Let's undertake a simple FINITE DIFFERENCE EXERCISE based on the simplistic set-up that we used to illustrate how finite differences work. Recall the problem involved a one-dimensional confined aquifer, with a constant initial head across its length. Then instantly drop the head on the right end of the aquifer while maintaining a constant head on the left side.

we defined a grid on it, one unit thickness into the computer screen

initial head will be the same for each cell

cell 1 will be a constant head equal to the initial head, HL

cell 5 will be defined as a constant head equal to the head, HR that begins the stress on the right

for this exercise, let:

y = 3 ft
b = 3 ft
HL = h1 = 8.2 ft
HR = h5 = 3.6 ft
K = 0.02 ft/day T= 0.06 ft2/day
s = 0.00033 ft-1 S = 0.001

initially, h1 = h2 = h3 = h4 = h5 = 8.2 ft

for t>0 h5 = 3.6 ft

First follow the explicit option:


Then follow the implicit option: