3.2 Edge Meshing Commands

The following commands are available on the Mesh/Edge subpad.

The following sections describe the purpose and operation of each of the commands listed above.

The Mesh Edges command allows you to grade or mesh any or all edges in the model. When you grade an edge, GAMBIT applies the mesh node spacing specifications but does not create mesh nodes on the edge. When you mesh an edge, GAMBIT creates mesh nodes according to the specifications.

To perform a grading or meshing operation, you must specify the following parameters:

• Edge(s) to which the grading specifications apply
• Grading scheme
• Mesh node spacing (number of intervals)
• Edge meshing options

When you specify one or more edges for a grading or meshing operation, you must specify the following options:

• Soft-link
• Reverse

When you soft-link two or more edges, GAMBIT links the edges for meshing purposes so that any grading or meshing specifications applied to one edge can be simultaneously applied to the other edges as well. When you reverse an edge, GAMBIT reverses the sense of the edge; therefore, any directional grading scheme associated with the edge is also reversed.

In addition to the soft-link and reverse options described above, GAMBIT allows you to specify whether or not to impose the grading parameters of the first edge specified in the Edges list on all other parameters in the list (see "Imposing First-Edge Grading and Spacing Parameters," below).

Soft-linking Edges

When you specify more than one edge for a grading or meshing operation, GAMBIT allows you to create soft links between the specified edges. When you grade or mesh an edge that is soft-linked to other edges, you can simultaneously apply the grading or meshing specifications to all of the edges that are soft-linked to the specified edge.

When you specify two or more edges for a grading or meshing operation, you must specify the status of any soft links that involve the edges. The three soft-link status options are as follows:

• Form—forms soft links between the edges
• Maintain—maintains all existing soft links that involve the edges
• Break—breaks any existing soft links that involve the edges

When you Form soft links between two or more edges, GAMBIT creates a "chain" of links between the specified edges. If you form a soft link involving an edge that is part of an existing soft-link chain, GAMBIT breaks the existing soft link associated with the edge. That is, no single edge is allowed to constitute part of more than one soft-link chain.

When you Maintain soft links, GAMBIT does not form or break any existing soft links associated with the specified edge(s).

When you Break a soft link associated with an edge, GAMBIT removes the edge from the soft-link chain but does not break any other soft links in the chain. That is, any other edges that are part of the soft-link chain remain soft-linked to each other.

When you grade or mesh an edge that constitutes part of an existing soft-link chain, GAMBIT allows you to specify whether the grading or meshing specifications apply to all edges that belong to the chain (the Pick with links option). The general rules pertaining to the Pick with links option are as follows.

• To grade or mesh all edges that belong to an existing chain, select the Pick with links option on the Mesh Edges form and specify one of the edges that belongs to the chain.
• To grade or mesh an edge that constitutes part of a soft-link chain without grading or meshing the other edges in the chain, unselect the Pick with links option before specifying the edge. To maintain all links between the specified edge and all edges to which it is soft-linked, select the Soft links: Maintain option before specifying the edge.

When you mesh an edge using a non-uniform grading scheme, GAMBIT grades or meshes the edge relative to its sense. For example, if you mesh an edge using a First Length scheme (see below) and specify a first interval length of 2, GAMBIT locates the first mesh node at a distance of 2 units from the edge start vertex.

When you specify edges for a grading or meshing operation, GAMBIT allows you to change their respective senses by means of the Reverse command button on the Mesh Edges form. If you reverse the sense of an edge the grading of which is non-uniform, the grading or meshing scheme is also reversed. For example, if you mesh an edge using a First Length grading scheme and specify a first interval length of 2, then click Reverse to reverse the sense of the edge, GAMBIT meshes the edge such that the last mesh node is located at a distance of 2 from the edge end vertex.

If you apply the Reverse option to an edge that is part of a soft-link chain and select the Pick with links option, GAMBIT reverses the sense and, therefore, the grading of all edges in the chain.

Imposing First-Edge Grading and Spacing Parameters

Grading Parameters

• If you select the Use first edge settings option, the Grading settings remain active and display the settings of the first edge specified in the Edges list.
• If you unselect the Use first edge settings option and select an edge the grading parameters of which differ from the currently displayed parameters, the Grading settings become inactive and the displayed settings are those of the most recently selected edge.

NOTE: The Grading and Spacing sections of the Mesh Edges form behave independently of each other with respect to the Use first edge settings option.

Specifying the Grading Scheme

GAMBIT provides the following types of edge mesh grading schemes.

• Successive Ratio
• First Length
• Last Length
• First Last Ratio
• Last First Ratio
• Exponent
• Bi-exponent
• Bell Shaped

The first six schemes listed above are non-symmetric schemes-that is, they can produce grading patterns that are not necessarily symmetric about the center of the edge. The last two schemes are symmetric schemes-that is, they are constrained to produce grading patterns that are symmetric about the center of the edge.

For each of the non-symmetric grading schemes, GAMBIT positions mesh nodes along the edge such that the ratio of any two succeeding interval lengths is constant. That is,

where and are the lengths of intervals i and i+1, respectively, and R is a fixed value (see Figure 3-11). For any given number of intervals (n), the grading schemes differ from each other only with respect to the manner in which GAMBIT determines the value of the interval length ratio, R.

Figure 3-11: Edge mesh grading parameters

NOTE: When you mesh an edge, GAMBIT positions the mesh nodes based, in part, on the edge element type as currently specified on the Set Edge Element Type form (see "Set Edge Element Type," below). If you specify 2-node edge elements, GAMBIT creates mesh nodes only at the endpoints of the edge mesh intervals. If you specify 3-node edge elements, GAMBIT creates an additional mesh node at the center of each mesh interval. For example, if you specify the 3-node edge element type and grade an edge such that it includes five mesh intervals, GAMBIT creates 11 mesh nodes on the edge. Six of the mesh nodes define the endpoints of the mesh intervals; the other five are located at the centers of the intervals. The mesh node locations presented throughout this section are based on the 2-node edge element type.

Grading Scheme Input Parameters

For all non-symmetric grading schemes other than the Exponent scheme, the interval length ratio, R, is a function of the following parameters:

• Total edge length, L
• Number of intervals, n
• Length of the first interval () or last interval () on the edge

For the Exponent scheme, R is a function of L, n, and a user-specified input parameter, x.

The following table lists the formulas that GAMBIT uses to determine the interval length ratios (R) for each of the non-symmetric grading schemes. The table also lists the pertinent input parameters and the corresponding titles of the input fields on the Mesh Edges form.

As an example of the differences between input parameters for the non-symmetric grading schemes, consider the straight, graded edge shown in Figure 3-12. The edge possesses a length of 15 units (L = 15) and is to be graded such that it contains four intervals (n = 4), each of which is twice as long as the previous interval (R = 2).

Figure 3-12: Edge grading example

The grading parameters required by each of the non-symmetric schemes to create the grading shown in Figure 3-12 are as follows.

When you grade or mesh an edge using a non-symmetric scheme, you must specify whether the grading scheme is single-sided or double-sided. Double-sided grading differs from single-sided grading in that the edge is divided into two separate segments for grading purposes, and each segment is graded according to its own grading parameter. (NOTE: GAMBIT does not allow you to specify different grading schemes for each segment.) If you specify more than one edge and select a double-sided grading scheme, GAMBIT applies the double-sided scheme to all edges in the set of specified edges.

NOTE: Double-sided grading is not explicitly available for the Exponent grading scheme. To apply an Exponent scheme to two segments of a single edge, use the Bi-exponent symmetric grading scheme (see below).

Center of Grading

When you specify double-sided grading, GAMBIT positions either a node or an interval at the center of grading for the edge. The form of the grading center (node or interval) depends on the total number of edge intervals (n) as follows (see Figure 3-13).

• If n is even, GAMBIT locates a mesh node at the center of grading.
• If n is odd, GAMBIT locates a mesh interval at the center of grading.

Figure 3-13: Double-sided grading—location of grading center

The location of the center node (n even) or the location and size of the center interval (n odd) is determined according to the following rules.

• If n is even, GAMBIT grades the edge such that the lengths of the intervals on either side of the center node are equal.
• If n is odd, GAMBIT grades the edge such that the length of the center interval conforms to the meshing parameters specified for both segments of the edge.

As an example of the effect of interval number on double-sided grading, consider the edge shown in Figure 3-14. The edge possesses a length of 8 units and is to be graded such that and .

Figure 3-14: Double-sided grading scheme-example

Figure 3-15 and Figure 3-16 show the effect of specifying 7 and 8 intervals, respectively, on the grading of the edge shown in Figure 3-14.

Figure 3-15: Double-sided grading scheme, n = 7

Figure 3-16: Double-sided grading scheme, n = 8

The following table lists the interval lengths for the double-sided grading schemes shown in Figure 3-15 and Figure 3-16.

Note that, if you specify seven intervals for the edge (), GAMBIT grades the edge such that the length of the center interval satisfies the grading ratios for both edge segments (see Figure 3-15). That is,

and

.

If you specify eight intervals for the edge (), GAMBIT grades the edge such that the lengths of the intervals on either side of the center node are equal (see Figure 3-16). That is,

and

.

When you grade or mesh an edge by means of a double-sided grading scheme, you must specify grading parameters for both segments of the edge. The following table lists double-sided grading input parameters as they appear on the Mesh Edges form for each of the available grading schemes. (For descriptions of the parameters, see Figure 3-13.)

As an example of the specification of double-sided grading input parameters, consider the examples shown in Figure 3-15 and Figure 3-16, above. The following tables list the parameters that are required to create the grading schemes shown in the figures.

Double-sided grading input parameters, Figure 3-15 ():

Double-sided grading input parameters, Figure 3-16 ()

GAMBIT provides two symmetric grading schemes for edge meshing:

• Bi-exponent
• Bell Shaped

Both schemes grade a given edge such that mesh node placement is symmetric about the center of the edge. The schemes differ from each other in the manner in which GAMBIT determines the mesh node spacing along the edge.

The Bi-exponent scheme divides the edge into two segments of equal length and applies the Exponent grading scheme separately to each segment. The Exponent input parameter, x—specified by means of the Ratio field on the Mesh Edges form-produces the following grading characteristics for the Bi-exponent scheme.

The Bell Shaped scheme grades the edge such that the mesh node density obeys a normal distribution centered at the geometric center of the edge. The user-specified input parameter for the Bell Shaped scheme-specified by means of the Ratio field on the Mesh Edges form-produces grading characteristics identical to those shown above for the Bi-exponent scheme.

The interval length ratio, R, is a function of both the edge length, L, and the number of intervals, n (see above). GAMBIT provides three different ways to specify the number of intervals on an edge.

• Interval count
• Interval size
• Shortest edge (%)

When you select the Interval count option, you must input the actual number of mesh intervals to be placed on the edge. GAMBIT grades or meshes the edge with enough nodes to result in the specified number of intervals. That is,

where m is the total number of mesh nodes on the edge, including the endpoints. For example, if you specify an interval count of 6 (n = 6), GAMBIT grades or meshes the edge with 7 nodes (m = 7), thereby creating 6 intervals on the edge.

When you select the Interval size option, you must input an interval length. GAMBIT uses the interval length to determine the total number of intervals on the edge according to the following equation:

where n is the number of intervals on the edge, L is the edge length, and d is the interval size (user input). If n is a non-integer, GAMBIT rounds to the nearest whole number to determine the number of intervals on the edge.

When you select the Shortest edge (%) option, you must input an interval size value expressed as a percentage of edge length. GAMBIT calculates the global interval size (d) for the current edge-meshing operation as follows:

where x is the Shortest edge (%) input value, and is the length of the shortest edge currently existing in the entire model. (NOTE: When you select the Shortest edge (%) option, GAMBIT highlights the graphics window display of the shortest edge.)

GAMBIT uses the resulting value of d to calculate the total numbers of intervals for all edges specified for the current edge-meshing operation. For example, if the shortest edge in the model is 10 units in length, and you mesh an edge that is 30 units long and specify the Shortest edge (%) option with , GAMBIT calculates the number of intervals, n, on the meshed edge as follows:

.

Therefore, GAMBIT creates 15 intervals on the meshed edge.

GAMBIT provides the following edge meshing options:

• Mesh
• Remove old mesh
• Ignore size functions

If you select the Mesh option, GAMBIT creates mesh nodes when it applies the grading specifications listed on the Mesh Edges form. If you Apply the currently specified parameters without selecting the Mesh option, GAMBIT applies the node distribution parameters to the edge(s) but does not create mesh nodes.

If you select the Remove old mesh option, GAMBIT deletes any currently existing mesh and/or grading information from the specified edge(s).

If you select the Ignore size functions option, GAMBIT ignores any existing size-function specifications that would otherwise affect the edge mesh.

Using the Mesh Edges Form

To open the Mesh Edges form (see below), click the Create Mesh command button on the Mesh/Edge subpad.

The Mesh Edges form contains the following options and specifications.

The middle section of the Mesh Edges form contains slide bars that allow you to specify grading parameters. GAMBIT displays only those slide bars that are applicable to the currently specified grading scheme. The following subsections describe the parameters associated with the slide bars for each of the five grading types. For a detailed description of the parameters associated with each type of grading, see "Grading Scheme Input Parameters," above.

3.2.2 Set Edge Element Type

The Set Edge Element Type command allows you to specify the number of edge nodes upon which all face and volume meshes are based.

The edge element type determines the number of edge mesh nodes corresponding to face and volume elements in the model. There are two edge element type options:

• 2 node
• 3 node

When you specify the 2 node option, GAMBIT creates meshes such that every edge node constitutes one endpoint of an mesh edge element and, therefore, one corner of a mesh face or volume element. When you specify the 3 node option, GAMBIT creates an additional mesh node in the center of each edge mesh element. As a result, only two out of every three edge mesh nodes constitute corners of mesh face or volume elements.

Figure 3-17 shows the effect of edge element type on quadrilateral face mesh elements. In Figure 3-17(a), the edge element type is specified as 2 node, therefore, each edge mesh node constitutes one corner of a face element. In Figure 3-17(b), the edge element type is specified as 3 node, therefore, only two out of every three edge mesh nodes constitute corners of face elements.

Figure 3-17: 2 node and 3 node edge element types

The Effect on Face and Volume Element Types

When you change the edge element type specification, GAMBIT automatically changes all corresponding face and volume element types. Likewise, when you change the face or volume element types, GAMBIT automatically changes the edge element type. The following table summarizes the general correspondence between GAMBIT edge, face, and volume element types.

For a description of the face and volume element types listed above, see "Set Face Element Type" and "Set Volume Element Type," below.

Using the Set Edge Element Type Form

To open the Set Edge Element Type form (see below), click the Set Edge Element Type command button on the Mesh/Edge subpad.

The Set Edge Element Type form contains the following options.

3.2.3 Link/Unlink Edge Meshes

The Link/Unlink Edge Meshes command button allows you to perform the following operations.

The following sections describe the procedures and specifications required to execute the operations listed above.

Link Edge Meshes

The Link Edge Meshes command allows you to create a hard link between two or more edges. When you create hard links between edges in a set, GAMBIT associates the edges with each other such that any meshing or splitting operation applied to one or more of the edges is similarly applied to all edges in the set. For example, if you grade or mesh an edge that is hard-linked to another edge, GAMBIT grades or meshes both edges according to the grading scheme and parameters applied to the specified edge. Likewise, if you split an edge that is hard-linked to another edge, GAMBIT splits both edges.

Linking Edge Endpoint Vertices

When you hard-link a set of edges, GAMBIT automatically creates hard links between the endpoint vertices of the edges. The vertex links are created such that the start endpoint vertices of all edges in the set are hard-linked to each other, and the end endpoint vertices of all edges in the set are hard-linked to each other.

GAMBIT does not allow you to hard-link two edges if their endpoint vertices are already linked to each other by means of an existing hard link. As an example of this restriction, consider the set of connected edges shown in Figure 3-18.

Figure 3-18: Edge hard-link restriction—example

If you create a hard link between edge.1 and edge.4 (Link 1), GAMBIT does not allow you to also create a hard link between edge.2 and edge.3 (Link 2), because vertex.1 and vertex.2 are already linked to vertex. 3 and vertex.4, respectively.

Reversing the Grading Orientation

When you select an edge for hard-linking, GAMBIT allows you to reverse the orientation of the grading on the edge relative to its start and end vertices. To reverse the grading orientation of an edge, Shift-middle-click the edge in the graphics window when selecting it for hard-linking. (NOTE: If you reverse the grading orientation, GAMBIT does not change the sense of the edge.)

As an example of the effect of reversing the grading orientation, consider the two hard-linked edges shown in Figure 3-19, one of which is meshed using a successive-ratio grading scheme with a first ratio of 2.

Figure 3-19: Linked edge meshes—effect of reverse orientation

If you do not reverse the grading orientation, the grading scheme for edge.1 is exactly duplicated on edge.2 (see Figure 3-19(a)). If you do reverse the grading scheme, the grading scheme on edge.2 is exactly reversed relative to that of edge.1 (see Figure 3-19(b)).

Specifying the Periodic Option

The Link Edge Meshes command includes a Periodic option that allows you to specify that the specified edges are periodically linked. Periodically linked edges are constrained such that they must behave identically to each other with respect to any virtual edge-split and vertex-move operations.

As an example of the effect of periodic linking, consider the square, planar face shown in Figure 3-20, two edges (edge.1 and edge.3) of which are hard-linked to each other.

Figure 3-20: Virtual splitting of two hard linked edges

If you perform a virtual split of edge.1 at the split point shown in Figure 3-20(a), GAMBIT splits both edges to create the geometric entities shown in Figure 3-20(b). (NOTE: In this example, the hard link was created such that the grading orientations of edge.1 and edge.3 point in the same direction, therefore v_edge.5 and v_edge.7 are equal in length. If the grading orientations had opposed each other when the link was created, v_edge.8 would be equal in length to v_edge.5, and v_edge.7 would be equal in length to v_edge.6).

If you move v_vertex.5 in Figure 3-20 by means of the Slide Virtual Vertex command (see Section 2.2.2), the final state of v_vertex.6 depends on two factors:

• The state of the Move with links option on the Slide Virtual Vertex form
• Whether or not the link between edge.1 and edge.3 is Periodic

For example, if edge.1 and edge.3 are periodically linked, GAMBIT moves v_vertex.6 regardless of the state of the Move with links option. Likewise, if you specify the Move with links option, GAMBIT moves v_vertex.6 regardless of whether the link between edge.1 and edge.3 is periodic.

Figure 3-21: v_vertex.6 move states—Periodic and Move with links options

Using the Link Edge Meshes Form

To open the Link Edge Meshes form (see below), click the Link command button on the Mesh/Edge subpad.

The Link Edge Meshes form contains the following specifications.

Unlink Edge Meshes

The Unlink Edge Meshes command allows you to delete existing hard links associated with one or more edges. When you unlink an edge, GAMBIT deletes the link(s) between the specified edge and the edge to which it is hard-linked.

Using the Unlink Edge Meshes Form

To open the Unlink Edge Meshes form (see below), click the Unlink command button on the Mesh/Edge subpad.

The Unlink Edge Meshes form contains the following specifications.

3.2.4 Split Meshed Edge

The Split Meshed Edge command allows you to split a real or virtual edge at a mesh node.

When you split an edge at a mesh node, GAMBIT splits the edge into two virtual edges that share a common virtual endpoint vertex. The common vertex is located at the position of the specified node.

When you specify the edge to be split, GAMBIT displays its existing mesh in the graphics window. To specify the exact mesh node at which the edge is to be split, either pick the node in the graphics window (using the mouse) or select the mesh node by means of the Mesh Node pick-list form.

Using the Split Meshed Edge Form

To open the Split Meshed Edge form (see below), click the Split Edge command button on the Mesh/Edge subpad.

The Split Meshed Edge form contains the following specifications.

3.2.5 Summarize Edge Mesh

The Summarize Edge Mesh command summarizes edge mesh information in the Transcript window and displays edge mesh nodes in the graphics window. GAMBIT also allows you to display numbers corresponding to the intervals and nodes associated with the specified edge.

Using the Summarize Edge Mesh Form

To open the Summarize Edge Mesh form (see below), click the Summarize command button on the Mesh/Edge subpad.

The Summarize Edge Mesh form contains the following options and specifications.

3.2.6 Delete Edge Meshes

The Delete Edge Meshes command allows you to delete mesh nodes on one or more edges.

Using the Delete Edge Meshes Form

To open the Delete Edge Meshes form (see below), click the Delete command button on the Mesh/Edge subpad.

The Delete Edge Meshes form contains the following specifications.

© Fluent, Inc. 11/26/01