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, H_L

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



for this exercise, let:

y = 3 ft
b = 3 ft
H_L = h₁ = 8.2 ft
H_R = 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:

EXPLICIT OPTION

Then follow the implicit option:

IMPLICIT OPTION