The following commands are available on the Mesh/Volume subpad.
|Mesh Volumes||Creates mesh nodes throughout a volume|
|Smooth Volume Meshes||Adjusts volume mesh node positions to improve uniformity of node spacing|
|Set Volume Element Type||Specifies volume element types used throughout the model|
Link Volume Meshes
Unlink Volume Meshes
|Creates or removes mesh hard links between volumes|
|Modify Meshed Volume||Converts mesh edges and faces to topological equivalents|
Summarize Volume Mesh
Check Volume Meshes
|Displays mesh information in the graphics window; displays 3-D mesh quality information|
|Delete Volume Meshes||Deletes existing mesh nodes from volumes|
The following sections describe the purpose and operation of each of the commands listed above.
The Mesh Volumes operation (volume mesh and volume modify commands) creates a mesh for one or more volumes in the model. When you mesh a volume, GAMBIT creates mesh nodes throughout the volume according to the currently specified meshing parameters.
NOTE: When meshing a volume, GAMBIT meshes any unmeshed faces on the volume boundary before creating the volume mesh. If any newly created face mesh includes elements the default quality metric of which exceeds the current default upper limit, GAMBIT aborts the volume meshing operation without creating the volume mesh.
The default quality metric and default upper limit are specified by means of two MESH.EXAMINE default variables:
GAMBIT does not apply the criteria described above to any boundary faces that are pre-meshedthat is, meshed prior to the volume meshing operation.
To mesh a volume, you must specify the following parameters:
GAMBIT allows you to specify any volume for a meshing operation; however, the shape and topological characteristics of the volume, as well as the vertex types associated with its faces, determine the type(s) of mesh scheme(s) that can be applied to the volume.
To specify the meshing scheme, you must specify the following parameters:Elements parameter defines the shape(s) of the elements that are used to mesh the volume. The Type parameter defines the meshing algorithm and, therefore, the overall pattern of mesh elements in the volume. The Smoother specification determines the type of smoothing algorithm (if any) used to smooth a mapped mesh during the meshing operation.
The following sections describe the parameters listed above and their effects on the overall volume mesh.
GAMBIT allows you to specify any of the following volume meshing Elements options.
|Hex||Specifies that the mesh includes only hexahedral elements|
|Hex/Wedge||Specifies that the mesh is composed primarily of hexahedral elements but includes wedge elements where appropriate|
|Tet/Hybrid||Specifies that the mesh is composed of tetrahedral, hexahedral, pyramidal, and wedge elements where appropriate|
Each of the Elements options listed above is associated with a specific set of Type options (see below).
GAMBIT provides the following volume meshing Type options.
|Map||Creates a regular, structured grid of hexahedral mesh elements|
|Submap||Divides an unmappable volume into mappable regions and creates a structured grid of hexahedral mesh elements in each region|
|Tet Primitive||Divides a four-sided volume into four hexahedral regions and creates a mapped mesh in each region|
|Cooper||Sweeps the mesh node patterns of specified "source" faces through the volume|
|Stairstep||Creates a regular hexahedral mesh and a corresponding faceted volume that approximates the shape of the original volume|
|TGrid||Specifies that the mesh is composed primarily of tetrahedral mesh elements but may include hexahedral, pyramidal, and wedge elements where appropriate|
|Hex Core||Creates a core of regular hexahedral elements surrounded by transition layers of tetrahedral, pyramidal, and wedge elements. (NOTE: GAMBIT provides two methods of generating a Hex Core meshGAMBIT native (Native) and TGrid (TGrid).)|
As noted above, each of the Elements options is associated with a specific set of one or more of the Type options. The shaded cells marked with an "X" in the following table indicate the allowable combinations of Elements and Type options.
|NOTE (1): Of the Type options listed above, only the Cooper option is associated with more than one Elements option. Therefore, in the following sections, the volume meshing scheme types are differentiated from each other only by their respective Type namesfor example, Tet Primitive.|
|NOTE (2): When you specify a volume on the Mesh Volumes form, GAMBIT automatically evaluates the volume with respect to its shape, topological characteristics, and vertex types and sets the Scheme option buttons to reflect a recommended volume meshing scheme. If you specify more than one volume for a meshing operation, the scheme represented by the Scheme option buttons reflects the recommended scheme for the most recently picked volume. If you enforce a meshing scheme, by means of the Scheme option buttons on the Mesh Volumes form, GAMBIT applies the specified scheme to all currently picked volumes.|
Each of the Type options listed in the table above is associated with an allowable set of solvers in the GAMBIT Solver menu on the main menu bar. The following table shows the correspondence between the meshing Type and the allowable Solver options. (NOTE: The FLUENT 4 solver requires a structured grid, and the NEKTON solver requires hexahedral mesh elements.)
|Solver||Map||Submap||Tet Primitive||Cooper||Stairstep||TGrid||Hex Core|
The correspondences shown in this table indicate which meshing schemes can produce usable meshes for any given solver, but they do not guarantee that all meshes created using a given meshing scheme will create usable meshes. For example, the Stairstep and Hex Core meshing schemes can create meshes usable by the FIDAP solver; however, they are also capable of creating meshes that cannot be used by FIDAPfor example, those with hanging nodes.
When you apply the Map meshing scheme to a volume, GAMBIT meshes the volume using an array of hexahedral mesh elements, such as those shown in Figure 3-77.
Figure 3-77: Map meshing schemepartial array of hexahedral elements
Each mesh element includes at least eight nodes-located at the corners of the element. If you specify an alternative volume element node pattern, GAMBIT creates either 20 or 27 nodes per mesh element (see "Set Volume Element Type," below).
Specifying the Smoother Algorithm
If you mesh a volume using a Map meshing scheme, you can automatically smooth the mesh during meshing by means of a Smoother algorithm. (NOTE: You can manually smooth any existing volume mesh by means of the Smooth Volume Meshes command (see Section 3.4.2, below).)
GAMBIT provides two Smoother options for volumes:
The Map volume meshing scheme can only be applied to volumes that can be meshed such that the mesh represents a logical cube. To represent a logical cube, a volume mesh must satisfy the following general requirements.
Although the strict definition of volume mappability is best expressed in terms of the mesh itself, it is possible to state mappability requirements in terms of the general geometrical configuration of a given volume. Specifically, volume mappability criteria may be stated as follows.
|NOTE: Any side of the volume may consist of more than one face.|
As an example of the application of the general rule stated above, consider the volumes shown in Figure 3-78.
Figure 3-78: Map volume meshing schemeexample volumes
Of the volumes shown in the figure, only the brick shown in Figure 3-78(a) is mappable in its primitive form. However, it is possible to transform the other volumes into mappable volumes by means of vertex-type assignments and virtual geometry operations. The following sections describe the operations required to render each volume mappable.
Transforming Volumes Into Mappable Forms
As noted above, the volumes shown in Figure 3-78(b), (c), and (d) are not mappable in their primitive forms, but each can be transformed into a mappable volume by means of either vertex-type specifications or virtual geometry operations. Specifically, the operations that are required to transform each volume are as follows.
|(b)||Pentagonal prism||Vertex-type specification|
|(d)||Clipped cube||Virtual face collapse|
Pentagonal PrismSpecifying Vertex Types
To transform the pentagonal prism shown in Figure 3-78(b) into a mappable volume, you must specify its vertex types such that the top and bottom faces are mappable. To do so, you must specify one vertex on each of the top and bottom faces as a Side vertex and all other vertices as End vertices (see Figure 3-79(a)).
Figure 3-79: Mappable pentagonal prism volume
Figure 3-79(b) shows the Map volume mesh that results from the vertex specifications shown in Figure 3-79(a). Note that faces A and B in the figure comprise one side of the logical mesh cube and that face C, by itself, constitutes the opposing side.
When you assign vertex types to transform a prism into a mappable volume, you must specify the vertex types such that the Side vertices on the top and bottom faces are connected to each other by means of a single vertical edge. For example, if you assign vertex types according to the specifications shown in Figure 3-80, GAMBIT cannot create a Map volume mesh in the prism, because the configuration cannot be made to represent a logical mesh cube.
Figure 3-80: Unmappable pentagonal prism volume
Cylinder-Splitting Edges and Faces
The cylinder shown in Figure 3-78(c) is not mappable in its primitive form, but it is possible to transform the cylinder into a mappable volume by means of virtual edge-split and face-split operations. (For descriptions of the virtual edge-split and face-split operations, see the Appendix of this guide.)
If you split the edges that circumscribe the end caps and use the resulting vertices to split the cylindrical face into four separate faces, the end faces become mappable (see Figure 3-81(a)), and the cylinder becomes topologically equivalent to the brick shown in Figure 3-78(a). As a result, the cylinder can be meshed according to the Map meshing scheme (see Figure 3-81(b)).
Figure 3-81: Mappable cylinder
Clipped CubeCollapsing a Face
The clipped cube shown in Figure 3-78(d) is not mappable in its primitive form, but it can be rendered mappable by means of a virtual face collapse operation. (For a description of the virtual face collapse operation, see the Appendix of this guide.) When you collapse the triangular face between its three neighboring faces, GAMBIT creates the virtual volume shown in Figure 3-82(a).
Figure 3-82: Mappable brick without corner
The volume shown in Figure 3-82(a) is topologically equivalent to the brick shown in Figure 3-78(a). If all of its vertices are specified as End vertices, the volume represents a logical meshing cube and can, therefore, be meshed according to a Map volume meshing scheme (see Figure 3-82(b)).
Mapping Volumes with Fewer Than Six Faces
As a general rule, the Map volume meshing scheme is applicable only to volumes that include six or more faces. It is possible, however, to transform some volumes that contain fewer than six faces into mappable volumes. As an example of such a transformation, consider the sliver-shaped volume shown in Figure 3-83(a). The volume is bounded by four faces and is not mappable in its primitive form.
Figure 3-83: Mappable volume with four faces
You can transform the sliver-shaped volume shown in Figure 3-83 into a mappable form by performing a virtual split operation on each of the curved edges and specifying the vertex types as follows (see Figure 3-83(b)):
When you apply the Submap meshing scheme to a volume, GAMBIT subdivides the volume into logical mesh cubes each of which can be mapped according to a Map meshing scheme.
|NOTE: The Submap volume meshing scheme, cannot be used to mesh volumes that include "dangling" facesthat is, faces that do not constitute parts of the closed volume boundary.|
To be submappable, a volume must be configured such that it satisfies both of the following criteria:
Face Mappability and Submappability
In order for GAMBIT to apply a Submap meshing scheme to a volume, each face that bounds the volume must be either mappable or submappable. Figure 3-84 shows four volumes, three of which meet the criteria described above. The volumes shown in Figure 3-84(a), (b), and (c) are submappable, because the faces of each volume are, themselves, submappable. The volume shown in Figure 3-84(d) is not submappable, because the end face of the cylindrical protrusion on the top of the volume is neither mappable nor submappable.
Figure 3-84: Submap volume meshing schemesubmappability criterion
Opposing-Face Vertex Types
The face mappability/submappability criterion described above constitutes a necessary but insufficient condition for volume submappability. It is possible, for example, to construct a volume that cannot be meshed according to the Submap meshing scheme even though all of its faces are either mappable or submappable.
To apply the Submap meshing scheme to a volume, the face vertex types must be specified such that the face submap meshes on opposing faces of the volume are similar in shape and form. As an example of this requirement, consider the volume shown in Figure 3-85. The volume consists of an L-shaped brick the outside corner of which is truncated at an angle.
Figure 3-85: Submap volume meshing schemeL-shaped volume
The L-shaped faces that comprise the top and bottom sides of the volume can be submapped in a number of ways, each of which is a function of the vertex types that are assigned to the faces. Figure 3-85 shows face submap meshes that result from three different configurations of vertex types.
The configurations shown in Figure 3-85(a) and (b) can be meshed according to the Submap volume meshing scheme, because the vertex types and meshes on the top and bottom faces of the volume are consistent with each other. By contrast, GAMBIT cannot apply the Submap volume meshing scheme to the volume shown in Figure 3-85(c), because the Submap meshes on the top and bottom faces differ in form.
The Tet Primitive volume meshing scheme applies only to volumes that constitute logical tetrahedra. To constitute a logical tetrahedron, a volume must include only four sides, each of which constitutes a logical triangle. (NOTE: Any side of the logical tetrahedron may consist of more than one face.) When you apply the Tet Primitive meshing scheme, GAMBIT creates Tri Primitive meshes on each of the faces of the tetrahedron, then subdivides the volume into four hexahedral quadrants and creates a Map-type volume mesh in each quadrant.
As an example of the Tet Primitive meshing scheme, consider the tetrahedral volume shown in Figure 3-86(a). If you apply the Tet Primitive meshing scheme to the volume, GAMBIT creates Tri Primitive meshes on each face (see Figure 3-86(b)), then subdivides the volume into four quadrants and meshes each quadrant with hexahedral mesh elements. Figure 3-86(c) shows a cutaway view of the final mesh.
Figure 3-86: Tet Primitive volume meshing scheme
When you apply the Cooper meshing scheme to a volume, GAMBIT treats the volume as consisting of one or more logical cylinders each of which is composed of two end caps and a barrel (see Figure 3-87). Faces that comprise the caps of such cylinders are called "source" faces; faces that comprise the barrels of the cylinders are called "non-source" faces. (For restrictions related to the specification of faces for the Cooper meshing scheme, see "Face Characteristics," below.)
Figure 3-87: Cooper volume meshing schemelogical cylinder
The Cooper meshing scheme involves the following operation sequence.
Figure 3-88: Cooper volume meshing scheme-example volume
If you apply the Cooper meshing scheme to the volume shown in Figure 3-88, GAMBIT performs the following operations (see Figure 3-89).
Figure 3-89: Cooper volume meshing schemeexample volume
In general, the Cooper meshing scheme applies to volumes that demonstrate either of the following characteristics.
|NOTE: The Submap volume meshing scheme, described above, constitutes a special version of the Cooper meshing scheme. If a volume is configured such that it can be meshed by either the Submap scheme or the Cooper scheme, it is usually desirable to mesh the volume by means of the Submap scheme.|
The Cooper volume meshing scheme imposes the following restrictions on the volumes to which it applies.
Figure 3-90: Non-Cooper-able volumes
The volumes shown in Figure 3-90 violate the restrictions outlined above for the following reasons.
|Figure 3-90(a)||(1)||It is impossible to construct a logical cylinder the barrel of which is mappable.|
|Figure 3-90(b)||(2)||GAMBIT cannot imprint the mesh from faces B and C onto face A, because face A possesses an existing mesh.|
|Figure 3-90(c)||(3)||Opposing faces (A and B) that constitute the caps of the logical cylinder contain interior edge loops the projections of which overlap.|
|Figure 3-90(d)||(4)||Face A is linked to face B, therefore GAMBIT cannot imprint the face A mesh onto face B, because the imprint would violate the operation of the mesh link.|
As noted above, cap faces on the logical cylinder of the Cooper-able volume can include interior edge loops, but the projections of the loops must not partially intersect each other, as they do in Figure 3-90(c). Figure 3-91 shows two allowable cases involving interior edge loops on the caps of the logical cylinder. Figure 3-91(a) is Cooper-able because the projections of the interior edge loops do not intersect each other at all. Figure 3-91(b) is Cooper-able because the interior edge loops fully intersect. (NOTE: If such fully intersecting edge loops are premeshed, the mesh specifications on both loops must be identical to each other.)
Figure 3-91: Cooper-able volumes with internal edge loops
Specifying Source Faces
When you apply the Cooper volume meshing scheme to a volume, you must specify the source faces that define the end caps of the logical cylinder. The source faces also define the longitudinal direction of the logical cylinder. For certain volumes, there exist more than one valid set of source faces. For such volumes, the final form of the mesh depends, in part, on the selection of source faces.
|NOTE: When you specify a Cooper meshing scheme for a volume, GAMBIT automatically determines which faces are likely source faces. To override the automatically selected set of source faces, specify an alternative set of faces on the Mesh Volumes form.|
As an example of the effect of source-face selection on a mesh, consider the annular volume shown in Figure 3-92. The volume includes four faces-the end faces, labeled A and B, and the inner and outer cylindrical faces, labeled C, and D, respectively.
Figure 3-92: Annular volume
If you mesh the annular volume by means of a Cooper volume meshing scheme and specify faces A and B as the source faces, GAMBIT maps the inner and outer cylinders and paves the end faces, then sweeps the paved mesh through the annular volume along its axis. The resulting mesh appears as shown in Figure 3-93(a), below.
Figure 3-93: Cooper mesh of an annular volume, end source faces
If you specify faces C and D as the source faces, GAMBIT maps the end faces and paves the inner and outer cylindrical faces, then sweeps the paved mesh node pattern in a radial direction through the volume. The resulting mesh appears as shown in Figure 3-93(b).
|NOTE (1): In the example given above, the inner and outer faces are regular in shape, therefore, the paved meshes on the cylindrical faces are identical in appearance to mapped mesh node patterns.|
|NOTE (2): There are no restrictions on the types of face-meshing schemes that can be applied to faces that constitute source faces for the Cooper volume meshing scheme. For example, if you apply a Tri:Pave meshing scheme to a source face and employ a Cooper meshing scheme, GAMBIT creates wedge elements in the meshed volume.|
The Stairstep meshing scheme creates and meshes a faceted volume the shape of which approximates the volume to be meshed. GAMBIT does not mesh the original volume itself, and the created faceted volume is not connected to any existing geometryincluding geometry to which the original volume is connected.
As an example of the effect of the Stairstep meshing scheme, consider the volume shown in Figure 3-94. The volume is an elliptical cylinder 10 units long with major and minor axis radii of 5 and 3 units, respectively.
Figure 3-94: Stairstep meshing schemeoriginal elliptical, cylindrical volume
If you mesh the elliptical cylinder shown in Figure 3-94, above, by means of the Stairstep scheme using an overall interval size of 0.75, GAMBIT creates and meshes the faceted volume shown in Figure 3-95. Note that the shape of the faceted volume crudely approximates the shape of the original elliptical cylinder and that all mesh elements are cubic hexahedra of uniform size.
Figure 3-95: Stairstep meshing schemecreation of faceted volume
Stairstep Mesh Refinement
If you apply the Stairstep meshing scheme to a volume for which a size function has been attached, GAMBIT refines the mesh in the region of the size function. For example, if you attach a size function to the elliptical front face of the volume shown in Figure 3-94, above, and specify a start size, growth rate, and size limit of 0.2, 1.3, and 0.75, respectively, the Stairstep scheme produces the meshed, faceted volume shown in Figure 3-96. In this case, the mesh elements are small near the elliptical face and large in the bulk volume.
NOTE (1): GAMBIT ignores mesh interval size specifications when meshing a volume to which a size function is attached.
NOTE (2): Refined Stairstep meshes often include hanging nodesthat is, mesh nodes that bisect other mesh element edges (see Figure 3-96).
Figure 3-96: Stairstep meshing schemefaceted volume with transition region
GAMBIT provides two options for refining the mesh in the Stairstep scheme. One option allows the existence of hanging nodes such as those shown in Figure 3-96. The other option disallows the existence of hanging nodes by propagating the refined mesh throughout the entire volume. You can select the Stairstep mesh refinement option by means of a GAMBIT default variable named STAIRSTEP_MESH_TYPE. To modify the variable:
Allows hanging nodes in the region of mesh refinement
Disallows hanging nodes by propagating the refined mesh throughout the volume
As an example of the effect of the STAIRSTEP_MESH_TYPE default variable on the Stairstep mesh, consider the volume shown in Figure 3-97. The volume consists of a cube with a spherical cut-out in one corner. Each edge of the cube is 10 units long, and the sphere radius is 3 units.
Figure 3-97: Stairstep meshing schemecube with cutout corner
Figure 3-98 shows the effect of the STAIRSTEP_MESH_TYPE default variable value on the final Stairstep mesh configuration. In Figure 3-98(b) and Figure 3-98(c), a size function with a start size, growth rate, and size limit of 0.25, 1.5, and 1.0, respectively, has been attached to the curved, cut-out face.
Figure 3-98: Effect of STAIRSTEP_MESH_TYPE default variable
The Stairstep meshing scheme is applicable to all volumes.
When you mesh a volume by means of the TGrid meshing scheme, GAMBIT attempts to create a mesh that consists primarily of tetrahedral mesh elements but which can also contain hexahedral, pyramidal, and wedge elements where appropriate. Hexahedral, pyramidal, and wedge elements are typically created in regions that are adjacent to pre-meshed faces and/or affected by pre-existing boundary layers (see "Effect of Pre-meshed Faces" and "Effect of Boundary Layers," below).
As an example of the TGrid meshing scheme, consider the cubic volume shown in Figure 3-99(a). The faces of the cube are unmeshed and the volume does not serve as an attachment entity for any boundary layer. If you mesh the volume by means of the TGrid scheme, GAMBIT creates a mesh composed solely of tetrahedral elements such as those shown in Figure 3-99(b). (NOTE: The elements shown in Figure 3-99(b) represent only a few of those created in the meshing operation.)
Figure 3-99: Simple TGrid meshing scheme
Effect of Pre-meshed Faces
If any of the volume boundary faces are pre-meshed using quadrilateral mesh elements prior to volume meshing, the TGrid scheme (by default) creates a layer of pyramidal mesh elements adjacent to the pre-meshed face. For example, if you pre-mesh the bottom face of a cube using quadrilateral elements, as shown in Figure 3-100(a), the TGrid scheme creates a layer of pyramidal elements adjacent to the pre-meshed face (see Figure 3-100(b)). The TGrid scheme produces tetrahedral elements throughout the rest of the cube.
Figure 3-100: Effect of pre-meshed face on TGrid scheme
NOTE (1): You can alter the default TGrid meshing behavior illustrated in Figure 3-100, above, by means of the MESH.TETMESH.QUAD_SURFACE_SPLIT default variable (see "Effect of QUAD_SURFACE_SPLIT Default Variable," below).
NOTE (2): In general, it is advisable to avoid creating quadrilateral face mesh elements with aspect ratios greater than five (5) on the boundaries of any volume to be meshed by means of the TGrid meshing scheme. Face mesh elements with high aspect ratios produce highly skewed transition pyramidal elements, and the subsequent TGrid scheme may fail or produce low-quality elements.
Effect of Boundary Layers
If one or more boundary layers are attached to a volume prior to meshing, the TGrid scheme generates hexahedral or wedge elements in the regions affected by the boundary layer(s). The types of elements generated depend, in part, on whether or not the boundary layer source faces are pre-meshed with quadrilateral elements prior to creation of the volume mesh.
Boundary Layers Without Pre-meshed Source Faces
If a boundary layer source face is not pre-meshed with quadrilateral elements prior to meshing the volume, the TGrid scheme automatically meshes the source face with triangular elements and creates wedge elements in the boundary layer region. As an example of this behavior, consider the cube shown in Figure 3-101(a). In this case, a boundary layer has been applied to the bottom face of the cube, and the bottom (source) face is not pre-meshed. If you apply the TGrid meshing scheme to the cube, GAMBIT generates wedge elements in the boundary layer region such as those shown in Figure 3-101(b). (NOTE: The wedge elements shown in Figure 3-101(b) represent only a portion of all elements created in the boundary layer region.)
Figure 3-101: Effect of boundary layer with non-pre-meshed source face
In the region of the cube that lies outside the boundary layer, the TGrid scheme generates tetrahedral elements such as those shown in Figure 3-99(b), above.
Boundary Layers with Pre-meshed Source Faces
If a boundary layer source face is pre-meshed with quadrilateral elements prior to meshing the volume, the TGrid scheme retains the quadrilateral face elements and creates hexahedral elements in the boundary layer region. As an example of this behavior, consider the cube shown in Figure 3-102(a). In this case, a boundary layer has been applied to the bottom face of the cube, and the bottom (source) face is pre-meshed with quadrilateral elements. If you apply the TGrid meshing scheme to the cube, GAMBIT generates hexahedral elements in the boundary layer region (see Figure 3-102(b)).
Figure 3-102: Effect of boundary layer with pre-meshed source face
In addition to creating hexahedral elements in the boundary layer region for this case, the TGrid scheme generates a layer of pyramidal elements on the boundary layer cap (see Figure 3-103(a)) and fills the rest of the volume with tetrahedral elements, some of which are shown in Figure 3-103(b).
Figure 3-103: Pyramidal and tetrahedral elements with pre-meshed source face
Effect of QUAD_SURFACE_SPLIT Default Variable
GAMBIT allows you to modify the default TGrid meshing behavior described above for volumes with boundary faces that are pre-meshed with quadrilateral elements. The modification is made by means of the MESH.TETMESH.QUAD_SURFACE_SPLIT default variable, which specifies whether GAMBIT splits quadrilateral elements on pre-meshed faces and/or boundary layer caps prior to applying the TGrid meshing scheme. Allowable values for the QUAD_SURFACE_SPLIT default variable are as follows.
|Value||Split Elements on Faces||Split Elements on Caps|
As an example of the effect of the QUAD_SURFACE_SPLIT default variable on volume meshes generated by the TGrid scheme, consider the cubic volume shown in Figure 3-104. The top and bottom faces of the cube are pre-meshed with quadrilateral elements, and the bottom face serves as the source face for a boundary layer.
Figure 3-104: Cube with boundary layer and pre-meshed faces
Figure 3-105 and Figure 3-106 illustrate the effect of the QUAD_SURFACE_SPLIT value on mesh-element splitting for the top face and boundary layer cap. (NOTE: The quadrilateral elements on the pre-meshed bottom face are not split regardless of the QUAD_SURFACE_SPLIT value because the bottom face serves as a source face for the boundary layer.)
Figure 3-105: Effect of QUAD_SURFACE_SPLIT values 0 and 1
Figure 3-106: Effect of QUAD_SURFACE_SPLIT values 2 and 3
Applying Meshed Size Functions on Boundary Layer Caps
When you apply the TGrid meshing scheme to a volume to which boundary layers are attached, you can automatically apply a meshed size function at the boundary layer cap. This capability is invoked by the Meshed S.F. on B.L. cap option on the Mesh Volumes form.
|NOTE (1): If you select the Meshed S.F. on B.L. cap option when meshing a volume to which boundary layers are not attached, GAMBIT ignores the option when applying the TGrid meshing scheme.|
|NOTE (2): The Meshed S.F. on B.L. cap option is not affected by the Ignore size functions option on the bottom of the Mesh Volumes form.|
To apply a meshed size function to a boundary layer cap, you must specify two parameters: Growth rate and Max. size. For a description of meshed size functions and the effect of these parameters, see "Create Size Function" in Section 5.2.2 of this guide.
As an example of the effect of the Meshed S.F. on B.L. cap option, consider the cubic volume shown in Figure 3-107. Two of the bottom edges (a and b) are graded to create increasing mesh density near the front corner of the cube; the other two (c and d) are meshed uniformly.
Figure 3-107: Cube with boundary layer and pre-meshed edges
Figure 3-108 illustrates the effect of the S.F. on B.L. cap option on the TGrid volume mesh. For this example, the effect can be summarized as follows.
Figure 3-108: Effect of S.F. on B.L. cap option
GAMBIT provides two types of Hex Core meshing schemesHex Core (Native) and Hex Core (TGrid). Both schemes employ the same general technique for generating the mesh but differ from each other with regard to the characteristics of the central mesh core (see "Hex Core Scheme Types," below). In general, when you apply either scheme to a volume, GAMBIT performs the following sequence of operations:
As a general example of this type of meshing scheme, consider the elliptical cylinder shown in Figure 3-94, above. If you mesh the volume by means of a Hex Core (Native) meshing scheme with an element size of 0.5, GAMBIT produces a mesh the cross section of which is shown in Figure 3-109.
Figure 3-109: General Hex Core meshing schemecross section
The mesh shown in Figure 3-109 consists of a core of hexahedral elements surrounded by a transition region of pyramidal elements adjacent to the core itself and a shell of tetrahedral elements filling the remainder of the volume. The existence of the hex core significantly reduces the total number of mesh elements relative to that of a purely tetrahedral mesh.
Effect of Internal Dangling Faces
If the volume to be meshed includes an internal dangling face, GAMBIT treats the face as a boundary face with respect to construction of the hex core. That is, GAMBIT constructs the mesh such that layers of pyramidal and tetrahedral elements can exist between the core and the dangling face. Figure 3-110 illustrates the effect of an internal dangling face for the mesh core of the elliptical cylinder shown in Figure 3-109, above.
Figure 3-110: General Hex Core meshing schemewith internal dangling face
Hex Core Scheme Types
As noted above, GAMBIT provides two types of Hex Core meshing schemes:
Hex Core (Native) Scheme
The Hex Core (Native) meshing scheme produces a core of uniformly sized hexahedral elements surrounded by pyramidal and/or tetrahedral elements. Specification of the Hex Core (Native) scheme involves the following parameters:
Offset layers Value
As noted above, GAMBIT creates the core of a hex-core mesh by generating a hexahedral mesh throughout the volume “bounding box” and removing the elements that either exist outside or intersect the volume boundaries. In addition, GAMBIT removes at least one inner layer of elements immediately adjacent to those that intersect the volume boundaries. When using the Hex Core (Native) scheme, you can specify the removal of additional element layers by means of the Offset layers value.
As an example of the effect of the Offset layers specification, consider the two hex cores shown in Figure 3-111. Both hex cores are generated by meshing a conical cylinder using the Hex Core (Native) scheme. They differ from each other only with regard to their Offset layers values.
Figure 3-111: Effect of Offset layers value on conical cylinder hex cores
The hex core shown in Figure 3-111(a) is larger than that of Figure 3-111(b) because fewer of its outer layers have been removed in the mesh generation process.
|NOTE: The Offset layers value must be greater than or equal to two (2), so that the mesh can include both tetrahedral elements adjacent to the volume boundaries and pyramidal elements in the surrounding region.|
Quad surface split Option
The Quad surface split option allows you to control the types of face elements created on the hex-core boundary. If you select the option, GAMBIT splits (diagonally) all quadrilateral face elements on the hex-core boundary, thereby replacing them with triangular elements. As a result, the mesh created adjacent to the hex-core boundary contains tetrahedral elements rather than the pyramidal elements that would be created if the quadrilateral face elements were not split. (NOTE: If you do not select the Quad surface split option, GAMBIT may still split some hex-core boundary elements when generating the mesh.)
In addition to splitting the hex-core boundary face elements, the Quad surface split option automatically smoothes the mesh on the hex core boundary, thereby slightly warping the outer hex-core elements. Figure 3-112 shows the effect of the option on the outer shape of the hex core for the mesh shown in Figure 3-111(b), above. (NOTE: The inner hex-core elements are not affected by the automatic smoothing operation (see Figure 3-113).)
Figure 3-112: Effect of Quad surface split option on outer hex-core elements
Figure 3-113: Effect of Quad surface split option on hex core regions
NOTE (1): The splitting of the quadrilateral face elements results in the creation of a "nonconformal" mesh hex-core boundary interface. If the Hex Core (Native) mesh does not include hanging nodes (see below), the nonconformal interface consists of two triangular elements for each quad element at the boundary surface. If the mesh does include hanging nodes, the nonconformal interface can consist of two, three, or four triangular elements for each quadrilateral element. (NOTE: Hanging nodes produce nonconformal meshes even if you do not split the quadrilateral elements at the hex-core boundary.)
In either case, when you export a nonconformal mesh produced by a Hex Core meshing scheme, GAMBIT includes information in the exported mesh file that allows the solver to process the nonconformal mesh data without further input from the user.
|NOTE (2): It is possible to produce a nonconformal mesh by meshing adjacent, unconnected volumes by means of different schemes. For example, if you create a volume consisting of two rectangular bricks that are adjacent but unconnected by a common face, then mesh one brick with a Map scheme and the other with a TGrid scheme, the resulting mesh includes a nonconformal interface at the boundary between the two volumes. In such cases, GAMBIT does not include information concerning the nonconformity in the exported mesh file. If the two volumes represent a continuous region in the model (for example, a flow channel), the user must explicitly specify the nonconformity when importing the mesh into the solver.|
Allow hanging nodes Option
If you select the Allow hanging nodes option, GAMBIT permits the creation of hanging nodes when generating the Hex Core (Native) mesh. Otherwise, GAMBIT prohibits the creation of hanging nodes.
Hex Core (TGrid) Scheme
The Hex Core (TGrid) meshing scheme differs from the Hex Core (Native) scheme in that its hex core can consist of hexahedral elements of various sizes. Specifically, a Hex Core (TGrid) hex core typically consists of an inner core of larger elements surrounded by one or more buffer layers of smaller elements. The element size in each succeeding buffer layer decreases toward the hex core boundary (see "Buffer layers Value," below).
Specification of the Hex Core (TGrid) scheme involves the following parameters:
Peel layers Value
The effect of the Peel layers value for the Hex Core (TGrid) meshing scheme is similar to that of the Offset layers value for the Hex Core (Native) scheme (see "Offset layers Value," above.) Specifically, the Peel layers value determines the number of outer layers of hexahedral elements that are removed when creating the hex core.
Buffer layers Value
As noted above, a Hex Core (TGrid) hex core typically consists of an inner core of larger elements surrounded by one or more buffer layers of smaller elements. The Buffer layers value allows you to specify (generally) the number of buffer layers and to thereby influence the shape and characteristics of the hex core.
As an example of the effect of the Buffer layers value on a Hex Core (TGrid) mesh, consider the volume shown in Figure 3-114, the geometry of which represents a catalytic converter. The mesh cross sections shown in Figure 3-115 illustrate the general effect of the Buffer layers value on the characteristics of the hex core for this example.
Figure 3-114: Catalytic converter volume
Figure 3-115: Hex Core cross sectioneffect of Buffer layers value
Size limit Value
The Size limit value determines the maximum element size in the hex core. GAMBIT provides two Size limit options:
Figure 3-116 illustrates the general effect of the Size limit value on the hex core characteristics for the catalytic-converter geometry shown in Figure 3-114, above.
Figure 3-116: Hex Core cross sectioneffect of Size limit value
Specifying the Element Size
The procedures outlined above require that the specified element size is small enough to allow both the creation of a hexahedral core and two layers of elements (pyramidal and tetrahedral) surrounding the core. If you specify an element size that is too large to accommodate both the core and the transition layers, GAMBIT meshes the volume using only tetrahedral elements. For example, if you employ the Hex Core (Native) meshing scheme for the elliptical cylinder shown in Figure 3-94, above, and specify an element size of 1, GAMBIT creates a mesh the cross section of which is shown in Figure 3-117.
Figure 3-117: Hex Core (Native) meshing schemeelement size = 1
Specifying the Number of Transition Layers
You can specify the number of layers of transition elements, and thereby control the size of the core, by means of the MESH.CARTESIAN.HEXCORE_ OFFSET_LAYERS default variable. By default, the variable is set equal to -1, which invokes automatic determination of the number of transition layers. If you specify a value for the variable, the assigned value represents the number of transition layers between the core and the volume boundaries. (NOTE: You must specify at least two layers, so that the scheme includes both tetrahedral elements adjacent to the volume boundaries and pyramidal elements adjacent to the core hexahedral elements.)
The Hex Core (Native) and Hex Core (TGrid) meshing schemes are applicable to all volumes but is useful mainly for volumes with large internal regions and few internal boundaries such as intrusions or holes.
GAMBIT includes the following universal options on the Mesh Volumes form:
If you select the Mesh option, GAMBIT meshes the picked volume(s) according to the parameters as currently specified on the Mesh Volumes form. If you Apply the meshing specifications without selecting the Mesh option, GAMBIT applies the currently specified mesh parameters to the volume(s) but does not create the mesh.
If you select the Remove old mesh option, GAMBIT removes any currently existing mesh from the specified volume(s) before creating the new volume mesh(es). GAMBIT also enables the Remove lower mesh option (see below), which specifies whether or not to remove the mesh on the volume boundary faces and edges. If you do not select the Remove lower mesh option, GAMBIT retains the existing lower-topology mesh(es) when meshing the volume.
As noted above, when you select the Remove old mesh option, GAMBIT enables the Remove lower mesh option, which allows you to specify whether or not to remove any existing mesh(es) on the boundary faces and edges of the volume(s) to be meshed.
If you select the Ignore size functions option, GAMBIT ignores any existing size function specifications that would otherwise affect the volume mesh.
To open the Mesh Volumes form (see below), click the Mesh command button on the Mesh/Volume subpad.
The Mesh Volumes form contains the following options and specifications.
|Volumes||specifies the volume(s) to be meshed.|
|Apply||specifies that the meshing scheme indicated on the option button is applied to all currently picked volumes.|
|Default||resets the meshing scheme option button to its default algorithm value (Undetermined).|
|specifies the types of elements to be used in meshing the volume(s).|
Hex Core (Native)
Hex Core (TGrid)
|specifies the type of meshing scheme to apply to the volume(s).|
|Smoother:||(Map meshing scheme only)|
|specifies the algorithm used to smooth the volume mesh while meshing.|
|Sources||(Cooper meshing scheme only) specifies source faces for the Cooper scheme.|
|Meshed S.F. on B.L. cap||(TGrid meshing scheme only) applies a meshed size function to any boundary layer cap. The meshed size function is defined by two input parameters:
|Offset layers||(Hex Core (Native) meshing scheme only) specifies the number of layers of outer mesh elements to be removed when creating the hex core.|
|Quad surface split||(Hex Core (Native) meshing scheme only) specifies that all quadrilateral mesh elements on the outer boundaries of the hex core are split when creating the core.|
|Allow hanging nodes||(Hex Core (Native) meshing scheme only) allows the creation of hanging nodes when creating the mesh.|
|Peel layers||(Hex Core (TGrid) meshing scheme only) specifies the number of layers of outer mesh elements to be removed when creating the hex core.|
|Buffer layers||(Hex Core (TGrid) meshing scheme only) specifies the number of buffer layers to use for the Hex Core (TGrid) scheme.|
|Size limit||(Hex Core (TGrid) meshing scheme only) specifies the size limit for core elements generated by the Hex Core scheme. The Size limit option includes two suboptions:
|Apply||specifies that the current mesh node spacing parameters are applied to all currently specified volume(s).|
|Default||resets the mesh node spacing parameters to their default values.|
|Value||specifies the numerical component of the mesh node spacing parameters.|
Shortest edge (%)
|specifies the measurement unit for the mesh node spacing parameters.|
|Mesh||specifies that a new mesh is created in the specified volume(s).|
|Remove old mesh||specifies the deletion of any current mesh that is associated with the specified volume(s) and created by means of the Mesh Volumes form.|
|Remove lower mesh||specifies that all lower-topology (face and edge) meshes associated with the specified volume(s) are deleted when the volume mesh is deleted unless they are associated with other meshed topology.|
|Ignore size functions||specifies that GAMBIT ignores any existing size-function specifications that would otherwise affect the volume mesh. (NOTE: This option does not affect the operation of the Meshed S.F. on B.L. cap option for the TGrid meshing scheme.)|
The Smooth Volume Meshes operation (volume smooth command) smoothes the spacing of mesh nodes throughout one or more volumes. When you smooth a volume mesh, GAMBIT automatically adjusts mesh node locations in order to improve the uniformity of spacing between nodes throughout the mesh. To smooth a volume mesh, you must specify the following parameters:
GAMBIT provides the following mesh smoothing schemes:
|Length-weighted Laplacian||Uses the average edge length of the elements surrounding each node|
|Equipotential||Adjusts node locations to equalize the volumes of the mesh elements surrounding each node|
To open the Smooth Volume Meshes form (see below), click the Smooth Mesh command button on the Mesh/Volume subpad.
The Smooth Volume Meshes form contains the following options and specifications.
|Volumes||specifies the volume(s) for which the mesh is to be smoothed.|
|specifies the mesh smoothing algorithm. (For a general description of each algorithm, see "Specifying the Smoothing Scheme," above.)|
The Set Volume Element Type operation (default set command for the MESH.NODES.HEX default variable) specifies the number of mesh nodes and the node pattern associated with any of four available volume element shapes.
To set the volume element type, you must specify the numbers of nodes associated with each of the volume element shapes. There are four volume element shapes available in GAMBIT:
|Shape||Numbers of Nodes|
|Hexahedron||8, 20, 27|
|Wedge||6, 15, 18|
|Pyramid||5, 13, 14|
When you set a volume element type, GAMBIT applies the specified mesh node pattern to all volume elements of the specified shape. For example, if you specify 20-node wedge volume elements, GAMBIT locates mesh nodes according to the 20-node pattern for all wedge volume elements produced in the subsequent volume meshing operation.
Figure 3-118, Figure 3-119, Figure 3-120, and Figure 3-121 show the placement of nodes for each of the node patterns listed above.
Figure 3-118: Hexahedron volume element node patterns
Figure 3-119: Wedge volume element node patterns
Figure 3-120: Tetrahedron volume element node patterns
Figure 3-121: Pyramid volume element node patterns
To open the Set Volume Element Type form (see below), click the Set Volume Element Type command button on the Mesh/Volume subpad.
The Set Volume Element Type form contains the following specifications.
|Hexahedron||specifies the hexahedron volume element type: 8 node, 20 node, or 27 node.|
|Wedge||specifies the wedge volume element type: 6 node, 15 node, or 18 node.|
|Tetrahedron||specifies the tetrahedron volume element type: 4 node or 10 node.|
|Pyramid||specifies the pyramid volume element type: 5 node, 13 node, or 14 node.|
The Link/Unlink Volume Meshes command button allows you to perform the following operations.
|Link Volume Meshes||Creates hard links between volumes|
|Unlink Volume Meshes||Deletes hard links between volumes|
The following sections describe the procedures and specifications required to execute the operations listed above.
The Link Volume Meshes operation (volume link command) creates a hard link between two volumes. When you mesh a volume that is hard-linked to another volume, GAMBIT applies identical mesh parameters to both volumes.
|NOTE: When you select a volume for the Link Volume Meshes operation, GAMBIT automatically highlights the graphic display of any volumes to which the volume is currently linked.|
The volumes to be linked must satisfy the following criteria:
Figure 3-122: Example volumes to be hard-linked
To create a hard link between the two volumes, you must first create hard links between face.1 and face.4, face.2 and face.5, and face.3 and face.6. (For instructions on the creation of hard links between faces, see "Link Face Meshes," in Section 3.3.6, above.)
To open the Link Volume Meshes form (see below), click the Link command button on the Mesh/Volume subpad.
The Link Volume Meshes form contains the following specifications.
|Volume||specifies the first of two volumes to be hard-linked.|
|Volume||specifies the second of the two volumes to be hard-linked.|
The Unlink Volume Meshes operation (volume unlink command) deletes hard mesh links associated with one or more volumes.
|NOTE: When you select a volume for the Unlink Volume Meshes operation, GAMBIT automatically highlights the graphic display of any volumes to which the volume is currently linked.|
To open the Unlink Volume Meshes form (see below), click the Unlink command button on the Mesh/Volume subpad.
The Unlink Volume Meshes form contains the following options and specifications.
|Volumes||specifies the volumes between which the link is to be deleted.|
|Lower topology||unlinks all lower-topology entities that are associated with the specified volumes.|
The Modify Meshed Volume operation (volume split edgenodes command) converts mesh edges on the exterior faces of a meshed volume to topological edges and creates faceted faces where appropriate. For a description of the procedures and specifications involved in creating a conversion list, see "Modify Meshed Face," in Section 3.3.7, above.
|NOTE: When GAMBIT executes the Modify Meshed Volume command, the original meshed volume is deleted.|
To open the Modify Meshed Volume form (see below), click the Modify Meshed Volume command button on the Mesh/Volume subpad.
For a general description of the procedures and specifications involved in using the Modify Meshed Volume form, see "Using the Modify Meshed Face Form," in Section 3.3.7, above.
The Summarize Volume Mesh / Check Volume Meshes command buttons let you perform the following operations.
|Summarize Volume Mesh||Summarizes general volume mesh information in the Transcript window|
|Check Volume Meshes||Displays 3-D mesh quality information in the Transcript window|
The following sections describe the procedures and specifications required to execute the operations listed above.
The Summarize Volume Mesh operation (volume msummarize command) displays volume mesh information in the Transcript window and allows you to highlight specific mesh nodes and/or mesh elements in the graphics window. (NOTE: For a general discription of the GAMBIT mesh summary functionality, see "Summarize Face Mesh," in Section 3.3.8, above.)
To open the Summarize Volume Mesh form (see below), click the Summarize command button on the Mesh/Volume subpad.
For a description of the use of the Summarize Volume Mesh form, see "Using the Summarize Face Mesh Form," in Section 3.3.8, above.
The Check Volume Meshes operation (volume check quality command) displays 3-D mesh quality data. When you execute the Check Volume Meshes command, GAMBIT displays the following elements in the Transcript window:
The Check Volume Meshes tabular output represents the statistical distribution of element mesh quality values for the current default 3-D quality metric. Table 3.2 shows an example of such output for a volume mesh evaluated according to the EquiAngle Skew quality metric. Output such as that shown in Table 3.2 constitutes a numerical representation of the mesh quality histogram that is displayed on the Examine Mesh form when you choose the Display Type:Range option (see Section 3.4.2 of the GAMBIT User's Guide).
Table 3.2: Example Check Volume Meshes tabular output
Summarizing EQUIANGLE SKEW of 3D elements for 1 meshed volume: Volume volume.1 meshed using Map scheme and size of 1.000000. From value To value Count in range % of total count (1463) ----------------------------------------------------------------- 0 0.1 286 19.55 0.1 0.2 671 45.86 0.2 0.3 341 23.31 0.3 0.4 88 6.02 0.4 0.5 66 4.51 0.5 0.6 11 0.75 0.6 0.7 0 0.00 0.7 0.8 0 0.00 0.8 0.9 0 0.00 0.9 1 0 0.00 ----------------------------------------------------------------- 0 1 1463 100.00In addition to the tabular output shown in Table 3.2, the Check Volume Meshes command displays the minimum and maximum values of element quality for the set of specified volumes. The minimum and maximum element quality information is not available by means of any other GAMBIT operation.
As noted above, the Check Volume Meshescommand evaluates mesh element quality according to the current default 3-D mesh quality metric. To change the metric used to evaluate element quality for the Check Volume Meshes command, you must modify the default 3-D mesh quality metric by means of the Edit Defaults form. To do so:
For example, to evaluate 3-D elements on the basis of the Aspect Ratio metric:
|NOTE: Check Volume Meshes command tabular output, such as that shown in Table 3.2, includes all 3-D elements that possess shapes for which the current default quality metric applies. For example, if you specify EquiAngle Skew as the default 3-D quality metric, the tabular output includes all hexahedral, tetrahedral, prism, and wedge elements associated with the volumes specified on the Check Volume Meshes form. However, if you specify Aspect Ratio as the default 3-D quality metric, the tabular output includes only hexahedral and tetrahedral elements, because the Aspect Ratio metric does not apply to prism or wedge elements.|
The Check Volume Meshes summary statement indicates the number of specified volumes that "fail" the mesh checkfor example,
0 out of 1 meshed volume failed mesh check for skewed elements (> .98). 0 out of 1 meshed volume failed mesh check for inverted elements.In the context of the Check Volume Meshes command, any volume that includes at least one inverted mesh element fails the mesh check.
To open the Check Volume Meshes form (see below), click the Check command button on the Mesh/Volume subpad.
The Check Volume Meshes form contains the following specification.
|Volumes||specifies the volumes for which mesh element quality is to be evaluated.|
The Delete Volume Meshes operation (volume delete onlymesh command) deletes the mesh from one or more volumes. When you delete a volume mesh, GAMBIT allows you to retain or delete all face meshes and edge meshes associated with the volume.
To open the Delete Volume Meshes form (see below), click the Delete command button on the Mesh/Volume subpad.
The Delete Volume Meshes form contains the following options and specifications.
|Volumes||specifies the volume(s) for which the mesh is to be deleted.|
|Remove unused lower mesh||removes all unused lower-topology meshes associated with the specified volume(s).|