|Groundwater modelling with MicroFEM • Lesson 6A: FemMesh grid generation|
One of the advantages of finite element models above finite difference models is that finite element models are far more flexible with respect to the grid. The irregularly shaped elements allow you to take care of all kinds of linear or curved inner and outer boundaries (aquifer boundaries, faults, meandering rivers, etc.). Nodes can be located at the exact position of pumping and observation wells.
This flexibility also has disadvantages, since it takes more effort to create a well-designed grid. However, when our ambitions are not very high, we can do with a type of grid typical for finite difference models (like ModFlow). In such models the shape is a simple rectangle and the grid is more refined somewhere in the middle part because that is the area of interest.
To create such a grid is very simple with the FemMesh generator. It requires the location of 8 nodes: 4 boundary nodes and 4 nodes that define the four-sided more refined inner area. For each of these 8 nodes we also have to specify the element sizes near that node. Around the four-sided inner rectangle we define 4 trapezoidal quadrangles. These five quadrangles cover the full model area. In the following example we will create such a simple FemMesh grid.
The model area is about 7,500 by 5,500 m, while the centre part with the finer spacing is 1,500 by 1,500 m.
Start MicroFEM /
Menu bar: Files / New grid ... / Create New grid / Large contrast grid (FemMesh) / [OK]
Enter the Model name in the upper cell: "Lesson 6" / [OK]
Table: Fixed nodes tab / Enter 8 in the cell above the table / [Change number to]
Clicking the [Change number to] button increases the size of the Fixed nodes table to 8 rows.
Enter the following data one-by-one in the table of 8*3 cells.
The easiest way is to open the upper left cell and then only use the Keyboard: enter 0 / [Enter] / 0 / [Enter] / 400 / [Enter] / 7500 / etc.
When there are tabs (not spaces) between the numbers, you can also paste all data into the table. In that case right-click the upper-left cell when it is blue (not open) and select "Paste" in the pop-up menu. We do not use Triangular regions (skip that Tab) since our grid will be based on five quadrangular regions.
Table: Quadrangles tab
Change the number to "5" / [Change number to]
Enter the following data one-by-one in the table of 5*4 cells (pasting doesn't work here)
Toolbar: [F8] / [F8] / [F8]
When you are still unsure how the five quadrangles are defined, click on each row of the Quadrangles table.
Finish the grid generating procedure.
Toolbar: [F8] / [F8] / [F8]
Of course it is not required to create such a symmetrical grid.
Change data fixed node 3 into: 9000 7000 700
And fixed node 7 into: 4600 3600 70
Generate the grid (six times [F8])
Since the maximum number of regions is 100 quadrangles and 100 triangles a quite complex grid can be generated with FemMesh.
Not let us make the grid slightly more complex.
Add a Fixed node (no 9): 3700 -1500 and spacing 500.
Add three trianles: 1,5,9; 5,6,9 and 9,6,2.
Delete the first Quadrangle (Click on one of its cells / Right-click / Delete / Quadrangle
Generate the grid.
When you are not satisfied with the results, you may press the [Esc] key anytime to interrupt, modify input data and then restart the grid generation process.
Save the grid [F9]
The shape of the triangles and quadrangles is free to choose as long as they do not overlap, and together cover the whole model area. Actually, small regions within the model area may be left undefined. In such regions no nodes will be added during the "Nodes within regions" step.
Load the Example input [F4] and check the above remark about small undefined region.