6.3.2 Structured grids

Extrude { expression-list } { extrude-list layers }

Extrudes both the geometry and the mesh using a translation (see section Extrusions). The layers option determines how the mesh is extruded and has the following syntax:

layers:

  Layers { expression } | 
  Layers { { expression-list }, { expression-list } } | 
  Recombine; …
  QuadTriNoNewVerts <RecombLaterals>; | 
  QuadTriAddVerts <RecombLaterals>; ...

In the first Layers form, expression gives the number of elements to be created in the (single) layer. In the second form, the first expression-list defines how many elements should be created in each extruded layer, and the second expression-list gives the normalized height of each layer (the list should contain a sequence of n numbers 0 < h1 < h2 < … < hn <= 1). See ‘t3.geo’, for an example.

For line extrusions, the Recombine option will recombine triangles into quadrangles when possible. For surface extrusions, the Recombine option will recombine tetrahedra into prisms, hexahedra or pyramids.

Please note that, starting with Gmsh 2.0, region numbers cannot be specified explicitly anymore in Layers commands. Instead, as with all other geometry commands, you must use the automatically created entity identifier created by the extrusion command. For example, the following extrusion command will return the id of the new “top” surface in num[0] and the id of the new volume in num[1]:

num[] = Extrude {0,0,1} { Surface{1}; Layers{10}; };

QuadTriNoNewVerts and QuadTriAddVerts allow to connect structured, extruded volumes containing quadrangle-faced elements to structured or unstructured tetrahedral volumes, by subdividing into triangles any quadrangles on boundary surfaces shared with tetrahedral volumes. (They have no effect for 1D or 2D extrusions.) QuadTriNoNewVerts subdivides any of the region’s quad-faced 3D elements that touch these boundary triangles into pyramids, prisms, or tetrahedra as necessary, all WITHOUT adding new vertices. QuadTriAddVerts works in a simular way, but subdivides 3D elements touching the boundary triangles by adding a new vertex inside each element at the vertex-based centroid. Either method results in a structured extrusion with an outer layer of subdivided elements that interface the inner, unmodified elements to the triangle-meshed region boundaries.

In some rare cases, due to certain lateral boundary conditions, it may not be possible make a valid element subdivision with QuadTriNoNewVerts without adding additional vertices. In this case, an internal vertex is created at the vertex-based centroid of the element. The element is then divided using that vertex. When an internal vertex is created with QuadTriNoNewVerts, the user is alerted by a warning message sent for each instance; however, the mesh will still be valid and conformal.

Both QuadTriNoNewVerts and QuadTriAddVerts can be used with the optional RecombLaterals keyword. By default, the QuadTri algorithms will mesh any free laterals as triangles, if possible. RecombLaterals forces any free laterals to remain as quadrangles, if possible. Lateral surfaces between two QuadTri regions will always be meshed as quadrangles.

Note that the QuadTri algorithms will handle all potential meshing conflicts along the lateral surfaces of the extrusion. In other words, QuadTri will not subdivide a lateral that must remain as quadrangles, nor will it leave a lateral as quadrangles if it must be divided. The user should therefore feel free to mix different types of neighboring regions with a QuadTri meshed region; the mesh should work. However, be aware that the top surface of the QuadTri extrusion will always be meshed as triangles, unless it is extruded back onto the original source in a toroidal loop (a case which also works with QuadTri).

QuadTriNoNewVerts and QuadTriAddVerts may be used interchangeably, but QuadTriAddVerts often gives better element quality.

If the user wishes to interface a structured extrusion to a tetrahedral volume without modifying the original structured mesh, the user may create dedicated interface volumes around the structured geometry and apply a QuadTri algorithm to those volumes only.

Extrude { { expression-list }, { expression-list }, expression } { extrude-list layers }

Extrudes both the geometry and the mesh using a rotation (see section Extrusions). The layers option is defined as above.

Extrude { { expression-list }, { expression-list }, { expression-list }, expression } { extrude-list layers }

Extrudes both the geometry and the mesh using a combined translation and rotation (see section Extrusions). The layers option is defined as above.

Extrude { Surface { expression-list }; layers < Using Index[expr]; > < Using View[expr]; > < ScaleLastLayer; > }

Extrudes a boundary layer from the specified surfaces. If no view is specified, the boundary layer is created using gouraud-shaped (smoothed) normal field. Specifying a boundary layer index allows to extrude several independent boundary layers (with independent normal smoothing).

ScaleLastLayer scales the height of the last (top) layer of each normal’s extrusion by the average length of the edges in all the source elements that contain the source vertex (actually, the average of the averages for each element–edges actually touching the source vertex are counted twice). This allows the height of the last layer to vary along with the size of the source elements in order to achieve better element quality. For example, in a boundary layer extruded with the Layers definition ’Layers{ {1,4,2}, {0.5, 0.6, 1.6} },’ a source vertex adjacent to elements with an overall average edge length of 5.0 will extrude to have a last layer height = (1.6-0.6) * 5.0 = 5.0.

Transfinite Line { expression-list } | "*" = expression < Using Progression | Bump expression >;

Selects the lines in expression-list to be meshed with the 1D transfinite algorithm. The expression on the right hand side gives the number of nodes that will be created on the line (this overrides any other mesh element size prescription—see Specifying mesh element sizes). The optional argument ‘Using Progression expression’ instructs the transfinite algorithm to distribute the nodes following a geometric progression (Progression 2 meaning for example that each line element in the series will be twice as long as the preceding one). The optional argument ‘Using Bump expression’ instructs the transfinite algorithm to distribute the nodes with a refinement at both ends of the line.

Transfinite Surface { expression-list } | "*" < = { expression-list } > < Left | Right | Alternate | AlternateRight | AlternateLeft > ;

Selects surfaces to be meshed with the 2D transfinite algorithm. The expression-list on the right-hand-side should contain the identification numbers of three or four points on the boundary of the surface that define the corners of the transfinite interpolation. If no identification numbers are given, the transfinite algorithm will try to find the corners automatically. The optional argument specifies the way the triangles are oriented when the mesh is not recombined. (Alternate is a synonym for AlternateRight).

Transfinite Volume { expression-list } | "*" < = { expression-list } > ;

Selects five- or six-face volumes to be meshed with the 3D transfinite algorithm. The expression-list on the right-hand-side should contain the identification numbers of the six or eight points on the boundary of the volume that define the corners of the transfinite interpolation. If no identification numbers are given, the transfinite algorithm will try to find the corners automatically.

TransfQuadTri { expression-list } | "*";

Applies the transfinite QuadTri algorithm on the expression-list list of volumes ("*" can be used to apply TransfQuadTri to all existing volumes). A transfinite volume with any combination of recombined and un-recombined transfinite boundary surfaces is valid when meshed with TransfQuadTri. When applied to non-Transfinite volumes, TransfQuadTri has no effect on those volumes.

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