3. MESHING THE MODEL

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.

The following sections of this chapter describe the commands associated with each of the command buttons listed above.

3.1 Boundary Layers

3.1.1 Overview

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:

• Boundary-layer algorithm
• Height of the first row of mesh elements
• Growth factor—which specifies the height of each succeeding row of elements
• Total number of rows—which defines the depth of the boundary layer
• Edge or face to which the boundary layer is attached
• Face or volume that defines the direction of the boundary layer

3.1.2 Boundary Layer Commands

The following commands are available on the Mesh/Boundary Layer subpad.

The Create Boundary Layer command allows you to define the spacing of mesh nodes in the vicinity of an edge or face.

To create a boundary layer, you must specify the following parameters:

• Definition
• Transition characteristics
• Attachment

Specifying the Definition

To define the boundary layer, you must specify the following characteristics:

• Algorithm
• Size
• Internal continuity
• Corner shape

Specifying the Algorithm

As noted above, a boundary-layer definition consists of a set of size parameters that includes the height of the first row (that is, the row adjacent to the attachment entity), a growth factor, and the total number of rows in the boundary layer. The algorithm specification determines the method that GAMBIT uses to calculate the height(s) of the elements in the first row of the boundary layer. GAMBIT provides the following algorithm types.

• Uniform
—specifies that heights of all first-row boundary-layer elements are equal to each other across the entire span (edge length or face surface area) of the attachment entity.
• Aspect ratio based
—computes the first-row element heights as a fixed percentage of the edge mesh element lengths for the edge or face to which the boundary layer is attached.

Figure 3-1: Comparison of Uniform and Aspect ratio based algorithms

For the Uniform boundary layer (Figure 3-1(a)), the first row of the boundary layer exhibits a uniform height across the span of the attachment edge. As a result, each succeeding row of the boundary layer also exhibits a uniform height.

For the Aspect ratio based boundary layer (Figure 3-1(b)), the heights of the elements in the first row of the boundary layer vary according to the corresponding element length on the attachment edge. Consequently, the first-row elements increase in height from left to right across the edge, because the edge mesh is graded to increase from left to right. In this case, the first-row element heights for the boundary layer elements represent 20% of the corresponding edge element lengths.

Figure 3-1 illustrates that the first-row heights—and, therefore, the choice of algorithm—affect(s) the shape of the entire boundary layer. In this case, both boundary layers employ a growth factor of 1.2, therefore each row of the boundary layer is 20% thicker than the preceding row. Figure 3-1 shows that the growth factor amplifies the effect of the first-row heights on boundary layer shape across the span of the boundary layer.

For boundary layers that are attached to uniformly graded edges, the shape of the boundary layer is independent of the algorithm specified for its construction. For example, Figure 3-2 shows Uniform and Aspect ratio based boundary layers for a configuration similar to that shown in Figure 3-1, above, but for which the attachment edge is uniformly graded. Because the edge element lengths are uniform across the edge, the heights of all first-row elements for the Aspect ratio based boundary layer are equal to each other, therefore the boundary layer is identical to the Uniform boundary layer in this case.

Figure 3-2: Uniform vs. Aspect ratio based algorithms—uniformly graded edge

Specifying the Size Characteristics

To define the size of the boundary layer, you must specify three of four parameters that describe the sizes of the boundary-layer rows. The parameters to be specified differ slightly from each other according to the algorithm used to determine the first-row heights (see "Specifying the Algorithm," above).

Parameters for the Uniform Algorithm

For boundary layers that employ the Uniform algorithm, the boundary-layer size specification involves three of the following parameters.

• First-row height
• Growth factor
• Number of rows
• Total depth

The first three parameters listed above are defined as follows (see Figure 3-3).

• The first-row height (a) specifies the distance between the edge or face to which the boundary layer is attached and the first full row of mesh nodes.
• The growth factor represents the ratio

• The number of rows (n) specifies the total number of full rows of mesh nodes in the boundary layer.

All three parameters affect the total depth (D) of the boundary layer.

Figure 3-3: Boundary layer size characteristics—Uniform algorithm

Parameters for the Aspect-Ratio-Based Algorithm

For boundary layers that employ the Aspect ratio based algorithm, the boundary-layer size specification involves three of the following parameters.

• First percent
• Growth factor
• Number of rows
• Last percent

The first three parameters listed above are defined as follows (see Figure 3-4).

• The first percent (F) specifies the the height of the first row, at any given edge node, relative to the average length of the edge elements on either side of the node. The effect of the first-percent value on boundary layer row height depends, in part, on whether a given node is interior or exterior to the attachment entity (see below).
• The growth factor represents the ratio
  

  where b is the distance between the first and second rows at a given edge node, and a is the height of the first row at the node. The distance between any two rows in the boundary layer at a given edge node is equal to the distance between the preceding two rows times the growth factor.

• The number of rows (n) specifies the total number of full rows of mesh nodes in the boundary layer.

Figure 3-4: Boundary layer size characteristics—Aspect ratio based algorithm

For interior nodes on the attachment entity, the general specification of row height can be expressed mathematically as

where is the height of the first row at node i, F is the ;First percent value specified on the ;Create Boundary Layer form, and and are the lengths of the attachment-entity edge elements on either side of node i.

For exterior nodes on the attachment entity—for example, nodes located at edge endpoints—the row height can be expressed as

where is the height of the first row at the exterior node, and is the length of the attachment-entity edge element adjacent to the node.

Specifying Internal Continuity

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 3-5(a)). If you attach boundary layers to two or more adjoining faces of a volume, the boundary-layer imprints necessarily overlap on any faces that are shared as common neighbors by the faces to which the boundary layers are attached (see Figure 3-5(b)).

Figure 3-5: Boundary-layer imprints

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.

• If you select the Internal continuity option, GAMBIT does not imprint the boundary layers of adjoining faces onto each other. In addition, GAMBIT modifies the mesh patterns in the overlap regions such that the imprints are "dovetailed" together (see Figure 3-6(a)).
• If you do not select the Internal continuity option, GAMBIT imprints boundary layers on adjoining faces in the manner described above (Figure 3-6(b)).

Figure 3-6: Effect of the 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 3-6(b) can be meshed using a Map meshing scheme-resulting in the mesh shown in Figure 3-7(a). By contrast, the volume shown in Figure 3-6(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 3-6(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 3-7(b)).

Figure 3-7: Effect of Internal continuity option on allowable meshing schemes

Specifying the Corner Shape

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 3-8):

• If you select the Wedge corner shape option, GAMBIT creates a wedge-shaped boundary-layer region surrounding the connecting vertex (Figure 3-8(a)).
• If you unselect the Wedge corner shape option, GAMBIT creates a block-shaped boundary-layer region surrounding the connecting vertex (Figure 3-8(b)).

Figure 3-8: 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 wedge-shaped boundary layer at the corner, you must select the Wedge corner shape option when creating each separate boundary layer.

Specifying the Transition Characteristics

The boundary-layer transition characteristics consist of two components:

• Transition pattern
• Number of transition rows

Specifying the Transition Pattern

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

A: B

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 3-9 shows four different two-row boundary layers representing each of the four transition patterns listed above.

Figure 3-9: Boundary layer transition patterns

NOTE: Edges can host any of the four transition patterns, but faces can host only the 1:1 transition pattern.

Specifying the Number of Transition Rows

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. Figure 3-10 shows the effect of the number of transition rows on a boundary layer consisting of three rows with the transition pattern 4:2.

Figure 3-10: 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:

• The boundary layer as currently specified
• An arrow that indicates the direction of the boundary layer

You can change the direction of the boundary layer either by means of the Attachment (Edge or Face) list box on the Create Boundary Layer form or by means of the mouse.

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.

1. Specify the edge or face again in the Attachment list box
2. Use the Edge List or Face List paired pick-list form to specify the entity and direction of the boundary layer (see "Using the Edge List or Face List Form," below).

To change the direction of the boundary layer by means of the mouse, Shift-middle-click 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:

• Input the entity name directly in the Attachment list box or select the entity from the entity pick-list form
• Pick the entity in the graphics window

Using the Create Boundary Layer Form

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 two radio buttons that specify the boundary layer algorithm. GAMBIT provides two algorithm options: Uniform Aspect ratio based For a description of the algorithm options, see "Specifying the Algorithm," above.
First row (a)	(Uniform algorithm only) specifies the height of the row nearest to the edge or face to which the boundary layer is attached (see "Parameters for the Uniform Algorithm," above).
First percent	(Aspect ratio based algorithm only) specifies the height of the row nearest to the edge or face to which the boundary layer is attached (see "Parameters for the Aspect-Ratio-Based Algorithm," above).
Growth Factor (b/a)	specifies the growth factor—that is, the ratio of the height of each row relative to that of the immediately preceding row.
Rows	specifies the total number of rows in the boundary layer.
Depth (D)	(Uniform algorithm only) specifies the total depth of the boundary layer.
Last percent	(Aspect ratio based algorithm only) specifies the height of the uppermost boundary layer row as a percentage of the edge element length on the attachment entity.
Internal continuity	specifies that boundary-layer imprints are dovetailed in overlapping regions (see "Specifying Internal Continuity," above).
Wedge corner shape	specifies that the boundary-layer 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. NOTE: When you click the pick list button on the Attachment entity list box, GAMBIT opens a paired pick list form titled Edge List or Face List. For instructions in using the paired pick list form, see "Using the Edge List or Face List Form," below.
Label	specifies a label for the boundary layer.

Using the Edge List or Face List Form

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 pick-list 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 pick-list form operates in a manner similar to that of conventional pick-list 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 left column lists the edge to which the boundary layer is attached.
• The right column lists the face that defines the direction of the boundary layer.

When you add an edge to the Picked scroll list by means of the right-arrow command button, GAMBIT adds the edge to the Edge column and automatically includes one of its associated faces in the Face column. (The face defines the direction of the boundary layer.) If you add the same edge again to the Picked scroll list, GAMBIT creates a second entry for the edge in the Edge column and includes another of its associated faces in the Face column. When the Face column includes all faces associated with a given edge, GAMBIT removes that edge from the Available column.

Modify Boundary Layer

The Modify Boundary Layer command allows you to modify the specifications for any existing boundary layer.

Using the Modify Boundary Layer Form

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.)

Modify Boundary Layer Label

The Modify Boundary Layer Label command allows you to change the label associated with any boundary layer.

Using the Modify Boundary Layer Label Form

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.

Summarize Boundary Layers

The Summarize Boundary Layers command displays one or more existing boundary layers in the graphics window.

Using the Summarize Boundary Layers Form

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.

Delete Boundary Layers

The Delete Boundary Layers command allows you to delete one or more existing boundary layers.

Using the Delete Boundary Layer Form

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.

© Fluent, Inc. 10/29/01