56
Figure 4.1: Definition sketch of grid nomenclature and coordinate system.
equations for N unknowns. Returning to the illustrative example where N is equal to four,
the matrix Eq. (4.31) becomes
6i + 7\d\ ci
02 f>2 C%
O3 63
CS
' A\+1 '
di '
A'2+1
d2
4+1
3
[ 4+1J
. d< .
(4.37)
where 7\ and 7n represent the functional relationships as described above on the j=l and
j= N boundaries.
Equation (4.37) is solved easily for the unknown A)+1 using a double sweep method.
In the computer program the subroutine CTRIDA uses an algorithm of Carnahan, Luther,
and Wilkes (1969) to efficiently accomplish the double sweep solution of eq. (4.37).
4.3 Boundary Conditions in the Circulation Model
As shown in figure 4.3 a staggered grid system is used so that velocities are expressed
at the grid edge and fj and the wave properties are defined at the grid center. So that the
wave model will have full grids it is desirable to place the boundaries of the model at the
grid edges on all sides, with the exception of the offshore grid row where the wave conditions
are an input or boundary condition for the wave model. Figure 1.1 can also be referred to.
The offshore boundary condition that is used in the circulation model is that the mean