|Groundwater modelling with MicroFEM • Lesson 4A: Hexagonal FemMesh grid|
From the previous lesson we learned that a small spacing between nodes is required when we want to model the head inside a pumping well. For example, when the well diameter is 0.4 m, its radius is 0.2 m and the nodal spacing around the well should be 1.2 m. Such a small local spacing can best be obtained with the "FemMesh" grid generator.
In this lesson we will build a new model, now in 5 steps. The purpose is to compute the drawdown inside and around the well accurately. We will first consider a fully confined aquifer, and change this to a leaky aquifer in the next lesson.
Step 1: Create a grid for well flow
Menu bar: Files / New grid ... / Create New grid / Large contrast grid (FemMesh) / [OK]
Enter the Model name: "Lesson 4" / [OK]
Toolbar: [F5] / Radius = 10000 / [OK]
The hint of this F5 button reads: "Start with a hexagon", similar to the button we used in Lesson 1 with the "FemGrid" generator. With this F5 button we automatically filled the Table (right-hand side) with all the required information to generate our grid. This Table is somewhat different from what we saw in Lesson 1, when using the FemGrid generator.
The "fixed nodes" tab shows that there are 7 fixed nodes. Do not confuse "fixed nodes" of the grid generator with "fixed head" boundary conditions. The positions of fixed nodes are given in the table. These positions remain fixed during the grid generation process.
The coordinates of the fixed nodes are given in the first two columns. The 3rd column shows the (approximate) spacing near that node when the grid will be generated. This spacing is 2000 m at the boundary and 100 m for the centre node.
Toolbar: [F8] / [F8]
When we clicked [F8] the second time, this button showed the text "Nodes on segments". As a result a number of nodes appear in the shape of 6 triangles. The nodal spacing towards the centre becomes gradually smaller. The 6 triangles are defined on the Triangles tab.
Table: Triangles tab
Click on each of the 6 lines of the Triangles Table or click on one, and then use the Up & Down-arrow keys
Each triangle is defined by three fixed nodes.
Table: Quadrangles tab
There are no quadrangles defined for this grid.
Toolbar: [F8] / [F8]
Read the texts on the button before you click on it.
All nodes within the triangles are shifted (one by one, but very quickly) to the centre of their neighbouring (connected) nodes. Since the neighbouring nodes are also shifted, this process is repeated a few times. The purpose of this process is to improve the shape of the elements. Grids with equilateral elements produce the best (most accurate) results. Elements with obtuse angles are preferably avoided.
The "renumbering nodes" step shows no visible action.
Zoom in on the centre node (x = 0.00 y=0.00) until the surrounding grid is clearly visible.
The position of the node near the cursor is given on the Status bar. Click on the node just right of the centre node and check that the spacing between these nodes = 94.38 m. In our model we want this spacing much smaller, only 1.2 m.
Table: Fixed nodes tab
Table: Enter a spacing of 1.2 for the centre node (line 4, column 3)
Toolbar: [F8] / [F8] / [F8] / [F8] / [F8] / [F8]
The Status line shows that the grid now consists of 675 nodes. When you want to repeat the grid generation process, you can start by entering a new (or the same) value in any cell of the table, or you press the Esc-key. Zoom in on the centre node. Click on the node just right of the centre node and check that the spacing here is 1.18 m.
Save the grid and continue with Lesson 4B.
Toolbar: [F9] / Save fen-file / [F10] / [OK]