Environmental Engineering Reference
In-Depth Information
Sidebar 15.1: Summary of the Analytical Method
In summary, the set-up of a model based on an analytical solution can be
divided into 4 steps, which are repeated here in brevity with some comments:
Step 1
Choose the analytical formulae that are appropriate for the situation to be
modelled.
See Table
15.1
.
Step 2
Compute the analytical solution by superposition of the chosen elements; that
means: add all potential and streamfunction elements!
Step 3
Numerical Postprocessing
Compute hydraulic heads
= KðÞ
1
2
K H
2
'ðx; yÞþ
'
0
for the confined aquifer
p
2
'ðx; yÞ'
0
hðx; yÞ¼
ð
Þ=K
for the unconfined aquifer
Compute flux vector components
q
x
ðx; yÞ¼
@'ð
x
;
y
Þ
@x
q
y
ðx; yÞ¼
@'ð
x
;
y
Þ
@y
8
<
9
=
8
<
9
=
q
x
ðx; yÞ¼
@Cðx; yÞ
@y
q
y
ðx; yÞ¼
@Cðx; yÞ
@x
or
:
;
:
;
Compute velocity vector components
q
x
ðx; yÞ=H
for the confined aquifer
v
x
ðx; yÞ¼
and
q
x
ðx; yÞ=hðx; yÞ
for the unconfined aquifer
q
y
ðx; yÞ=H
for the confined aquifer
v
y
ðx; yÞ¼
q
y
ðx; yÞ=hðx; yÞ
for the unconfined aquifer
The last two formulae are to be processed for groundwater flow based on
the discharge potential. For free fluids the potential has to be transformed in
terms of pressure (see Chap. 14.2).
Step 4
Graphical Postprocessing
Plot (optionally):
- Hydraulic heads
- Velocity vectors
- Streamfunction contours
- Path lines
