Create a Prolate Spheroidal Mesh and Convert to Cartesian Coordinates
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Contents
- Create a Prolate Spheroidal Mesh and Convert to Cartesian Coordinates
- Description
- Start Continuity
- Create coordinates and basis functions
- Read prolate spheroidal nodal coordinates and element
- Calculate and render mesh
- Refine mesh circumferentially into four elements
- Change basis functions to cubic Hermite and render mesh
- Convert coordinates to rectangular Cartesian
- Pre-built model
Description
- In this example, a 3-D ellipsoidal mesh is created in prolate spheroidal coordinates using one trilinear Lagrange element. It is then converted to a 4-element cubic Hermite mesh in Cartesian coordinates.
- The nodal coordinates and element connectivities are read from tab-delimited spreadsheets.
The steps below are saved in a script that can be found in the examples directory on your Continuity client .../continuity/pcty/examples/mesh04/convertToCartesianUnit.py which can be executed automatically with File→Scripts→Read Script→Python script
Start Continuity
- Launch the Continuity Client
On the About Continuity startup screen
leave the mesh checkbox checked under Use Modules:
Click OK to bring up the main window
Create coordinates and basis functions
Select prolate spheriodal in the Global Coordinates: pop-up menu
Enter 3.75 in the Focus Position field
Click OK to submit Coordinate Form
Choose Hermite Basis Function→3D→Linear-Cubic-Cubic
Click Add Linear-Cubic-Cubic
Choose Hermite Basis Function→3D→Cubic-Cubic-Cubic
Click Add Cubic-Cubic-Cubic
- Verify that the list of basis functions now contains:
- Linear-Cubic-Cubic Hermite 3*3*3
- Linear-Cubic Hermite 3*3
- Cubic-Cubic Hermite 3*3
- Cubic-Linear Hermite 3*3
- Cubic-Cubic-Cubic Hermite 3*3*3
Click OK to submit Basis Form
Read prolate spheroidal nodal coordinates and element
Click Import/Export/Graph button to open Continuity Table Manager
Continuity Table Manager→File→Open...
Select tab-delimited nodes file ( nodes.xls )
Under Coordinate 1, Coordinate 2, and Coordinate 3, verify that the basis function for each coordinate is Linear-Cubic-Cubic Hermite. If it is Cubic-Cubic-Cubic Hermite or anything else, make sure to change it to Linear-Cubic-Cubic Hermite.
In the Node Form under Dervatives with respect to, select the Angle Changes radio button
- You should now have nodes numbered 1-4
Click OK to submit Node Form
Click Import/Export button to open Continuity Table Manager
Continuity Table Manager→File→Open...
Select tab-delimited elements file [( elems.xls )
- You should now have only one element in the list
Click OK to submit Element Form
Calculate and render mesh
Click lines radio button
Click Render to display mesh
- The mesh should now look similar to the first screenshot
Refine mesh circumferentially into four elements
Enter 4 for xi1, 1 for xi2, and 1 for xi3 under New Element per old element in
Select the Local coordinates radio button under New nodal derivatives with respect to:
Click OK to submit
Change basis functions to cubic Hermite and render mesh
Select Cubic-Cubic-Cubic under Coordinate 1, Coordinate 2, and Coordinate 3
- All derivatives for all three coordinates should now be enabled
Click OK to submit Node Form
If the Dimensions Form appears, simply click Apply Marked Recommendations and then OK
Click lines radio button
Click Render to display mesh surface
Click on elements lines2 in the list on the left
Click on the Colors tab
Change the R,G,B color field to 1.0, 0.0, 0.0 to change the color to the brightest red and hit Enter
Click on elements lines1 in the list on the left
Check and uncheck the Visibility checkbox a couple times to compare the two different renderings
Close the window by clicking the X button
- The mesh should now look similar to the second screenshot
Convert coordinates to rectangular Cartesian
Mesh→Convert nodes to Cartesian...
Leave the update nodes and update coordinates checkboxes checked
Click OK
Select the Save, reset, and reload radio button on the bottom
Click OK
Click lines radio button
Click Render to display mesh surface
Click on elements lines3 in the list on the left
Click on the Colors tab
Change the R,G,B color field to 0,0,0 to change the color to black and hit Enter
Click on elements lines2 in the list on the left
Check and uncheck the Visibility checkbox a couple times to compare the two different renderings
Close the window by clicking the X button
- The mesh should now look similar to the third screenshot
Pre-built model
This cont6 file contains all data and parameters for this problem: mesh7.cont6 (As this is the final model, rendering elements will produce the mesh like the last screenshot)