|Groundwater modelling with MicroFEM • Lesson 5B: Boundary conditions|
When we chose a fixed-head boundary, the head is specified (given) by us, while the boundary flux (and the head gradient) is computed by the model. When we chose a no-flow boundary, the boundary flux (and the gradient) is given by us (zero), while the head is computed by the model.
From the latest computations it appears that the model boundary condition (fixed head or no-flow) has so little effect on the drawdown in the well that we find a well head of –0.720 in both cases. When the model boundary is chosen far enough from the well, the boundary condition has a negligible effect on the model results.
The drawdown at the no-flow boundary is 0.000 m at the corners of the model boundary, and –0.001 m in the middle of the North and South boundary sides. When you drag the bar between the Table and the Map a little to the left (as we did in Lesson 1C, Step 6) these values appear to be –0.00040 and –0.00066 m respectively (when "Error of heads" is still set at 1E–12, or 10–12, on the Calculation options window).
Menu bar: Files / Save all
When discussing boundary conditions this usually refers to the outer boundary of the model. However, this is not necessarily always the case. It is perfectly permitted to define an inner fixed-head boundary. The heads of such nodes remain fixed when the model heads are computed. This implies that water will flow into or out of the model via such inner open boundaries.
Example: In our present single layer well flow model we discharge 1000 m3/d and compute a head in the well of –0.71975 m. We can consider this as a constant (or given) boundary flux condition. Alternatively, we can set the well discharge to zero and make this single node an open boundary with a fixed head of –0.71975 m.
Zoom in on the well node (e.g. scale 1:100)
[Walking mode] / [Del] / [Automarker (F10)] / Click the well node / [F10]
The well node is now marked, but this is only obvious from the yellow bordered node numbers on the Status line. To recognise a single marked node in the map you can "toggle" all marks with the [F9] button. This button invokes that all marked nodes become unmarked, and all unmarked nodes become marked. Only marked nodes are connected with yellow lines. Click [F9] again to restore the situation with the well node marked only.
We will now set the fixed-head boundary condition:
[Input mode] / H1 / [F9] / [Del]
and remove the well discharge (set Discharge to zero):
Select Q1 / Open cell / 0 / [Enter]
The well node head is now fixed at –0.71975 and the well discharge is zero.
Menu bar: Calculate / Go calculate
[Walking mode] / [F5]
The boundary outflow appears to be 1000 m3/d, the same as the original well discharge. We can now specify any fixed-head well level and compute the discharge. Drawdown and discharge are linearly related. Check this with well levels of –0.36 m (50%), –1.4395 (200%) and when the well level is reset to –0.71975.
[Walking mode] / [F2]
The lateral flow component is the (horizontal) flow across the internal boundary of the water balance area (i.e. the boundary between the shaded water balance area and the other (non-shaded) parts of the model). In this case the lateral flow is the inflow over the six-sided boundary of the shaded area.
The inflow from leakage (in this small = 1.2 m2 area) is given as 0.00 m3/d. When we compute this manually, we find a very small value indeed: Leakage = a*(H0–H1)/C1 = 1.2*(0.71975)/1500 = 0.000576.
This ends lesson 5. The model has already been saved.