8.2. Seawater Intrusion
269
and for the seawater equation as
h s [
*h
*h ] oh s - 0
7f + D - Zo + Ps s - Pf f on - ,
(8.2.28)
where D is the elevation of sea level, Zo is the elevation of the aquifer bottom,
and IX and ß are parameters to be identified.
8.2.3 Numerical Methods Jor Determining the
Location oJ I nterJaces
The discrete form of Eqs. (8.2.25) and (8.2.26) can be obtained using the
standard procedure of the Galerkin FEM. First, the two equations are rewritten into the following operator form
Ls(hs, h f ) == 0 and L f(h" h f ) == O.
(8.2.29)
Define the trial functions
(8.2.30a)
and
N
h f = L Hfj(t) (h(x, y)
(8.2.30b)
j=l
as the approximations of h s and h f , where {(MX, y), j = 1,2, ... , N} is a set of
basis functions. The (h(x, y) are also used as the weighting functions based on
the principle of Galerkin FEM, so we will have the following weighted
residual equations:
r Ls(h s , h f )(h dO = 0, (i = 1,2, ... , N);
J(O)
r Lf(h"hf)(h dO = 0, (i = 1,2, .. . ,N).
J (n)
(8.2.31a)
(8.2.31b)
Substituting Eq. (8.2.29) into the above two equations and using Green's
formulas to eliminate the terms with second-order derivatives, we then have