5.4 Meshing Schemes
Meshing schemes in Cubit can be divided into four broad categories as detailed in the following sections.
If no scheme is selected, Cubit will attempt to assign a scheme using the automatic scheme selection methods.
5.4.1 Traditional Meshing Schemes
Traditional meshing schemes are used to apply a mesh to an existing geometry using the methods described in Meshing the Geometry (i.e. setting a scheme, applying interval sizes, and meshing). Traditional meshing schemes are available for all geometry types.
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5.4.2 Free Meshing Schemes
Free meshing schemes will create a free-standing mesh without any prior existing geometry. The final mesh will have mesh-based geometry.
5.4.3 Conversional Meshing Schemes
Conversional meshing schemes are used to convert an existing mesh into a mesh of different element type or size. For example, the THex scheme will convert a tetrahedral mesh into a hexahedral mesh.
5.4.4 Duplication Meshing Schemes
Duplication meshing schemes are used to copy an existing mesh from one geometry onto another similar geometry.
5.4.5 Parallel Meshing Scheme
The Sculpt algorithm is an all-hex, automatic, parallel meshing scheme available in the Cubit Pro version.
5.4.6 General Meshing Information
Information on specific mesh schemes available in Cubit is given in this section. The following sections have important meshing-related information as well, and should be read before applying any of the mesh schemes described below.
In most cases, meshing a geometric entity in Cubit consists of three steps:
Set the interval number or size for the entity (See Interval Assignment.)
Set the scheme for the object, along with any scheme-specific information, using the scheme setting commands described below.
Mesh the object, using the command:
Mesh {geom_list}
After meshing is completed, the mesh quality is automatically checked (see Mesh Quality Assessment), then the mesh is drawn in the graphics window.
The following table classifies the meshing schemes with respect to their applicable geometry.
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5.4.7 Automatic Scheme Selection
{geom_list} Scheme Auto
5.4.7.1 Default Scheme Selection
If the user does not set a scheme for a particular entity and chooses to mesh the entity, Cubit will automatically run the auto scheme selection algorithm and attempt to set a scheme. In cases where the auto scheme selection fails to choose a scheme, the meshing operation will fail. In this case explicit specification of the meshing scheme and/or further geometry decomposition may be necessary.
Set Default Element [Tet|Tri|HEX|QUAD|None]
Previous functionality of Cubit used a default scheme of map and interval of 1 for all surface and volume entities. For backwards compatibility and if this behavior is still desired, the none option may be used on the set default element command.
5.4.7.2 Auto Scheme Selection General Notes
In general, automatic scheme selection reduces the amount of user input. If the user knows the model consists of 2.5D meshable volumes, three commands to generate a mesh after importing or creating the model are needed.
To automatically calculate the meshing scheme
On the Command Panel, click on Mesh and then Volume.
Click on the Mesh action button.
Enter the appropriate value for Select Volumes. This can also be done using the Pick Widget function.
Select Automatically Calculate from the drop-down menu.
Click Apply Scheme then click Mesh.
volume all size <value>
volume all scheme auto
mesh volume all
The model shown in the following figure was meshed using these three commands (part of the model is not shown to reveal the internal structure of the model).
Figure 220: Non-trivial model meshed using automatic scheme selection
5.4.7.3 Scheme Firmness
Meshing schemes may be selected through three different approaches. They are: default settings, automatic scheme selection, and user specification. These methods also affect the scheme firmness settings for surfaces and volumes. Scheme firmness is completely analogous to interval firmness.
{geom_list} Scheme {Default | Soft | Hard}
Scheme firmness settings can only be applied to surfaces and volumes.
This may be useful if the user is working on several different areas in the model. Once she/he is satisfied with an area’s scheme selection and doesn’t want it to change, the firmness command can be given to hard set the schemes in that area. Or, if some surfaces were hard set by the user, and the user now wants to set them through automatic scheme selection then she/he may change the surface’s scheme firmness to soft or default.
5.4.7.4 Surface Auto Scheme Selection
Surface auto scheme selection (White, 99) will choose between Pave, Submap, Triprimitive, and Map meshing schemes, and will always result in selecting a meshing scheme due to the existence of the paving algorithm, a general surface meshing tool (assuming the surface passes the even interval constraint).
[Set] Scheme Auto Fuzzy [Tolerance] {value} (value in degrees)
5.4.7.5 Volume Auto Scheme Selection
When automatic scheme selection is called for a volume, surface scheme selection is invoked on the surfaces of the given volume. Mesh density selections should also be specified before automatic volume scheme selection is invoked due to the relationship of surface and volume scheme assignment.
Volume scheme selection chooses between Map, Submap and Sweep meshing schemes. Other schemes can be assigned manually, either before or after the automatic scheme selection.
Volume scheme selection is limited to selecting schemes for 2.5D geometries, with additional tool limitations (e.g. Sweep can currently only sweep from several sources to a single target, not multiple targets); this is due to the lack of a completely automatic 3D hexahedral meshing algorithm. If volume scheme selection is unable to select a meshing scheme, the mesh scheme will remain as the default and a warning will be reported to the user.
Volume scheme selection can fail to select a meshing scheme for several reasons. First, the volume may not be mappable and not 2.5D; in this case, further decomposition of the model may be necessary. Second, volume scheme selection may fail due to improper surface scheme selection. Volume schemes such as Map, Submap, and Sweep require certain surface meshing schemes, as mentioned previously.
5.4.8 Conversion
5.4.8.1 HTet
Applies to: Volumes
Summary: Converts an existing hex mesh into a conforming tetrahedral mesh.
HTet Volume <range> {UNSTRUCTURED | structured}
Unlike other meshing schemes in this section, The HTet command requires an existing hexahedral mesh on which to operate. Rather than setting a meshing scheme for use with the mesh command, the HTet command works after an initial hex mesh has been generated.
Two methods for decomposing a hex mesh into tetrahedra are available. Set the method to be used with the optional arguments unstructured and structured. The unstructured method is the default. Figure 221 shows the difference between the two methods:
Figure 221: Left: Unstructured method creates 6 tets per hex. Right: Structured method creates 28 tets per hex
5.4.8.1.1 Unstructured
This method creates 6 tetrahedra for every hexahedra. No new nodes will be generated. The orientation of the 6 hexahedra will be based upon the element node numbering, as a result orientations may change if node numbering changes. This method is referred to as unstructured because the number of tetrahedra adjacent each node will be relatively arbitrary in the final mesh. Tetrahedral element quality is generally sufficient for most applications, however the user may want to verify quality before performing analysis.
5.4.8.1.2 Structured
With this approach, 28 tetrahedra are generated for every hexahedra in the mesh. This method adds a node to each face of the hex and one to the interior. Although this method generates significantly more elements, the orientation and quality of the resulting tetrahedra are more consistent. Each previously existing interior node in the mesh will have the same number of adjacent tetrahedra.
5.4.8.2 QTri
Applies to : Surfaces
Summary: Meshes surfaces using a quadrilateral scheme, then converts the quadrilateral elements into triangles.
Surface <range> Scheme Qtri [Base Scheme quad_scheme>]
QTri {Surface <range> | Face <range> }
Set QTri Split [2|4]
Set QTri Test {Angle|Diagonal}
Discussion: QTri is used to mesh surfaces with triangular elements. The surface is, first, meshed with the quadrilateral scheme, and, then, the generated quads are split along a diagonal to produce triangles. The first command listed above sets the meshing scheme on a surface to QTri. The second form sets the scheme and generates the mesh in a single step.
In the first command, the user has the option of specifying the underlying quadrilateral meshing scheme using the base scheme <quad_scheme> option. If no base scheme is specified, Cubit will automatically select a scheme. For non-periodic surfaces, the base scheme will be set to scheme pave. For periodic surfaces, the base scheme will be set to scheme map.
Generally, the second command, Qtri Surface <range>, is used on surfaces that have already been meshed with quadrilaterals. If, however, this command is used on a surface that has not been meshed, a base scheme will automatically be selected using CUBIT’s auto-scheme capabilities. The user can over-ride this selection by specifying a quadrilateral meshing scheme prior to using the qtri command (using the Surface <range> Scheme <quad_scheme> command). QTri may also be performed on quadrilateral elements on a surface or a subset of quadrilateral elements on a surface. to split existing quadrilaterals the QTri command can be given a list of faces.
In addition to the default 2 tris per quad, the set qtri split command may alter the QTri scheme so that it will split the quad into 4 triangles per quad. Where the 4 option is used, an additional mesh node is placed at the centroid of each quad.
There are two methods that may be used to calculate the best diagonal to use for splitting the quadrilateral elements: angle or diagonal. The angle measurement uses the largest angle, while the diagonal option uses the shortest diagonal. The largest angle measurement will be more accurate but takes more time.
Also, the QTri scheme is used in the TriMesh command as a backup to the TriAdvance triangle meshing scheme.
5.4.8.3 THex
Applies to: Volumes
Summary: Converts a tetrahedral mesh into a hexahedral mesh.
THex Volume <range>
Discussion: The THex command splits each tetrahedral element in a volume into four hexahedral elements, as shown in Figure 223. This is done by splitting each edge and face at its midpoint, and then forming connections to the center of the tet.
When THexing merged volumes, all of the volumes must be THexed at the same time, in a single command. Otherwise, meshes on shared surfaces will be invalid. An example of the THex algorithm is shown in Figure 224.
Figure 223: Conversion of a tetrahedron to four hexahedra, as performed by the THex algorithm.
Figure 224: A cylinder before and after the THex algorithm is applied.
5.4.8.4 TQuad
Applies to: Surfaces
Summary: Converts a triangular surface mesh into a quadrilateral mesh.
TQuad Surface <range>
Discussion: The TQuad command splits each triangular surface element in four quadrilateral elements, as shown in Figure 225. This is done by splitting each edge at its midpoint, and then forming connections to the center of the triangle. The result is the same as using the THex algorithm, but only applies to surfaces. In general it is better to use a mapped or paved mesh to generate quadrilateral surface meshes. However, the TQuad scheme may be useful for converting facet-based triangular meshes to quadrilateral meshes when remeshing is not possible.
Figure 225: A triangle split into 3 quads using the TQuad scheme
5.4.9 Copying a Mesh
Applies to: Curves, Surfaces, Volumes
Summary: Copies the mesh from one entity to another
To copy a mesh on a curve
On the Command Panel, click on Mesh and then Curve.
Click on the Copy/Morph action button.
Enter the values for Source Curve ID(s) and Target Curve ID(s). This can also be done using the Pick Widget function.
Optionally, click on Optional Data to further specify the settings.
Click on Appy Scheme and then Mesh.
The Command Panel GUI is shown below:
Curve <range> Scheme Copy source Curve <range> [Source Percent [<percentage> | auto]] [Source [combine|SEPARATE]] [Target [combine|SEPARATE]] [Source Vertex <id_range>] [Target Vertex <id_range>]]
Copy Mesh Curve <curve_id> Onto Curve <curve_id_range> [Source Node <starting node id> <ending node id>] [Source Percent [<percentage>|auto]] [Source Vertex <id_range>] [Target Vertex <id_range>]
To copy a mesh on a surface
On the Command Panel, click on Mesh and then Surface.
Click on the Copy/Morph action button.
Using the pickwidgets in the command panel select source and target data.
To force copying of interior vertex loops select the "Interior Vertices" tab and enter in pairs of vertices to be matched when copying.
The Command Panel GUI is shown below:
Copy Mesh Surface <surface_id> Onto Surface <surface_id> Source Curve<id> Target Curve <id> Source Vertex <id>Target Vertex <id> [Interior (pair vertex <id><id>)...] [smooth] [mirror] [preview]
Surface <id> Scheme copy source surface <id> source curve <id> target curve <id> source vertex <id> target vertex <id> [nosmoothing][mirror]
To copy a mesh on a volume
On the Command Panel, click on Mesh and then Volume.
Click on the Copy/Morph action button.
Enter the values for Source Volume ID(s) and Target Volume ID(s). This can also be done using the Pick Widget function.
Optionally, click on Optional Data to further specify the settings.
Click on Appy Scheme and then Mesh.
The Command Panel GUI is shown below:
Volume <range> Scheme Copy [Source Volume] <id> [[Source Surface <id> Target Surface <id>] [Source Curve <id> Target Curve <id>] [Source Vertex <id> Target Vertex <id>]][Nosmoothing]
Copy Mesh Volume <volume_id> Onto Volume <volume_id> [Source Vertex <vertex_id> Target Vertex <vertex_id>] [Source Curve <curve_id> Target Curve <curve_id>] [Nosmoothing]
Set Morph Smooth {on | off}
Discussion: If the user desires to copy the mesh from a surface, volume, curve, or set of curves that has already been meshed, the copy mesh scheme can be used. Note that this scheme can be set before the source entity has been meshed; the source entity will be meshed automatically, if necessary, before the mesh is copied to the target entity. The user has the option of providing orientation data to specify how to orient the source mesh on the target entity. For example, when copying a curve mesh, the user can specify which vertex on the source (the source vertex) gets copied to which vertex on the target (the target vertex). If you need to reference mesh entities for the copy, use the copy mesh commands. If no orientation data is specified, or if the data is insufficient to completely determine the orientation on the target entity, the copy algorithm will attempt to determine the remaining orientation data automatically. If conflicting, or inappropriate, orientation data is given, the algorithm attempts to discard enough information to arrive at a proper mesh orientation.
Curve mesh copying has certain options that allow the copying of just a section of the source curves’ mesh. These options are accessed through the extra keyword options. The percent option allows the user to specify that a certain percentage of the source mesh be copied–in this context the auto keyword means that the percentage will be calculated based on the ratio of lengths of the source and target curves. The combine and separate keywords relate to how the command line options are interpreted. If the user wishes to specify a group of target curves that will each receive an identical copy of a source mesh, then the target separate option should be used (this is the default). If, however, the user wishes the source mesh to be spread out along the range of target curves, then the target combine option should be used. The source curves are treated in a similar fashion.
Surface mesh copying with multiple holes in the surface may require matching up interior pair vertices. This will be required if the algorithm cannot match them up spatially. Interior pair vertices can be specified with the option interior pair vertex ...
Volume mesh copying depends on the surface copying scheme. Because of this, the target volume must not have any of its surfaces meshed already.
copy mesh surf 23 onto surf 14 source curve 1 source vertex 1 target curve 24 target vertex 20
