By assuming the fluid ideal such that there exists a velocity potential function
with isolated space dependent term 
and employing linear hydrodynamic theory (for example, see [30]), accounting for wave radiation and diffraction, the
fluid-structure interaction behavior is described by the following set of equations in the
fixed reference axes (FRA):
Laplace equation:
(4–13)
applicable everywhere in the fluid domain, Ω.
Linear free surface equation of zero forward speed case:
(4–14)
Body surface conditions:
(4–15)
on the mean wetted body surface
. Here, 
represents the velocity potential function describing the initial
incoming sinusoidal wave system.Seabed surface condition at depth of
:
(4–16)
A suitable radiation condition must be added to these equations so that as
the generalized wave disturbance dies away.
A boundary integration approach is employed in Aqwa to solve the fluid velocity potential governed by the above control conditions. In this approach the frequency domain pulsating Green's function in finite depth water is introduced, which obeys the same linear free surface boundary condition, seabed condition, and far field radiation conditions as those given in Equation 4–14 and Equation 4–16, and the following condition in the fluid field is satisfied:
 | (4–17) |
where 
denotes the position of a source, and the Dirac delta function is
The Green's function is expressed as
 | (4–18) |
where 
is the Bessel function of the first kind, and
Using Green’s theorem, the velocity potential of diffraction and radiation waves can be expressed as a Fredholm integral equation of the second kind:
 | (4–19) |
where
Further introducing the source distribution over the mean wetted surface, the fluid potential is expressed as
 | (4–20) |
in which the source strength over the mean wetted hull surface can be determined by the hull surface boundary condition given by Equation 4–15, such as
 | (4–21) |
The Hess-Smith constant panel method is employed in Aqwa to solve the above equation, in which the mean wetted surface of a floating body is divided into quadrilateral or triangular panels. It is assumed that the potential and the source strength within each panel are constant and taken as the corresponding average values over that panel surface. The discrete integral form of Equation 4–20 and Equation 4–21 are therefore expressed as
 | (4–22) |
where 
is the total number of the panels over the mean wetted body surface,
is the area of the m-th panel, and
are the coordinates of panel geometric center over the m-th and k-th panels
respectively.
Directly evaluating the frequency domain by the pulsating Green's function in finite depth is time-consuming. Aqwa uses a Green's function database to efficiently calculate the Green's function and its first order derivatives. The low frequency limit (in rad/s) of this database is
 | (4–23) |
where 
is the water depth and 
is the acceleration due to gravity.