3.3 Face Meshing Commands

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

3.3.1 Mesh Faces

The Mesh Faces command allows you to create the mesh for one or more faces in the model. When you mesh a face, GAMBIT creates mesh nodes on the face according to the currently specified meshing parameters.

To mesh a face, you must specify the following parameters:

• Face(s) to be meshed
• Meshing scheme
• Mesh node spacing
• Face meshing options

Specifying the Faces

GAMBIT allows you to specify any face for a face meshing operation; however, the shape and topological characteristics of the face, as well as the vertex types associated with the face, determine the type(s) of mesh scheme(s) that can be applied to the face.

Specifying the Meshing Scheme

To specify the face meshing scheme, you must specify two parameters:

• Elements
• Type

The Elements parameter defines the shape(s) of the elements that are used to mesh the face. The Type parameter defines the pattern of mesh elements on the face.

The following sections describe the parameters listed above and their effects on the overall face mesh.

Specifying Scheme Elements

GAMBIT allows you to specify any of the following face meshing Elements options.

Each of the Elements options listed above is associated with a specific set of Type options (see below).

Specifying Scheme Type

GAMBIT provides the following face meshing Type options.

As noted above, each of the Elements options is associated with a specific set of one or more of the Type options listed above. The following table shows the correspondence between each of the face meshing Elements and Type options. (NOTE: Shaded cells marked with an "X" represent allowable combinations of options.)

Each of the allowable combinations shown in the table above results in a specific pattern of mesh nodes for any given face. In addition, each is associated with a set of restrictions that govern when it can or cannot be applied. The following sections describe the patterns and restrictions associated with each of the allowable combinations of Elements and Type options listed above.

NOTE (1): In the following sections, face meshing scheme types that allow more than one Elements option are differentiated from each other by means of prefixes that represent the options-for example, Quad-Map and Quad/Tri-Map. Scheme types that allow only one Elements option are referred to without an associated prefix-for example, Submap.

NOTE (2): When you specify a face on the Mesh Faces form, GAMBIT automatically evaluates the face with respect to its shape, topological characteristics, and vertex types and sets the Scheme option buttons to reflect a recommended face meshing scheme. If you specify more than one face for a meshing operation, the scheme represented by the Scheme option buttons reflects the recommended scheme for the most recently specified face. You can enforce a meshing scheme, and thereby override any recommended scheme, by means of the Scheme option buttons on the Mesh Faces form. When you enforce a meshing scheme, GAMBIT applies the specified scheme to all currently picked faces.

Quad-Map Meshing Scheme

When you apply the Quad-Map meshing scheme to a face, GAMBIT meshes the face using a regular grid of quadrilateral face mesh elements, such as those shown in Figure 3-22.

Figure 3-22: Quad-Map face meshing scheme—example mesh

The Quad-Map meshing scheme is applicable primarily to faces that are bounded by four or more edges, however not all such faces are suitable for mapping. To be "mappable," a face must not violate restrictions related to the following parameters:

• Vertex types
• Edge mesh intervals

The vertex-type and edge mesh interval restrictions for the Quad-Map meshing scheme are as follows.

Vertex Types

To be mappable, a face must represent a logical rectangle. (For the exception to this criterion, see NOTE (1), below.) To represent a logical rectangle, a face must include four End type vertices, and all other vertices associated with the face must be designated as Side type vertices.

Figure 3-23 shows four planar faces, two of which are mappable and two of which are not mappable. The faces shown in Figure 3-23(a) and (c) are mappable, because each includes four End type vertices and all other vertices associated with the face are Side type vertices. The face shown in Figure 3-23(b) is not mappable, because it includes only three End type vertices. The face shown in Figure 3-23(d) is not mappable, because one of its vertices is designated as a Reversal type vertex.

Figure 3-23: Quad-Map face meshing scheme—face suitability

NOTE (1): If a face is bounded by two edges each of which, by itself, constitutes a closed loop, GAMBIT can employ the Quad-Map meshing scheme even if the vertex type designations do not define a logical rectangle. For example, GAMBIT automatically applies the Quad-Map meshing scheme to a cylindrical face, even though the circles that constitute the face boundary edges possess only one vertex each and both vertices are, by default, designated as Side type vertices.

NOTE (2): If you enforce a Quad-Map meshing scheme on a face, GAMBIT evaluates the face with respect to its vertex type designations. If the vertex types do not meet the criteria outlined above, GAMBIT attempts to change the vertex types so that the face is rendered mappable.

If the specified face includes more than four vertices, there are multiple configurations of vertex types that satisfy the vertex-type criteria. For example, if the face includes five vertices, there are five possible vertex-type configurations that allow the creation of a Quad-Map mesh, because any of the five vertices can be designated as the Side vertex. When GAMBIT automatically changes vertex types, it attempts to employ the configuration that minimizes distortion in the mesh.

Each vertex-type configuration results in a unique node pattern for the mapped mesh. To enforce a specific node pattern on a mapped mesh, manually specify the vertex types such that they meet the Quad-Map scheme vertex-type criteria outlined above. (See "Set Face Vertex Type," below.)

Edge Mesh Intervals

If you grade or mesh the edges of a face prior to creating a mapped mesh, you must specify the edge mesh intervals such that the numbers of mesh intervals on opposing sides of the logical rectangle are equal. For meshing purposes, a single side of the logical rectangle consists of all edges that exist between any two End type vertices.

NOTE: If you do not grade or mesh the edges of a face prior to creating the mapped mesh, GAMBIT automatically assigns edge mesh intervals such that they satisfy the criteria described above.

As an example of the edge mesh interval restriction, consider the face shown in Figure 3-24. The face includes four End type vertices and one Side type vertex.

Figure 3-24: Mappable planar face consisting of five edges

The four sides of the logical rectangle that bounds the face can be defined as follows.

For the face to be mappable, the number of mesh intervals on edge.2 (Side 1) must be equal to that on edge.4 (Side 3). Likewise, the combined number of intervals on edge.1 and edge.5 (Side 4) must be equal to the number of intervals on edge.3 (Side 2).

NOTE (1): If you grade or mesh one or more edges of a face and apply a Quad-Map meshing scheme to the face, GAMBIT automatically meshes the remaining edges such that the numbers of intervals on opposing sides of the face satisfy the criteria outlined above. For example, if you grade or mesh edge.3 in Figure 3-24 such that it contains 10 intervals, GAMBIT meshes edge.1 and edge.5 such that they include a combined total of 10 intervals.

NOTE (2): GAMBIT does not include the edge mesh interval restriction when evaluating a face with respect to a recommended meshing scheme. As a result, GAMBIT may recommend a Quad-Map meshing scheme for a face that is mappable with respect to its vertex-type configuration but which cannot be mapped, because it violates the edge mesh interval restriction.

NOTE (3): If you create a mesh link between two edges that constitute opposing sides of a logical rectangle, the edges automatically satisfy the edge mesh interval restriction described above.

Quad/Tri-Map Meshing Scheme

The Quad/Tri-Map meshing scheme is applicable only to geometry that constitutes a narrow, logical sliver consisting of two sides-such as that shown in Figure 3-25. Either side may consist of more than one edge.

Figure 3-25: Quad/Tri-Map face meshing scheme—example mesh

When you apply the Quad/Tri-Map meshing scheme, GAMBIT creates triangular mesh elements at the two endpoints of the sides and creates quadrilateral elements across the rest of the face. The vertex-type and edge mesh interval restrictions for the Quad/Tri-Map meshing scheme are as follows.

Vertex Types

To employ the Quad/Tri-Map meshing scheme to a sliver-shaped face, you must specify the vertices as follows:

• Tips of the sliver - Trielement
• All other vertices - Side

Edge Mesh Intervals

If you grade or mesh the edges that comprise the sides of a sliver-shaped face before applying the Quad/Tri-Map meshing scheme, you must specify the edge grading such that the sides possess identical numbers of intervals.

Submap Meshing Scheme

When you apply the Submap meshing scheme to a face, GAMBIT divides the face into one or more mappable regions and creates a mapped mesh in each region. Like the Map meshing scheme, the Submap meshing scheme is subject to restrictions related to vertex types and edge mesh intervals. The vertex-type and edge mesh interval restrictions for the Submap meshing scheme are as follows.

Vertex Types

To constitute a submappable face, a face must possess only End, Side, Corner, and Reversal vertices. In addition, the total number of End vertices, , must satisfy the following equation:

where and are the total numbers of Corner and Reversal type vertices, respectively, on the face. That is, for every Corner type vertex, the face must possess an additional End vertex, and for every Reversal vertex, the face must possess two additional End vertices.

The shape of the mesh generated by means of the Submap face meshing scheme depends on the type and arrangement of vertex types on the face. As an example of the effect of vertex types, consider the faces shown in Figure 3-26 and Figure 3-27, each of which consists of an identical planar L-shaped face, one corner of which is truncated at an angle.

Figure 3-26: Submap face meshing scheme-inside Corner vertex

Figure 3-27: Submap face meshing scheme-inside Reversal vertex

In Figure 3-26, the inside corner vertex (C) is designated as a Corner vertex, therefore, in order to be submappable, the face must possess five End type vertices (A, B, D, E, and F). The Submap meshing scheme divides the face into the following two mapped regions:

• A, B, C, H, F, G
• C, D, E, H

In Figure 3-27, the inside corner vertex (C) is designated as a Reversal vertex, therefore, in order to be submappable, the face must possess six End type vertices (A, B, D, E, F, and G). In this case, the Submap meshing scheme divides the face into the following two mapped regions:

• A, B, C, H, G
• C, D, E, F, H

NOTE: If you enforce a Submap meshing scheme on a face, GAMBIT evaluates the face with respect to its vertex type designations. If the vertex types do not meet the criteria outlined above, GAMBIT attempts to change the vertex types so that the face is submappable.

For most submappable faces, there are multiple configurations of vertex types that satisfy the vertex-type criteria. Each vertex-type configuration results in a unique node pattern for the submapped mesh. When GAMBIT automatically changes vertex types, it attempts to employ the configuration that minimizes distortion in the mesh. To enforce a specific node pattern on a submapped mesh, manually specify the vertex types such that they meet the Submap scheme vertex-type criteria outlined above. (See "Set Face Vertex Type," below.)

Edge Mesh Intervals

If you grade or mesh the edges of a face before applying the Submap scheme, the edge mesh grading schemes must be specified such that the total numbers of intervals on opposite sides of any given submapped region are equal. For example, in Figure 3-26, the number of intervals (I) on each side of the submapped regions can be expressed as follows:

and
.

Similarly, in Figure 3-27, the number of intervals (I) on each side of the submapped regions are:

and
.

NOTE (1): If you grade or mesh one or more edges of a face before applying a Submap meshing scheme to the face, GAMBIT automatically meshes the remaining edges such that the numbers of intervals on opposing sides of the face satisfy the criteria outlined above.

NOTE (2): GAMBIT does not include the edge mesh interval restriction when evaluating a face with respect to a recommended meshing scheme. As a result, GAMBIT may recommend a Submap meshing scheme for a face that is submappable with respect to its vertex-type configuration but which cannot be submapped, because it violates the edge mesh interval restriction outlined above.

Quad-Pave Meshing Scheme

When you apply the Quad-Pave meshing scheme, GAMBIT creates an unstructured face mesh consisting of quadrilateral mesh elements (see Figure 3-28).

Figure 3-28: Quad-Pave face meshing scheme—example mesh

You can apply the Quad-Pave meshing scheme to any face that consists of a closed loop of edges. The vertex-type and edge mesh interval restrictions for the Quad-Pave meshing scheme are as follows.

Vertex Types

There are no restrictions on vertex types associated with a Quad-Pave mesh.

Edge Mesh Intervals

If you grade or mesh all of the boundary edges of a face before applying the Quad-Pave meshing scheme, you must specify the grading such that the total number of mesh intervals on all edges is an even number. If you grade some, but not all, of the face boundary edges, GAMBIT automatically meshes the remaining edges such that the total number of edge mesh intervals is even.

Tri-Pave Meshing Scheme

When you apply the Tri-Pave meshing scheme, GAMBIT creates a face mesh consisting of irregular triangular mesh elements, such as that shown in Figure 3-29.

Figure 3-29: Tri-Pave face meshing scheme—example mesh

The vertex-type and edge mesh interval restrictions for the Tri-Pave meshing scheme are as follows.

Vertex Types

There are no restrictions on vertex types associated with the Tri-Pave meshing scheme.

Edge Mesh Intervals

There are no restrictions on the edge mesh intervals for the Tri-Pave meshing scheme.

Quad/Tri-Pave Meshing Scheme

When you apply the Quad/Tri-Pave meshing scheme to a face, GAMBIT creates a paved mesh that consists primarily of quadrilateral elements but employs triangular mesh elements in any corners the edges of which form a very small angle with respect to each other. You can also impose the creation of triangular mesh elements in corners of the face by setting the associated vertices as Trielement vertices. Figure 3-30 shows a Quad/Tri-Pave mesh in which vertices A, D, and E are set as Trielement vertices.

Figure 3-30: Quad/Tri-Pave face meshing scheme—example mesh

The vertex-type and edge mesh interval restrictions for the Quad/Tri-Pave meshing scheme are as follows.

Vertex Types

There are no restrictions on vertex types associated with the Quad/Tri-Pave meshing scheme, however, you can enforce the creation of either triangular or quadrilateral corner elements by means of the Trielement or Notrielement vertex types, respectively, as follows:

• If you specify a vertex as a Notrielement vertex, GAMBIT creates a quadrilateral element at the vertex location regardless of the angle between its associated edges.
• If you specify a vertex as a Trielement vertex, GAMBIT creates a triangular element at the vertex location regardless of the angle between its associated edges.

Edge Mesh Intervals

If you grade or mesh all of the edges that comprise the boundary of a face before applying the Quad/Tri-Pave meshing scheme, you must specify the grading such that

is an even number, where is the total number of mesh intervals on all edges, and is the total number of triangle mesh elements. If you grade some, but not all, of the edges, GAMBIT automatically meshes the ungraded edges such that is an even number.

Tri Primitive Meshing Scheme

The Tri Primitive meshing scheme allows you to create a submapped mesh on a three-sided face. (NOTE: Any side of the three-sided face may consist of more than one edge.) When you apply the Tri Primitive meshing scheme to a three-sided face, GAMBIT locates a point internal to the face that serves as a common endpoint for three mappable subregions.

Figure 3-31 shows a triangular, planar face meshed according to the Tri Primitive meshing scheme. Note that the face is divided into three mappable regions, each of which shares a common endpoint (D). The regions are defined by the quadrilaterals AFDE, FBGD, and EDGC.

Figure 3-31: Tri Primitive face meshing scheme—example mesh

The vertex-type and edge mesh interval restrictions for the Tri Primitive meshing scheme are as follows.

Vertex Types

The Tri Primitive meshing scheme requires that the vertices at the corners of the three sides of the face are specified as End vertices (see Figure 3-31, above) and that all other vertices are specified as Side vertices.

Edge Mesh Intervals

If you grade or mesh the sides of the face before applying the Tri Primitive meshing scheme, you must specify the grading such that the total number of intervals on the three sides of the face is an even number. In addition, the grading must satisfy the following criterion:

where and are the numbers of intervals on any two sides, and is the number of intervals on the remaining side.

Wedge Primitive Meshing Scheme

The Wedge Primitive meshing scheme allows you to create a radial mesh on a three-sided face. (NOTE: Any side of the three-sided face may consist of more than one edge.) When you apply the Wedge Primitive meshing scheme, GAMBIT creates a mapped mesh that includes a group of triangular mesh elements emanating from common endpoint (see Figure 3-32).

Figure 3-32: Wedge Primitive face meshing scheme—example mesh

The vertex-type and edge mesh interval restrictions for the Wedge Primitive meshing scheme are as follows.

Vertex Types

The Wedge Primitive meshing scheme requires that the vertices at the corners of the three sides of the face are specified as End vertices (see Figure 3-33) and that all other vertices are specified as Side vertices.

Figure 3-33: Wedge Primitive face meshing scheme-vertex-types

Face meshes created by means of the Wedge Primitive mesh scheme consist of regular quadrilateral mesh elements and a group of triangular mesh elements that share a common endpoint. The group of triangular elements exists at the Trielement type vertex. To create the mesh, GAMBIT constructs a series of mesh grid lines that emanate from the Trielement type vertex to the opposite side of the logical triangle-that is, to the edges that exist between the two End type vertices (see Figure 3-33, above).

Edge Mesh Intervals

If you grade or mesh the face boundary edges before applying the Wedge Primitive meshing scheme, you must specify the grading such that the total numbers of intervals on opposite sides of the logical triangle are equal. For meshing purposes, the opposite sides of the logical triangle are defined as all edges that exist between the Trielement type vertex and each End type vertex. For example, in Figure 3-33, the combined numbers of edge mesh intervals on the edges AB and BC must equal the total number of intervals on edge AE.

Specifying Node Spacing

When you specify mesh node spacing on the Mesh Faces form, GAMBIT applies the specification to all edges associated with any specified faces that are not currently graded or meshed. GAMBIT provides three different ways to specify the number of intervals on the edges of a face.

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

For a description of the three edge mesh interval spacing options listed above, see "Specifying Node Spacing" in Section 3.2.1.

Specifying Face Meshing Options

GAMBIT includes the following primary options on the Mesh Faces form:

• Mesh
• Remove old mesh
• Ignore size functions

If you select the Mesh option, GAMBIT meshes the picked face(s) according to the parameters as currently specified on the Mesh Faces form. If you Apply the meshing specifications without selecting the Mesh option, GAMBIT applies the currently specified mesh parameters to the face(s) but does not create the mesh.

Remove old mesh Option

If you select the Remove old mesh option, GAMBIT deletes any currently existing mesh from the specified face(s). If you delete a face mesh using the Remove old mesh option, GAMBIT enables the Remove lower mesh option-which allows you to specify whether or not to delete the mesh on the face boundary edges. If you select the Remove lower mesh option, GAMBIT deletes the edge mesh(es) when it deletes the face mesh(es). If you do not select the option, GAMBIT deletes the face mesh but retains any associated edge meshes.

Ignore size functions Option

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

Using the Mesh Faces Form

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

The Mesh Faces form contains the following specifications.

3.3.2 Move Face Nodes/Split Quad Meshes

The Move Face Nodes/Split Quad 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.

Move Face Nodes

The Move Face Nodes command allows you to reposition any or all face-element corner nodes that exist in the interior of a meshed face. You can move the mesh nodes either by means of the Move Face Nodes form or by means of the mouse.

To move a face node, you must specify the following parameters:

• The meshed face upon which the nodes exist
• The number of the node to be moved
• The coordinates of the new node location

The following paragraphs describe the specifications listed above as well as the procedure required to move face mesh nodes by means of the mouse.

Specifying the Face

When you specify a face for which mesh nodes are to be moved, GAMBIT highlights the face the graphics window and displays the corresponding mesh as a series of grid lines. Face nodes are located at the intersections of the grid lines.

Specifying the Node Number

To specify a node to be moved, you must input the corresponding node number on the Move Face Nodes form. To open a complete list of available node numbers associated with the specified face:

1. Click the Node pick list button.
2. Click All on the Node pick list form.

When you click the All command button, GAMBIT fills the Node pick list with the numbers of all nodes associated with the specified face and displays the nodes on the mesh grid in the graphics window. (NOTE: The Node list includes only those nodes that constitute face-element corner nodes that are interior to the face.) When you select a node number from the Node pick list, GAMBIT highlights the node in the graphics window.

To move a series of nodes, select and specify the coordinates of each node in turn. When you have selected and moved all nodes, click Apply on the Move Face Nodes form.

Specifying Node Coordinates

To specify the new coordinates of a face mesh node, you must specify the reference coordinate system and the coordinate parameters corresponding to the new node location. You can input the coordinate parameters with respect to either the Global or Local coordinate system. If you specify a node location that does not lie on the specified face, GAMBIT automatically adjusts the coordinate parameters so that the new node location lies on the face.

Using the Mouse to Move Face Nodes

To use the mouse to move face nodes:

1. Pick the face upon which the nodes are to be moved.
2. Shift-right-click in the graphics window to accept the selection.
3. Pick (Shift-left-click) the node to be moved and drag it to its new location.

To move a series of mesh nodes, pick and drag each node in turn. When you have finished moving all nodes, Shift-right-click the mouse in the graphics window to accept and apply the new node positions.

Using the Move Face Nodes Form

To open the Move Face Nodes form (see below), click the Move Face Nodes command button on the Mesh/Face subpad.

The Move Face Nodes form contains the following specifications.

Split Quad Meshes

As an example of the Split Quad Meshes operation, consider the quad-meshed face shown in Figure 3-34(a). In this example, the face is bounded by an edge loop consisting of five edges and has been meshed by means of a Quad:Pave scheme.

Figure 3-34: Split Quad Meshes example

If you perform the Split Quad Meshes operation on the face shown in Figure 3-34(a), GAMBIT splits the quadrilateral mesh elements into triangular elements to create the mesh shown in Figure 3-34(b).

Excluding Boundary Layer Faces

The Split Quad Meshes form includes an Exclude boundary layer faces option that allows you to prohibit GAMBIT from splitting quad mesh elements in face boundary layers. As an example of the effect of the Exclude boundary layer faces option, consider the meshed face shown in Figure 3-35. The face is similar to that shown in Figure 3-34, above, but includes a boundary layer along the left side.

Figure 3-35: Quad-meshed face with boundary layer

Figure 3-36 shows the effect of the Exclude boundary layer faces option on the Split Quad Meshes operation for the face shown in Figure 3-35.

Figure 3-36: Effect of Exclude boundary layer faces option

The effects can be summarized as follows:

• If you do not select the Exclude boundary layer faces option when executing the Split Quad Meshes operation, GAMBIT splits all mesh quads on the face (see Figure 3-36(a)).
• If you do select the Exclude boundary layer faces option, GAMBIT splits only the quad mesh elements that do not constitute parts of the boundary layer (see Figure 3-36(b)).

Using the Split Quad Meshes Form

To open the Split Quad Meshes form (see below), click the Split command button on the Mesh/Face subpad.

The Split Quad Meshes form contains the following specifications.

3.3.3 Smooth Face Meshes

The Smooth Face Meshes command adjusts the node locations for one or more face meshes.

When you smooth a face mesh, GAMBIT automatically adjusts the mesh node locations to improve the uniformity of the spacing between nodes across the face. To smooth a face mesh, you must specify the following parameters:

• The face(s) for which the mesh is to be smoothed
• The smoothing scheme
• The Smooth edges option

Specifying the Smoothing Scheme

GAMBIT provides the following smoothing schemes:

• Length-weighted Laplacian (L-W Laplacian)
• Centroid Area (Centroid Area)
• Winslow (Winslow)

The following table summarizes the basic features of the algorithm employed by each scheme.

Specifying the Smooth edges Option

When you smooth a face mesh, by default, GAMBIT does not modify the positions of mesh nodes located on the boundary edges of the face. To allow GAMBIT to modify the positions of such edge mesh nodes, you must specify the Smooth edges option on the Smooth Face Meshes form.

Using the Smooth Face Meshes Form

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

The Smooth Face Meshes form contains the following specifications.

3.3.4 Set Face Vertex Type

The Set Face Vertex Type command allows you to define the characteristics of a face mesh in the vicinity of a specified vertex. The vertex-type specifications also determine which face meshing scheme GAMBIT selects as the default scheme.

To set vertex types, you must specify the following parameters.

• The face upon which the vertex types are to be defined
• The vertex type
• The vertices to which the type specification is to be applied

Specifying the Face

GAMBIT vertex types are specific to the faces upon which they are set. Therefore, to specify the type designation of an individual vertex, you must also specify a face associated with that vertex.

An individual vertex may possess as many vertex type designations as the number of faces to which it is attached. For example, it is possible for a vertex to possess a Side type designation with respect to one face and an End type designation with respect to another.

Specifying Vertex Types

The structure of any given face mesh in the vicinities of an individual vertex is a function of the face meshing scheme and vertex type. There are six vertex types (see Figure 3-37):

• End
• Side
• Corner
• Reversal
• Trielement
• Notrielement

Figure 3-37: Face vertex types

Each vertex type differs from the others in the following ways:

• The number of face mesh lines that intersect the vertex
• The angle between the edges immediately adjacent to the vertex
• The face mesh scheme to which it applies

The following table summarizes the characteristics of the vertex types shown in Figure 3-37.

NOTE: GAMBIT ignores vertex types when meshing a face according to the Pave mesh scheme.

The following sections describe the general effect of each vertex type on the shape of the face mesh in the vicinity of a specified vertex.

End Vertex Type

When you specify a vertex as the End vertex type and do not specify a Pave meshing scheme, GAMBIT creates the face mesh such that only two mesh element edges intersect at the vertex (see Figure 3-37(a)). As a result, the mapped and submapped face mesh patterns on both sides of the End vertex terminate at the edges adjacent to the vertex.

Side Vertex Type

When you specify a vertex as the Side vertex type and do not specify a Pave meshing scheme, GAMBIT creates the face mesh such that three mesh element edges intersect at the vertex (see Figure 3-37(b)). GAMBIT treats the two topological edges that are adjacent to the vertex as a single edge for the purposes of meshing.

Corner Vertex Type

When you specify a vertex as the Corner vertex type and do not specify a Pave meshing scheme, GAMBIT creates the face mesh such that four mesh element edges intersect at the vertex (see Figure 3-37(c)). The Corner vertex type cannot be applied to vertices the adjacent edges of which form angles less than 180.

Reversal Vertex Type

When you specify a vertex as the Reversal vertex type, GAMBIT creates the face mesh such that five mesh element edges intersect at the vertex (see Figure 3-37(d)). When you apply a Submap meshing scheme to a face that includes a Reversal vertex, GAMBIT creates a line of mesh edges that extends from the Reversal vertex to a topological edge on an opposite side of the face. GAMBIT treats the resulting line and each adjacent edge as a single edge for the purposes of meshing.

Trielement and Notrielement Vertex Types

When you specify a vertex as the Trielement vertex type, GAMBIT creates a triangular element (see Figure 3-37(e)) at the vertex, regardless of the default element type that would otherwise be created using either the Quad/Tri-Map, Tri-Primitive, or Wedge Primitive face meshing schemes.

When you specify a Notrielement vertex type, GAMBIT creates a quadrilateral element at the vertex, regardless of the default element type that would otherwise be created.

The Effects of Vertex Types on Face Meshes

To understand the general effects of vertex types on the structures of face meshes, consider the planar face shown in Figure 3-38. The following three examples illustrate the effects of different vertex-type specifications applied to vertices C, F, and G on the shape of the resulting mesh.

Figure 3-38: Seven-sided planar face

In Figure 3-39, vertices C, F, and G are specified as Side vertices, therefore, GAMBIT treats sides BCD and EFGA as if each were a single edge. As a result, the entire face represents a mappable region, and GAMBIT creates a single checkerboard pattern for the mesh.

Figure 3-39: Example face mesh—Side inside corner vertex

In Figure 3-40, vertices C, F, and G are specified as Corner, Side, and End type vertices, respectively. As a result, the face is submappable, and GAMBIT creates two separate checkerboard patterns for the mesh. The upper-left submapped region is defined by the polygon ABCHFG. The lower-right submapped region is defined by CDEH. For both regions, the node at point H serves as an End type vertex for the purposes of mesh creation.

Figure 3-40: Example face mesh—Corner inside corner vertex

In Figure 3-41, vertices C, F, and G are specified as Reversal, End, and End vertices, respectively. As a result, the face is submappable, similar to that shown in Figure 3-40. The upper-left submapped region is defined by the polygon ABCHG. The lower-right submapped region is defined by CDEFH.

Unlike the mesh shown in Figure 3-40, the mesh in Figure 3-41 does not terminate at vertex C. Instead, GAMBIT treats the sides BCH and HCD as single edges when creating the mesh.

Figure 3-41: Example face mesh—Reversal inside corner vertex

Using the Set Face Vertex Type Form

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

The Set Face Vertex Type form contains the following options and specifications.

3.3.5 Set Face Element Type

The Set Face Element Type command allows you to specify the mesh node configuration associated with either of two available face element shapes.

To set the face element type, you must specify the node pattern associated with each of the face element shapes. There are two face element shapes available in GAMBIT:

• Quadrilateral
• Triangle

Each face element shape is associated with three different node patterns, and each node pattern is characterized by the number of nodes in the pattern. Figure 3-42 and Figure 3-43 show the node patterns associated with the quadrilateral and triangular face element types, respectively.

Figure 3-42: Quadrilateral face element types

Figure 3-43: Triangular face element types

When you set a face element type, GAMBIT applies the type to all face elements of the specified shape. For example, if you specify 8-node quadrilateral face elements, GAMBIT locates mesh nodes according to the 8-node pattern for all quadrilateral face elements produced in the subsequent face meshing operation. (NOTE: For a description of the relationships between edge, face, and volume element types, see "Set Edge Element Type," above.)

NOTE: Finite-element solvers, such as the FIDAP solver, employ higher-order elements (for example, 8-node and 9-node quadrilateral elements). Finite-volume solvers, such as FLUENT/UNS, employ only linear elements (for example, 4-node quadrilateral elements).

Using the Set Face Element Type Form

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

The Set Face Element Type form contains the following specifications.

3.3.6 Link/Unlink Face Meshes

The Link/Unlink Face 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.

NOTE (1): Face-mesh linking is required for periodic and cyclic boundary zones, because it insures that meshes match on linked face pairs.

NOTE (2): When you mesh one of two faces that constitutes part of a linked pair of faces, GAMBIT stores only one copy of the mesh in the database as well as the transformation matrix. As a result, the linking of face meshes reduces memory use.

Link Face Meshes

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

To create a mesh hard-link between two faces, you must specify the following parameters for each face:

• The face to be hard-linked
• A vertex that serves as a reference point for the face mesh
• The orientation of the mesh on the linked face relative to its edge loop sense
• Whether or not the faces are periodically linked

When you hard-link two faces, the faces to be hard-linked must possess identical numbers of edges. In addition, if a face possesses more than one edge loop, any face to which it is hard-linked must possess an identical number of edge loops, and the edge loops that correspond to each other must possess identical numbers of edges.

As an example of this restriction, consider the six faces shown in Figure 3-44. Of all possible combinations represented by the faces in the figure, only the following faces may be hard-linked to each other:

• face.1 and face.2
• face.4 and face.5

Figure 3-44: Face edge loop hard-link examples

The rules governing the permissibility of hard-links for the faces shown in Figure 3-44 are as follows.

• face.1 and face.2 can be hard-linked, because each possesses a single edge loop consisting of five edges. Neither can be hard-linked to face.3, face.4, face.5, or face.6, however, because each of those faces is defined by an outer edge loop consisting of four edges.
• face.3 cannot be hard-linked to face.4, face.5, or face.6, because it possesses a single edge loop, whereas each of the other faces possesses at least two edge loops.
• face.4 and face.5 can be linked to each other, because each possesses outer and inner edge loops consisting of four and three edges, respectively.
• face.6 cannot be linked to either face.4 or face.5, because it possesses two inner edge loops-one consisting of three edges (triangle) and the other consisting of one edge (circle).

Specifying Reference Vertices

When you hard-link two faces, you must specify one reference vertex for each edge loop of each face. The reference vertex determines the relationship between the edges of each face with respect to meshing. As an example of the effect of reference vertex specification, consider the two hard-linked faces shown in Figure 3-45 and Figure 3-46. In both figures, face.1 possesses a boundary layer attached to its left edge.

Figure 3-45: Face hard-link-identical reference vertex positions

Figure 3-46: Face hard-link-differing reference vertex positions

In Figure 3-45, the reference vertices are located at identical positions on each face, therefore the mesh scheme applied to face.1 is exactly duplicated on face.2. In Figure 3-46, the reference vertex locations differ between faces, therefore the location of the boundary layer on face.2 is different from that on face.1.

Specifying Mesh Orientation

If you create a hard link between two faces the edge loop senses of which are reversed relative to each other, you must reverse the orientation of the linked mesh in order to create identical meshes on both faces. As an example of this principle, consider the two hard-linked faces shown in Figure 3-47. The bottom edge of face.1 is graded toward its left endpoint vertex, and the senses of the edge loops for the faces are reversed relative to each other.

Figure 3-47: Face hard-link-orientation relative to edge loop sense

If you specify reference vertices at identical positions on both faces, GAMBIT constructs a mesh on the linked face (for example, face.2) that is different in orientation from that constructed on the specified face (for example, face.1). To create identical meshes on both faces when you specify reference vertices as shown in Figure 3-47, you must specify the Reverse orientation option when you create the mesh hard link.

Specifying the Periodic Option

The Link Face Meshes command includes a Periodic option that allows you to specify that the faces are periodically linked. Periodically linked faces are constrained such that they must behave identically to each other with respect to any virtual edge-split and vertex-move operations. For a general description of the effect of periodic linking on the boundary edges of periodically linked faces, see "Link Edge Meshes," in Section 3.2.3, above.

Using the Link Face Meshes Form

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

The Link Face Meshes form contains the following specifications.

Unlink Face Meshes

The Unlink Face Meshes command allows you to delete existing hard links associated with two faces. To delete a hard link, you must specify both faces associated with the link.

Using the Unlink Face Meshes Form

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

The Unlink Face Meshes form contains the following specifications.

3.3.7 Modify Meshed Geometry / Split Meshed Face

The Modify Meshed Geometry / Split Meshed Face command button allows you to perform the following operations.

The following sections describe each of these operations.

Modify Meshed Geometry

The Modify Meshed Geometry command allows you to convert mesh edges to topological edges and to modify geometry associated with imported mesh information.

To perform a Modify Meshed Geometry operation, you must first create a conversion list-that is, a list of mesh edges that are to be converted to topological edges. To create the list, you must specify the following parameters:

• The meshed face of interest
• The mesh edges that are to be included in the list

Specifying the Face

You can specify any meshed face for a mesh-edge conversion operation. The number of edges that can be automatically added to the conversion list depends, in part, on the shape of the face (see below).

Specifying the Mesh Edges

GAMBIT provides two different methods of adding edges to the conversion list.

• Automatic
• Manual

When you use the automatic method, GAMBIT automatically adds mesh edges to the conversion list based on a criterion involving the angle between any two adjacent mesh element faces. When you use the manual method, GAMBIT allows you to select specific mesh edges to be added to or removed from the list (see below).

Using the Automatic Method

To employ the automatic method of adding mesh edges to the list, you must specify a minimum Angle criterion. The Angle criterion represents the value of in the equation

where is the maximum angle (in degrees) between adjacent mesh element faces the common edge of which is converted to a topological edge (see Figure 3-48).

Figure 3-48: Automatic-method angle criterion

When you employ the automatic method, GAMBIT applies the Angle criterion to all mesh element faces associated with the specified topological face. If for any two mesh element faces, GAMBIT adds the mesh edge that is common to the faces to the conversion list. If , GAMBIT does not add the mesh edge to the conversion list.

Note that, for a planar face, across the entire face. As a result, if you specify and employ the automatic method for a planar face, GAMBIT adds all of the mesh edges associated with the face to the conversion list. Similarly, if you specify and employ the automatic method for a planar face, GAMBIT does not add any mesh edges to the conversion list.

NOTE: When you perform a Modify Meshed Geometry operation, GAMBIT highlights mesh edges in the graphics window according to the following color code: Blue—Detected/picked mesh edges Orange—Undetected/unpicked mesh edges

Specifying the Manual Method

When you employ the manual addition method, GAMBIT allows you to perform the following operations each of which corresponds to a separate option on the Modify Meshed Geometry form.

Adding Edges

To add an individual mesh edge to the conversion list, you must select the Add option and specify the mesh edge to be added. To specify the mesh edge, you can either input its corresponding number in the Mesh edge list box on the Modify Meshed Geometry form, or pick (Shift-left-click) the edge in the graphics window by means of the mouse.

Removing Edges

You can remove an edge from the conversion list in either of two ways.

• Select the Remove option and specify the edge to be removed (see "Adding Edges," above).
• Use the standard procedure for deleting an item from a pick list (see the GAMBIT User's Guide, Chapter 3).

Removing Spurs

"Spurs" are defined as strings of one or more edges in the conversion list that do not attach at both ends to other topological boundaries (see Figure 3-49).

Figure 3-49: Example spur

When you select the Remove spurs option and specify an edge that constitutes part of a spur, GAMBIT removes from the conversion list all edges associated with the spur.

Using the Modify Meshed Geometry Form

To open the Modify Meshed Geometry form (see below), click the Modify Meshed Geometry command button on the Mesh/Face subpad.

The Modify Meshed Geometry form contains the following options and specifications.

Split Meshed Face

The Split Meshed Face command allows you to split a meshed face into two virtual faces.

When you split a face by means of the Split Meshed Face command, GAMBIT creates two virtual faces that share a common virtual edge. The shape of the virtual edge is determined by the nodes that define the split path. Once the virtual faces are created, GAMBIT retains them even if you delete the mesh that was used to define their shapes.

To split a meshed face by means of the Split Meshed Face command, you must specify the following parameters.

• The meshed face to be split
• The mesh nodes that define the split path

Specifying the Face

You can use the Split Meshed Face command to split any real or virtual face that is currently meshed.

Specifying the Split Path Mesh Nodes

To split a face using mesh nodes, you must specify two or more mesh nodes that define the path of the split. Two of the mesh nodes must be located on the edges of the face. The other mesh nodes that define the split path may exist anywhere else internal to the face, but none of them may lie on one of the edges of the face.

Figure 3-50 illustrates the effect of splitting a real face by means of the Split Meshed Face form. Figure 3-50(a) shows the mesh and four mesh nodes that define the split path. Figure 3-50(b) shows the two virtual faces that result from the split operation.

Figure 3-50: Face split by mesh nodes

Using the Split Meshed Face Form

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

The Split Meshed Face form contains the following specifications.

3.3.8 Summarize Face Mesh / Check Face Meshes

The Summarize Face Mesh / Check Face Meshes command button lets you perform the following operations.

The Summarize Face Mesh command summarizes general face mesh information in the Transcript window and displays face nodes in the graphics window. GAMBIT also allows you to display the numbers corresponding to the elements and nodes associated with the specified face.

Using the Summarize Face Mesh Form

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

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