CE 473/573 Groundwater
Fall 2007
Comments on homework 6
35. To show that you solved this problem correctly, plot the two numerical solutions along
with the analytical solution. Also, remember the advice for choosing the grid spacing:
Double the number of points until the results change by less than a specified amount
(say 1% or 0.1%). Finally, note that I wrote down the wrong formula for the effective
conductivity in class. For constant ∆x it should be
2
Ki+1/2,j
=
1
Ki+1,j
+
1
.
Ki,j
You can see that the formula I gave (without the 2) is incorrect because the conductivity at the phantom points was about half of the conductivity at the two neighboring
points. For 1D flow with fixed boundary heads, the magnitude of K does not matter; only the spatial variation affects the heads. Therefore, even with the incorrect
formula, you should get the same heads.
36. We discussed this problem to some extent in class. As with all problems involving
numerical simulation, it helps to show your formulation of the problem—that is, how
you solved for the heads. In computing the flow across the right boundary, two
groups used the difference in heads between the left and right boundary; this approach
is incorrect because it uses the average gradient, not the actual gradient. Instead,
compute the gradient using the heads in the last two columns, apply Darcy’s law, and
sum the flows to get the total flow. We also discussed how to interpret the output of
Modflow.
37. We discussed this problem in detail in class. I showed you how to formulate the
numerical solution of this problem and solve it in Excel. The groundwater divide
occurs where the specific discharge is zero (i.e., where the gradient is zero).