When you click the Mesh command button on the Operation toolpad, GAMBIT opens the Mesh subpad. The Mesh subpad contains command buttons that allow you to perform mesh operations involving boundary layers, edges, faces, volumes, and groups.
The symbols associated with each of the Mesh subpad command sets are as follows.
Symbol  Command Set 
Boundary Layer  
Edge  
Face  
Volume  
Group 
The following sections of this chapter describe the commands associated with each of the command buttons listed above.
Boundary layers define the spacing of mesh node rows in regions immediately adjacent to edges and/or faces. They are used primarily to control mesh density and, thereby, to control the amount of information available from the computational model in specific regions of interest.
As an example of a boundary layer application, consider a computational model that includes a cylinder representing a pipe through which flows a viscous fluid. Under normal circumstances, it is likely that the fluid velocity gradients are large in the region immediately adjacent to the pipe wall and small near the center of the pipe. By attaching a boundary layer to the face that represents the pipe wall, you can increase the mesh density near the wall and decrease the density near the center of the cylinder, thereby obtaining sufficient information to characterize the gradients in both regions while minimizing the total number of mesh nodes in the model.
To define a boundary layer, you must specify the following information:
The following commands are available on the Mesh/Boundary Layer subpad.
The Create Boundary Layer operation (blayer create and blayer attach commands) defines the spacing of mesh nodes in the vicinity of an edge or face. The operation requires the following specifications.
Figure 31: Uniform boundary layer algorithm (2D)
Figure 32: Aspect ratio (first) boundary layer algorithm (2D)
Figure 33: Aspect ratio (last) boundary layer algorithm (2D)
For the Uniform boundary layer (Figure 31), the first row exhibits a uniform height across the span of the attachment edge, and the growth factor is constant; therefore, each succeeding row of elements also exhibits a uniform height. For the Aspect ratio (first) boundary layer (Figure 32), the firstrow heights vary in proportion to the edge mesh interval lengths. Consequently, the first row of the boundary layer grows thicker from left to right across the edge, because the edge mesh interval lengths increase from left to right. For the Aspect ratio (last) boundary layer (Figure 33), the first row exhibits a uniform height across the span of the attachment edge, but the growth factor varies in proportion to the edge mesh interval widths. Consequently, the succeeding rows grow thicker from left to right across the edge.
NOTE: If the attachment edge shown in Figure 31, Figure 32, and Figure 33, above, were graded uniformly (Ratio = 1), all three Algorithm options would produce boundary layers of uniform height across the span of the edge. 
If you attach a boundary layer to a face (rather than an edge), GAMBIT applies the definition algorithm along the boundaries of the attachment face. For example, Figure 34 shows an Aspect ratio (first) boundary layer attached to one face of a cube. In this case, the boundary edges of the attachment face have been premeshed using five intervals and a grading ratio of 1.25.
Figure 34: Aspect ratio (first) boundary layer algorithm (3D)
When attaching a boundary layer to a face, care must be taken to ensure that the boundary layer is not discontinuous at any vertices on the face boundary. In Figure 34, above, the boundary edges of the attachment face are graded such that the mesh interval widths on either side of any corner vertex are equal to each other. As a result, the 3D boundary layer is continuous at all four corners of the attachment face. In Figure 35, the face boundary edges are graded such that edge mesh interval lengths differ on either side of three of the four corner vertices (b, c, and d). Consequently, the boundary layer exhibits discontinuities at those vertices.
Figure 35: Effect of discontinuous grading at face boundary vertices
The Uniform algorithm (see Figure 36) definition parameters are as follows.
Figure 36: Boundary layer dimensions—Uniform algorithm
The First row (a) value specifies the height of the first row (a)—that is, the absolute distance between the entity to which the boundary layer is attached and the first row of mesh nodes in the boundary layer. (NOTE: For the Uniform algorithm, the firstrow height, a, is uniform across the boundary layer.)
The Growth factor (b/a) value (G) represents the ratio
where b is the distance between the first and second rows and a is the height of the first row. The height of any row in the boundary layer (other than the first row) is equal to the height of the previous row times the Growth factor (b/a) value.
The Rows value specifies the total number of rows to be included in the boundary layer.
NOTE: When you specify the First row (a), Growth factor (b/a), and Rows values, GAMBIT computes the total depth (D) of the boundary layer and displays the value in the noneditable Depth (D) field on the Create Boundary Layer form. 
Aspect ratio (first) Algorithm
The Aspect ratio (first) algorithm (see Figure 37) definition parameters are as follows.
Figure 37: Boundary layer dimensions—Aspect ratio (first) algorithm
The First percent (a/w) value specifies the height of any first row boundary layer node () as a percentage of mesh interval width at the associated node on the attachment entity. For interior nodes on the attachment entity, the general specification of firstrow height can be expressed as
where is the height of the first row at node i, F is the First percent (a/w) value, and and are the widths of the attachmententity mesh intervals on either side of node i.
For exterior nodes on the attachment entity (for example, nodes located at edge endpoints) the firstrow heights can be expressed as
and
where and are the heights of the first rows at the exterior nodes.
The Growth factor (b/a) value (G) represents the ratio
where is the distance between the first and second rows at edge mesh node i and is the height of the first row at node i. (NOTE: For the Aspect ratio (first) algorithm, the Growth factor (b/a) value is constant across the boundary layer.) The height of any boundary layer row at a given edge node is equal to the height of the preceding row at that node times the growth factor, G.
The Rows value specifies the total number of rows to be included in the boundary layer.
NOTE: When you specify the First percent (a/w), Growth factor (b/a), and Rows values, GAMBIT computes the "last percent" value for the boundary layer and displays the value in the noneditable Last percent (c/w) field on the Create Boundary Layer form. The Last percent (c/w) value represents the height of the boundary layer top row at any given node relative to the corresponding mesh interval widths on the attachment entity. The Last percent (c/w) value can be computed from
where F and L are the First percent (a/w) and Last percent (c/w) values, respectively, G is the Growth factor (b/a) value, and R is the number of Rows. 
The Aspect ratio (last) algorithm (see Figure 38) definition parameters are as follows.
Figure 38: Boundary layer dimensions—Aspect ratio (last) algorithm
The First row (a) value specifies the height of the first row (a)—that is, the absolute distance between the entity to which the boundary layer is attached and the first row of mesh nodes in the boundary layer. (NOTE: For the Aspect ratio (last) algorithm, the firstrow height, a, is uniform across the boundary layer.)
The Rows value specifies the total number of rows to be included in the boundary layer.
The Last percent (c/w) value specifies the height of the boundary layer top row at any node relative to the corresponding mesh interval widths on the attachment entity. At any interior mesh node on the attachment entity (for example, the endpoints of an attachment edge), the relationship between the top row height (), the Last percent (c/w) value (L), and the mesh interval widths (w) can be expressed as
where and are the widths of the attachmententity mesh intervals on either side of node i.
NOTE: For the Aspect ratio (last) algorithm, the growth factor varies across the boundary layer and is computed at each mesh node on the attachment entity. For mesh nodes that are interior to the entity, the growth factor at any node i can be expressed as
where is the nodespecific growth factor and R is the number of Rows. Because the growth factor is not constant across the boundary layer, GAMBIT does not display the Growth factor (b/a) field on the Create Boundary Layer form. 
When you attach a boundary layer to a face that constitutes part of a volume, GAMBIT imprints the boundary layer on all adjoining faces that are also part of the volume (see Figure 39(a)). If you attach boundary layers to two or more adjoining faces of a volume, the boundarylayer imprints overlap on any faces that are common neighbors to the faces to (see Figure 39(b)).
Figure 39: Boundarylayer imprints (with shaded attachment faces)
The Internal continuity option on the Create Boundary Layer form determines the manner in which GAMBIT imprints boundary layers on adjoining faces as well as the mesh pattern in regions of imprint overlap.
Figure 310: Effect of the Internal continuity option
The effect of the Internal continuity option depends, in part, on the values of two GAMBIT default variables:
Figure 311 shows the effect of these default variables on the boundary layer created using the Internal continuity option. In Figure 311(a), both variables are set to zero; therefore, the angling of the boundary layer is confined to the corner region. In Figure 311(b), ANGLE_SMOOTH_FACTOR is set to 1; therefore, GAMBIT spreads the boundarylayer angling across the entire edge. In Figure 311(c), ADJUST_EDGE_BL_HEIGHT is also set to 1; therefore, GAMBIT adjusts the boundarylayer heights to maintain constant heights with respect to the edges adjacent to the corner.
Figure 311: Effect of default variables on Internal continuity option
In addition to affecting the mesh pattern in the imprint overlap regions, the Internal continuity option directly affects which types of meshing schemes are appropriate for volumes to which boundary layers have been applied. For example, the volume shown in Figure 310(b) can be meshed using a Map meshing schemeresulting in the mesh shown in Figure 312(a). By contrast, the volume shown in Figure 310(a) cannot be meshed using a Map scheme, because the vertex located at the lower right corner of the front face (and imprint overlap region) is necessarily treated as a Side vertex. To mesh the volume shown in Figure 310(a), it is most reasonable to apply a Pave meshing scheme to the front face, then apply a Cooper meshing scheme to the volume, using the front and back faces as source faces (see Figure 312(b)).
Figure 312: Effect of Internal continuity option on allowable meshing schemes
GAMBIT allows you to control the shape of the mesh in the region surrounding a Corner or Reversal vertex that connects two edges to which boundary layers are attached. To do so, you must select or unselect (default) the Wedge corner shape option on the Create Boundary Layer form. The Wedge corner shape option produces the following effects (see Figure 313):
Figure 313: Effect of Wedge corner shape option
If two edges meet at a Corner or Reversal vertex, and each edge possesses a separate boundary layer, then to create a wedgeshaped boundary layer at the corner, you must select the Wedge corner shape option when creating each separate boundary layer.
The boundarylayer transition characteristics consist of two components:
The transition pattern determines the arrangement of mesh nodes in the region near the outermost row of the boundary layer. Boundary layer transition patterns are defined by the ratio
where B is the number of mesh intervals in a given row and A is the number of mesh intervals in the immediately preceding full row. GAMBIT allows you to specify any of four transition patterns—1:1, 4:2, 3:1, or 5:1.
Figure 314 shows four different tworow boundary layers representing each of the four transition patterns listed above.
Figure 314: Boundary layer transition patterns
NOTE: Edges can host any of the four transition patterns, but faces can host only the 1:1 transition pattern. 
When you specify any transition pattern other than 1:1, you must also specify the number of transition rows—that is, the number of outermost rows to which the transition pattern is applied. GAMBIT applies the 1:1 pattern to all rows other than the transition rows. Figure315 shows the effect of the number of transition rows on a boundary layer consisting of three rows with the transition pattern 4:2.
Figure 315: Effect of number of transition rows
To define the location of a boundary layer, you must specify the edge or face to which the boundary layer is attached. If the edge or face is shared by two or more faces or volumes, respectively, you must also specify the face or volume that defines the direction of the boundary layer. For example, each edge of a rectangular brick volume is shared by two rectangular faces. If you attach a boundary layer to one of the edges of the volume, you must specify which of the corresponding faces defines the direction of the boundary layer.
When you specify an edge or face to which to attach a boundary layer, GAMBIT highlights the edge or face in the graphics window and displays the following items:
NOTE: If the boundarylayer attachment entity serves as an attachment entity for a size function or is part of a highertopology entity to which a size function is attached, GAMBIT might or might not reflect the sizefunction definition in the temporary display of the boundary layer. Specifically, the boundarylayer display reflects the definition of the size function only if the background grid for the size function has already been generated—for example, by meshing an edge that is also part of the sizefunction attachment entity. 
When you specify an edge or face in the Attachment list box on the Create Boundary Layer form, the list box displays both the specified entity itself and the face or volume that defines the direction of the boundary layer. To change the direction of the boundary layer by means of the list box, you can perform either of the following operations.
To change the direction of the boundary layer by means of the mouse, Shiftmiddleclick the entity to which the boundary layer is attached.
GAMBIT allows you to apply a given boundary layer definition to more than one edge or face at a time. To do so, you must include in the Attachment entity pick list all of the entities to which the currently defined boundary layer is to be attached.
You can add an edge or face to the Attachment entity pick list on one of the following ways:
If you attach 2D boundary layers to adjacent edges that share a common face or attach 3D boundary layers to adjacent faces that share a common volume, GAMBIT automatically smoothes the resulting mesh at the transition points between the boundary layers. You can control the range of elements over which the boundary layers are smoothed by means of the HEIGHT_TRANSIT_RATIO default variable. As an example of mesh smoothing at boundary layer transition points, consider the 2D boundary layers shown in Figure 316. In this case, the boundary layers are attached to adjacent edges that constitute one side of a square face. They differ from each other only with respect to their growth factors.
Figure 316: Example 2D boundary layers on adjacent edges
If you retain the default value for the HEIGHT_TRANSIT_RATIO default variable and mesh the face shown in Figure 316, GAMBIT creates the mesh shown in Figure 317. In this case, the discontinuity between the boundary layers is smoothed over three intervals on either side of the transition point.
Figure 317: Mesh with boundary layer smoothing at transition point
As noted above, you can use the HEIGHT_TRANSIT_RATIO default variable to control the number of intervals over which the mesh is smoothed. The effect of the default variable depends on whether its value is greater or less than one (1) and can be summarized as follows:
Figure 318: Boundary layer smoothing—HEIGHT_TRANSIT_RATIO = 2
In this case, the mesh is smoothed over a distance of two intervals on either side of the transition point.
To open the Create Boundary Layer form (see below), click the Create Boundary Layer command button on the Mesh/Boundary Layer subpad.
The Create Boundary Layer form contains the following specifications.
Show  displays the boundary layer(s) in the graphics window as they are created and defined. 
Definition:  
Algorithm:  contains radio buttons that specify the boundary layer definition algorithm. GAMBIT provides the following algorithm options.

The definition specifications differ according to Algorithm option as follows.
Uniform Algorithm Specifications
When you specify the Algorithm:Uniform option, GAMBIT displays the Definition fields as shown on the Create Boundary Layer form, above.
First row (a)  specifies the height of the boundary layer first row. 
Growth Factor (b/a)  specifies the growth factor—that is, the ratio of the height of each row relative to that of the preceding row. 
Rows  specifies the total number of rows in the boundary layer. 
Depth (D)  displays (noneditable field) the total depth of the boundary layer. 
Aspect ratio (first) Algorithm Specifications
When you specify the Algorithm:Aspect ratio (first) option, GAMBIT displays the following Definition fields on the Create Boundary Layer form.
First percent (a/w)  specifies the height of the boundary layer first row as a percentage of the edge element width on the attachment entity. 
Growth Factor (b/a)  specifies the growth factor—that is, the ratio of the height of each row relative to that of the preceding row. 
Rows  specifies the total number of rows in the boundary layer. 
Last percent (c/w)  displays (noneditable field) the height of the top row as a percentage of the average interval width. 
Aspect ratio (last) Algorithm Specifications
When you specify the Algorithm:Aspect ratio (last) option, GAMBIT displays the following Definition fields on the Create Boundary Layer form.
First row (a)  specifies the height of the boundary layer first row. 
Rows  specifies the total number of rows in the boundary layer. 
Last percent (c/w)  specifies the height of the top row as a percentage of the average interval width. 
General Specifications
The following Definition specifications are common to all of the Algorithm options.
Internal continuity 
specifies that boundarylayer imprints are dovetailed in overlapping regions (see "Specifying Internal Continuity," above). 
Wedge corner shape 
specifies that the boundarylayer forms a wedge shape in the region surrounding a Corner or Reversal vertex (see "Specifying the Corner Shape," above). 
Transition Pattern: 
contains four radio buttons that specify the transition pattern. The pattern options are 1:1, 4:2, 3:1, and 5:1. (See "Specifying the Transition Pattern," above.) 
Transition Rows 
specifies the number of transition rows for transition patterns 4:2, 3:1, and 5:1. (NOTE: You must use the slide bar, rather than the associated text box, to set the number of transition rows.) 
Attachment: 

Edges Faces 
specifies whether the boundary layer is attached to an edge or a face.  
Edges Faces 
specifies the edge or face to which the boundary layer is attached.


Label 
specifies a label for the boundary layer. 
When you specify an edge or face to which a boundary layer is attached, GAMBIT adds the edge or face to a paired pick list. The paired pick list includes both the attachment entity itself (edge or face) and the entity that defines the direction of the boundary layer (face or volume). You can modify the edge or face paired pick list by means of either the Edge List or Face List picklist form, respectively. Both forms operate according to the following general principles described for the Edge List form.
To open the Edge List form (see below), select Edge in the Attachment field on the Create Boundary Layer form and click the associated pick list button.
The Edge List paired picklist form operates in a manner similar to that of conventional picklist forms (see GAMBIT User's Guide, Chapter 3). It differs from the conventional forms only in that the Picked scroll list includes two columns.
The Modify Boundary Layer operation (blayer modify and blayer attach commands) modifies the specifications for any existing boundary layer.
To open the Modify Boundary Layer form (see below), click the Modify Boundary Layer command button on the Mesh/Boundary Layer subpad.
(For a description of the options and specifications available on the Modify Boundary Layer form, see "Create Boundary Layer," above.)
The View 3D Boundary Layers operation (blayer mesh command) allows you to examine volume meshes in regions affected by 3D boundary layers. When you execute the View 3D Boundary Layers command for any 3D boundary layer, GAMBIT meshes the volume associated with the boundary layer, renders the mesh invisible outside the boundary layer region, and automatically opens the Examine Mesh form.
Figure 319 illustrates the effect of the View 3D Boundary Layers operation for a cube with a uniform boundary layer attached to two adjoining faces. In this case, the boundary layer was created using the Internal continuity option; therefore, the boundary layer dovetails in its overlapping regions.
Figure 319: View 3D Boundary Layers operation
If you execute the View 3D Boundary Layers operation for the boundary layer shown in Figure 319(a), GAMBIT meshes the cube, renders the mesh invisible outside the boundary layer region, and automatically opens the Examine Mesh form to display the mesh (Figure 319(b)). By default, GAMBIT selects the Range option on the Examine Mesh form and displays all volume elements in the boundary layer region; however, you can use any of the Examine Mesh options (for example, Plane or Sphere) to customize the mesh display.
NOTE: It is advisable to close the Examine Mesh form before executing subsequent GAMBIT operations. When you close the Examine Mesh form, GAMBIT automatically executes an undo command to undo the blayer mesh command that generated the boundary layer mesh(es). 
To open the View 3D Boundary Layers form (see below), click the View command button on the Mesh/Boundary Layers subpad.
The View 3D Boundary Layers form includes the following specification.
B.L.s  specifies the boundary layer region(s) to be displayed. 
The Modify Boundary Layer Label operation (blayer modify command) changes the label associated with any boundary layer.
To open the Modify Boundary Layer Label form (see below), click the Modify Label command button on the Mesh/Boundary Layer subpad.
The Modify Boundary Layer Label form includes the following specifications.
B.L.  specifies the boundary layer to be modified. 
Label  specifies a new label for the boundary layer. 
The Summarize Boundary Layers operation (blayer summarize command) displays one or more existing boundary layers in the graphics window.
To open the Summarize Boundary Layers form (see below), click the Summarize command button on the Mesh/Boundary Layer subpad.
The Summarize Boundary Layers form contains the following specification.
B.L.s  specifies the boundary layer(s) for which summary information is to be displayed. 
The Delete Boundary Layers operation (blayer delete command) deletes one or more existing boundary layers.
To open the Delete Boundary Layers form (see below), click the Delete command button on the Mesh/Boundary Layer subpad.
The Delete Boundary Layers form includes the following specification.
B.L.s  specifies the boundary layer(s) to be deleted. 