|Groundwater modelling with MicroFEM • Lesson 2A: Drawing contour maps|
Start MicroFEM and load the "Lesson 1" model by clicking the project file "Lesson 1.fpr".
MicroFEM always starts in Walking mode, with the full model grid on the Map and the current node in the centre. We found that the head of the centre node is computed as –0.144 m or –0.14434 to be more precise.
Step 8: Draw contour lines of the computed heads
Toolbar [Drawing mode] (the third of the lower right 4 buttons).
The grid is automatically removed, and only the nodes are shown. The Toolbar for the Drawing mode is displayed. It is easily recognized by the 16 colours of the Palette.
Read the hints of all buttons of this toolbar.
The last button (Draw section (F12)) is grey and cannot yet be used. Note that the keyboard equivalents from left to right are: Ins, Del, F2, F3, F4, .... , F12. When you click Menu bar: Commands, you will see again that the available commands correspond one-to-one with the toolbar buttons. There is a little black star in the White box of the Palette. White is the current drawing colour. A drawing colour can be chosen by clicking one of the coloured squares.
Click a [Blue] square of the Palette / [Draw grid (Ins)]
[Red] / [F5] / [Green] / [F6] / The Spacing = 5000 / [OK]
The map grid are the green 5000-by-5000 m squares on the Map. All drawing objects are plotted on top of each other, e.g. the red model boundary on top of the blue element boundary lines.
Table: Make the "head [m]" cell (4th cell from the top) the active cell.
[Yellow] / [F7] /[OK]
A pop-up window with the Minimum value and the Maximum value of all nodal heads is displayed, together with a suggested Interval of 0.02 m. We accepted this Interval and as a result some kind of a "yellow spider web" is displayed on the Map.
[F7] / Interval = 0.01 / [OK]
You can choose almost any non-negative interval. When zooming and panning, the coloured figure is redrawn. Only when the model becomes extremely small, the very dense map grid is not displayed.
Right-click in the Map: a pop-up menu appears. Click on "Fit to scale".
Menu bar: Options / Map ... / Uncheck the "Model boundary" box / [OK]
In this way you have (temporarily) removed the red Model boundary drawing object from the drawing list.
From the spider web figure it may be clear that the head contours are drawn by linear interpolation within each element.
When a numerical model is computed, the unknown heads of the nodes are found by solving a set of water balance equations. In MicroFEM these equations are based on the assumption that the head gradient is constant within each element. It is also assumed that the transmissivity is constant within each element. This implies that the flow is uniform (has same magnitude and the same direction) within each element.
In the upper element the direction of flow is 180 degrees (South). We can compute the gradient here as delta_h/delta_y = 0.14434/4330.13. We can read y = 4330.13 from the Status line, when the cursor is near one of the northern nodes. Because the elements are equilateral, all element angles are 60 degrees and 4330.13 = 5000 * (1 /2) * √3. In all other elements the direction of the gradient is different, but its magnitude is the same.
Step 9: The drawdown cone
The spider web is a 2D representation of our (very simple) drawdown cone. In this case the drawdown cone looks like an upside down six-sided pyramid.
Menu bar: Tools / 3D Viewer
Use the mouse wheel to adjust the size. To rotate the view, move the mouse cursor with the left button pressed.
3D Viewer menu bar: Tools / Options ... / Heads / Uncheck the box next to the green square / [OK]
This removes the green "base" of the pyramid. The six-sided symmetry of our "drawdown cone" and the constant gradient for each side (element) are obvious.
Close the 3D Viewer by clicking on the [x] in the upper right corner of the 3D Viewer screen.