cavitation
number are determined from inverting
equation (6). The cavity surface of course is not known, and its
shape is determined iteratively. The method was shown in [3]
to converge quickly with number of iterations, where the cavity shape
in the first approximation was taken the same as that from linear cavity theory
[4].
