As shown in Figure 2, the entire domain is
separated into two sub-domains. Domain Ω is the
numerical model domain. Domain Ω 0 is the exterior
domain extending to infinity. We assume that
complicated topography, structures, and islands, are
located inside the circular boundary Γ (in domain Ω ).
In Ω 0, the total wave potential can be written as the
sum of incident wave potential and the scattered
Fig. 2 Definition sketch
ηext = ηI + ηS
For brevity, we write the governing Equation 4 in the general form:
∇ ⋅(~∇ η)+ b η = 0
~ ≡ CC and ~ ≡ C g σ2 + iσw + iC σγ.
Mei (1983) has shown that the problem of solving Equation 18 with boundary
conditions described by (9) on coastlines/structures and by Equation 11 at infinity is
equivalent to the stationary of the following functional J:
J = ⌠ ⌠ ~(∇ η) - b Φ 2 dA - ⌠ α ~η2ds +
⌠ ~ 1
( ηS + ηI )
$ S + ηI S - η
a 2 η
The solution of the wave potential can be found by minimizing J over domain Ω .