3.0 GROUNDWATER FLOW SOLUTION THEORY
The governing equation assumed to represent the tran-
sient distribution of groundwater head in a confined, homo-
geneous, isotropic aquifer in two dimensions is (adapted
from Reference 4):
D2h +  82h    S   h
t        +q                      (3.1)
3x2    D 2    T   t
Terms used in this section are defined at the begin-
ning of this report. The above equation cannot be solved
directly.   By imposing a grid over the problem domain and
approximating equation 3.1 in terms of its finite differ-
ences between the grid intersection points, a set of simul-
taneous equations, one representing each grid intersection
(node point), can be formulated. The unknown in each equa-
tion is the head condition at the node in question at a
given time. The known terms are the aquifer properties, T
and S, the flow rate q, and the x, y and t values of the
solution.    This  set of simultaneous    equations  is then
solved iteratively using the solution method presented by
Prickett  and  Lonnquist(3).    Figure 8.1   illustrates  the
Exxon Crandon Project study area overlain by a matrix of
discrete node points.     This  example case will    be used
throughout this report for demonstration purposes.
Solution of the simultaneous finite difference equa-
tions requires definition of the boundary conditions.
These boundary conditions are; (1) the initial head con-
figuration at each node point at the beginning of the anal-
ysis and (2) either "no-flow" or "constant head" nodes at
the periphery of the study area. These boundary conditions
are required to reduce the total number of unknowns to that
which can be uniquely solved.

Goider Associates

786085

March, 1982