Create a Prolate Spheroidal Mesh and Convert to Cartesian Coordinates

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

• Mesh→Edit→Coordinates…

  • Select prolate spheriodal in the Global Coordinates: pop-up menu

  • Enter 3.75 in the Focus Position field

  • Click OK to submit Coordinate Form

• Mesh→Edit→Basis…

  • 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

• Mesh→Edit→Nodes…

  • Click Import/Export/Graph button to open Continuity Table Manager

    • Continuity Table Manager→File→Open…

      • Select tab-delimited nodes file ( nodes.xls )

      • Continuity Table Manager→File→Close and update form

  • 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

• Mesh→Edit→Elements…

  • Click Import/Export button to open Continuity Table Manager

    • Continuity Table Manager→File→Open…

      • Select tab-delimited elements file [( elems.xls )

      • Continuity Table Manager→File→Close and update form

  • You should now have only one element in the list

  • Click OK to submit Element Form

Calculate and render mesh

• Mesh→Render→Elements…

  • 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

• Mesh→Refine…

  • 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

• Mesh→Edit→Nodes…

  • 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

• File→Send

  • If the Dimensions Form appears, simply click Apply Marked Recommendations and then OK

• Mesh→Calculate Mesh…

• Mesh→Render→Elements…

  • Click lines radio button

  • Click Render to display mesh surface

• View→Show Open Mesh…

  • 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

• File→Reset…

  • Select the Save, reset, and reload radio button on the bottom

  • Click OK

• Mesh→Render→Elements…

  • Click lines radio button

  • Click Render to display mesh surface

• View→Show Open Mesh…

  • 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)