How to Homogenize the Basic Fracture

The following describes how to use the JHomogenizer tool to homogenize a region of a small high permeability region surrounding a lower permeability region. The region around the boundary is small relative to the size of the entire region. The permeability value in the fracture is assumed to be at least one order of magnitude higher than the permeability in the interior of the region.

The fracture region can be homogenized using the following process. There are a few different things that would need to be done to produce the results shown on the main page for this test problem.

• If the JHomogenizer interface is not running, start up the interface. It is best to start the interface in the folder/directory where the data is stored. In particular, it is a good idea to start the tool in the parent folder of the fracture_data folder.
• Once the interface is up and running, you will need to bring up the MapEditor tool. This can be done using either the Show MapEditor button.
• When the MapEditor is showing, click on the Rectangular Fracture Map button. A dialog box will pop-up requesting the input data for the fracture pattern. The input includes the coefficient value in the fracture region, the coefficient value in the interior, and the number of grid blocks around the boundary that are used to represent the fracture zone. Note that the number of blocks in the region is determined by the dimension of the current map in the MapEditor tool. To change this, you can use the Build A Map button on the MapEditor. This will allow you to specify any size map you want.
• As an example, entering 100, 1, and 1 in the popup dialog will put a one block zone around the boundary with a coefficient of 100.0 and a center region, 19 by 19, with a coefficient value of 1.0.
• The next step is to get the data back into the JHomogenizer tool. Clicking on the Get All Data button on the JHomogenizer GUI will retrieve the data from the MapEditor tool. Once this is done, you can click on the Kill MapEditor tool to dismiss the MapEditor.
• To compute the homogenized value, choose a homogenization method from the Homogenization Method List in the JHomogenizer interface. For example, click on the HomCode choice in the list.
• Finally, click on the Homogenize! button. The interface will start the calculations and the status will be shown in the Status: line near the bottom of the interface. You will be prompted for a map name for the result of the homogenization process. Enter the name in the dialog and type a carriage return or click on the Okay button.
• You can display the values by clicking on the map in the map list and then you click on Display Values button. The values will be displayed in the text window. The values from the HomCode choice should be the following.
  
  

  11.3591	-0.000004	0.0000
  -0.000004	11.3591	0.0000
  0.0000	0.0000	19.810

• Once this is done, other methods can be applied to the initial map by clicking on the map in the map list. In our example, click on map in the list. Then click on another homogenization method choice and finally click on the Homogenize! button. To display the new values, click on the Display Values button.

We can also create a periodically extended map using the rectangular fracture as the basic periodic cell. To do this, we can use the MapEditor tool. To do this do the following.

• Start up the MapEditor tool.
• Once the map is loaded into the display area, click on the Periodically Repeat. The interface will popup a dialog that allows the user to specify the number of periodically repeated versions to be included in the new.jhm. For the example above, the entries should be changed to 4 and 4 in the first two coordinate direction. If the number of blocks in any direction is equal to one, then no periodic extension is done in the coordinate direction.
• The last step is to retrieve the data from the MapEditor tool. To do this click on the Get All Data in the JHomogenizer GUI. Enter the name of the file (e.g, 80x80hetero.map) and save the file if desired.

Finally, you can save the map data and all of the homogenized results by clicking on the Save Maps button. The data will be stored in a folder with the same name as the name of the file. All of the homogenized results will be stored in subfolders of the original folder.

To reload the data you can use the instructions in some of the other examples. These instructions will not be repeated here.