4 FINITE ELEMENT FORMULATION
4.1 Open Sea Problems
CGWAVE uses the finite-element method, which is a powerful approach for
modeling coastal phenomena in regions of complex shape. In the case of a group of
scatterers surrounded by an open sea of constant depth, the incident wave may be written
as (Demirbilek and Gaston, 1985)
∞
= A ∑ εn i n J n (kr)cos n(θ - θI )
ikr cos(θ- θI )
ηI = Ae
(15)
$
n =0
where A is the amplitude of the incident wave, θI is the incident wave angle with respect
to the x-axis, Jn is the n-th order Bessel functions of the first kind and
1 when n = 0
εn =
(16)
2 when n ≠ 0
The incident direction is defined such that the incident wave travels in the positive x-
direction when θI is equal to zero; the x-direction is obtained from the bathymetry data file
that is input to the CGWAVE program. This bathymetry file should be oriented such that
the x-axis points to the east.
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