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Fluent User Services Center
www.fluentusers.com
Introductory GAMBIT Training
GAMBIT 2.3 June 2006
Edge and Face Meshing
5-1 © 2006 Fluent Inc.
Edge and Face Meshing
Fluent User Services Center
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Introductory GAMBIT Training
GAMBIT 2.3 June 2006
Meshing - General
� To reduce overall mesh size, confine smaller cells to areas where they
are needed
� Locations of large flow field gradients.
� Locations of geometric details you wish to resolve.
� Controlling cell size distribution
� Edges, faces, and volumes can be meshed directly.
5-2 © 2006 Fluent Inc.
� Edges, faces, and volumes can be meshed directly.
� A uniform mesh is generated unless pre-meshing or size functions are
used.
� Pre-meshing
� Edge meshes can be graded (varying interval size on edge)
� A graded edge mesh can be used to control the cell size distribution of a
face mesh.
� Controlling distribution of cell size on face mesh also controls the cell size
distribution of the volume mesh.
� Size functions and boundary layers
� Allow direct control of cell size distribution on edges, faces and volumes
directly for automatic meshing.
Fluent User Services Center
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Introductory GAMBIT Training
GAMBIT 2.3 June 2006
Edge Meshing
� Edge mesh distribution is controlled through the
spacing and grading parameters on the Mesh Edges
form.
� Picking
� Temporary graphics
� Links, Directions
5-3 © 2006 Fluent Inc.
� Links, Directions
� Grading/Spacing
� Special characteristics
� Apply and Defaults
� Invert and Reverse
� Options
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Edge Meshing
� Sense
� Sense is used to show direction of grading
� Every picked edge will show its sense direction using an arrow
� The sense can be reversed by a shift+middle-click on the last edge picked
(this is in addition to the “next” functionality) or by clicking the Reverse
button
5-4 © 2006 Fluent Inc.
� Edge mesh preview
� When you pick an edge, the edge mesh is displayed using white nodes.
� This is a temporary mesh that has not been applied to the edge.
� Displayed edge mesh is based on current grading and spacing parameters
� If you modify the grading or spacing, the temporary mesh will be updated
immediately.
� Meshing the edge
� The edge mesh is generated by clicking the Apply button.
� The nodes will then be displayed in blue.
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Grading
� Controls mesh density distribution along an edge.
� Grading can produce single-sided or double-sided mesh
� Doubled-sided mesh can be symmetric or asymmetric.
� Symmetric schemes produce symmetric mesh about edge
center.
� Asymmetric schemes can produce asymmetric mesh about
edge center.
Single-sided grading
Symmetric grading
5-5 © 2006 Fluent Inc.
edge center.
� Single-sided grading:
� Uses a multiplicative constant, R, to describe the ratio of
the length of two adjacent mesh elements:
� R can be a user-specified value (Successive Ratio) or
calculated by GAMBIT.
� GAMBIT also uses edge length and spacing information to
determine R.
Asymmetric grading
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Double Sided Grading
� Double-sided grading can be generated by activating the
double sided option in the Mesh Edge form.
� Asymmetric grading is possible when the double-sided
option is used with:
� Successive Ratio, First Length, Last Length, First-Last
Ratio, and Last-First Ratio
� The mesh is symmetric if R = R
5-6 © 2006 Fluent Inc.
� The mesh is symmetric if R1 = R2
� The mesh is asymmetric if R1 ≠ R2.
� Edge center is determined automatically.
� Some schemes implicitly generate double sided grading
that is symmetric.
Fluent User Services Center
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Soft Links
� Picking and soft links
� Pick with links
� By enabling this option, soft-linked edges can be selected in a single pick
� Linked edges share the same information and can be picked in a single pick
� Modifying soft links
� At any time, you can
5-7 © 2006 Fluent Inc.
� At any time, you can
� Form links
� Break links
� Maintain links
� By default, GAMBIT will form links between unmeshed edges that are picked
together
� By default, GAMBIT will maintain links between meshed edges that are
picked together
Fluent User Services Center
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Introductory GAMBIT Training
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Spacing
� In all meshing forms, the following spacing functions can
be specified:
� Interval Count (recommended for edge mesh only)
� Example – Entering a value of 5 will create 5 intervals along
the selected edge(s) (6 nodes, including end nodes)
� Interval Size (default setting)
� Requires input of distance between nodes.
5-8 © 2006 Fluent Inc.
� Requires input of distance between nodes.
� Edge is meshed with “average” interval size if grading is
used.
� Example: An edge length of 10 and a value of 2 creates 5
intervals on the edge
� Shortest Edge %
� Meshes the selected edge according to a percentage of the
length of the shortest edge in the model.
� Example – Shortest edge in model has length of 1. Entering
a value of 20 will create a mesh with interval size 0.2.
Fluent User Services Center
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First Edge Settings
� Use First Edge Settings option
� If enabled:
� First edge selected in pick list updates all
entries in the form.
� This mode is useful to copy settings from one
meshed edge to other edge(s).
5-9 © 2006 Fluent Inc.
� If disabled:
� Use this setting any time you pick two or more
meshed edges where there is a difference in
type or spacing.
� The local Apply button for that option will be
turned off
� This allows you to maintain pre-existing grading
and/or spacing settings for each edge.
� Enforce a change in grading and/or spacing by
enabling Apply button.
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Meshing Options
� Mesh
� This option is useful in cases where you want to impose a scheme without prescribing the number of intervals
� The higher level meshing scheme will decide (and match) the intervals
5-10 © 2006 Fluent Inc.
� Remove old mesh
� Deletes old mesh
� When selected, option to also delete lower geometry mesh appears.
� Ignore size function
� Toggle to either obey or ignore size functions
� Size function takes precedence when this option is disabled.
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Specify interval
size, no grading,
apply without
meshing
Meshing Options – Example
Face Mesh Generated Using Quad
1
5-11 © 2006 Fluent Inc.
Specify grading
only, apply without
meshing
Face Mesh Generated Using Quad
Pave Scheme
(Pave face meshing schemes
require an even number of
elements on edge meshes)
Face Mesh Generated
Using Submap Scheme
2
Generate
face mesh.3
Fluent User Services Center
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Face Meshing� Mesh Faces form
� Upon picking a face:
� GAMBIT automatically chooses quad elements
� GAMBIT chooses the type based on the solver/face
vertex types
� Available element/scheme type combinations
� Quadrilaterial: Map, Submap, Tri-Primitive, Pave
5-12 © 2006 Fluent Inc.
� Quadrilaterial: Map, Submap, Tri-Primitive, Pave
� Triangular: Pave
� Quad/Tri (hybrid): Map, Pave, Wedge
� Quad-to-tri conversion utility.
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Face Meshing - Quad Examples
� Quad: Map
� Quad: Submap
5-13 © 2006 Fluent Inc.
� Quad: Tri-Primitive
� Quad: Pave
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Face Meshing - Quad/Tri and Tri Examples
Quad/Tri Map Quad/Tri Wedge
Face must be split to generate
5-14 © 2006 Fluent Inc.
Quad/Tri PaveTri Pave
Face must be split to generate
more than one cell across
Triangular
cell
Triangular
cell
Quad cells
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Deleting Old Mesh
� Existing mesh must be removed before
remeshing.
� Mesh can be deleted using
delete mesh form.
� Lower topology mesh can also be deleted (default)
5-15 © 2006 Fluent Inc.
� Alternatively, existing mesh can be deleted by
selecting the Remove Old Mesh option
� Remove old mesh alone will leave all lower
topology mesh
� Remove old mesh + remove lower mesh will delete
all lower topology mesh that is not shared with
another entity
� Undo after any meshing operation also works.
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� All vertices that are connected to a face are assigned initial face vertex types based on the angle between the edges connected to the vertex.
� Vertices shared by multiple faces can have multiple types, depending on which face you
Face Vertex Types
E
R
E
E
S
φ
5-16 © 2006 Fluent Inc.
multiple types, depending on which face you are considering.
� The combination of vertex types describes the topology of the face.
� Face vertex types are used automatically to determine all quad face meshing schemes (except quad pave and tri pave).
E E
S
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Face Vertex Types
End (E)
� zero internal grid lines
Side (S)
� One internal grid line
E
E E
S SS
oo 1200 <φ<
oo 216120 <φ<
5-17 © 2006 Fluent Inc.
Corner (C)
� Two internal grid lines
Reverse (R)
� Three internal grid lines
S S
CC C
RR
oo 309216 <φ<
oo 360309 <φ<
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Modifying Face Vertex Types
� Face vertex types can be changed from their default settings:
� Automatically
� By enforcing certain meshing schemes in face and volume meshing.
� Can sometimes result in undesirable mesh.
� Manually
� By direct modification in the Face Vertex Type form.
5-18 © 2006 Fluent Inc.
� By direct modification in the Face Vertex Type form.
� Select Face
� symbols appear in graphics window
� Select New Vertex Type
� Select Vertices to be affected
� Vertex Types can be applied to just Boundary Layers as option.
� A vertex can have multiple types; one for each associated face.
� For a given set of face vertex types, GAMBIT will choose which meshing scheme to use based on predefined formulae.
S E
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Formula for Submap Scheme
� A face can be made submappable by
manually changing vertex types
� Consider which vertex should be
changed to type S (side)
� In the Set Face Vertex Type form,
change vertex type to S by enforcing the
submap scheme.Which R
E
E E
R
E
E
E
E
E
S
E
5-19 © 2006 Fluent Inc.
submap scheme.
� In the Face Mesh form, change the
scheme from default to submap and
click Apply.
� GAMBIT will attempt to change the
vertex types so that the scheme is
honored.
� User has less control – the resulting
mesh may be undesirable!
( )( )[ ]ReverseEnd2
SideEnd4
+×+
+×Submap
Which
vertex to
change?
E
R
E
E
E
R
E
E
E
E
E
S
E
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Formula for Map Scheme
Map
E
E
E
ES+
E E
EE
( ) ( )SidenEnd4 ×+×
5-20 © 2006 Fluent Inc.
Periodic Map
Project intervals can be specified for more control.
E E
Siden×
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How to Make a Face Mappable
� Enforce the Map scheme (most common
method)
� In the Face Mesh form, change the scheme from
default to “Map” and click Apply.
� GAMBIT will attempt to change the vertex types so
that the chosen scheme is honored
E
E EE E
E
CC
( ) ( )SidenEnd4Map
×+×
5-21 © 2006 Fluent Inc.
� Manually change the vertex types
� In Set Face Vertex Type form, change vertices
(default) to "Side“.
� Open the Face Mesh form and pick the face.
� GAMBIT should automatically select the map
scheme)
E EE E
S
E EE E
S
SS
E
S
E
E
E
E
E
E
( ) ( )SidenEnd4Map
×+×
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Submap:
(additional terms when interior loops exist)
Formula for Submap Schemes
EE
C CC
S
E
E
E
( ) ( ) ( ) ( )End2ReversepCornerEndnSidemEnd4 ++++×+×
E
C
C
C
C
E
5-22 © 2006 Fluent Inc.
Periodic Submap where m > 2.
(additional terms when interior loops exist)
E E
C
EE
C
SE
E
E
S
S
( ) ( )CornerEndmSiden ++×
E
E
C
C
C
C
C
C
E E
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Tri-Primitive
� To mesh a rectangular face with the tri-primitive scheme:
Formula for Tri-Primitive Sheme
( ) ( )SidenEnd3 ×+×
E
E
E
S
5-23 © 2006 Fluent Inc.
� Manually change one of the vertex types to "Side" in this example
� The Tri Primitive scheme can not be enforced
E E
E S
E E
E E
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� Quad/Tri: Tri-Map
� The face vertex types must be changed manually to Trielement (T)
� The Tri-Map scheme must be selected.
� Quad/Tri: Pave
Triangle2×
Meshing Faces with Hybrid Quad/Tri Schemes
T T
T
5-24 © 2006 Fluent Inc.
� All vertex types are ignored except Trielement (T) and Notrielement (N)
� Trielement (T) will force a triangular element.
� Notrielement (N) will avoid a triangular element.
� Quad/Tri: Wedge
� Used for creating cylindrical/polar type meshes
� The Vertex marked (T) is where rectangular elements are collapsed into triangles
EC
N
T
E
E
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Hard Links
� Mesh linked entities have identical mesh
� Created for periodic boundary conditions
� Applicable to edge, face, and volume entities
� Best to use soft links for edge meshing
� To link volume meshes, all faces must be hard linked first.
� Hard links for faces
5-25 © 2006 Fluent Inc.
� Hard links for faces
� Select faces and reference vertices
� The sense of each edge appears.
� Reverse orientation on by default
� Periodic option should be used for periodic boundary conditions, which creates a matched mesh even if the edges are split differently.
� Meshing one of the faces either before or after hard linking will generate an identical mesh on the linked face.
� Multiple pairs of hard links can be created.
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Mesh Smoothing
� Smoothing can increase mesh quality beyond that of the default meshing algorithms
� Most noticable in complicated geometry.
� May have little or no effect in simple geometries.
� Mesh smoothing algorithms adjust interior node locations to obtain marginal improvement in mesh quality.
� Boundary meshes are not altered.
5-26 © 2006 Fluent Inc.
� Boundary meshes are not altered.� The mesh at the boundary is not altered.
� Face and volume meshes are smoothed using a default scheme.
� Different schemes can be selected and applied after meshing.� Face mesh smoothing
� Length-weighted Laplacian: Uses the average edge length of the elements surrounding each node to adjust the nodes.
� Centroid Area: Adjust node locations to equalize areas of adjacent elements.
� Winslow (quad meshes only): Optimizes element shapes with respect to perpendicularity.
� Volume mesh smoothing� Length-weighted Laplacian: same as for face mesh smoothing
� Equipotential: Adjusts node locations to equalize the volumes of the mesh elements surrounding each node.
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Examining the Mesh
� Display Type
� Plane/Sphere
� View mesh elements that fall in plane or sphere.
� Range
� View mesh elements within quality range.
� Histogram shows quality distribution.
Show worst element zooms the view to the worst
5-27 © 2006 Fluent Inc.
� Show worst element zooms the view to the worst element
� Select 2D/3D and element type
� Select Quality Type
� Display Mode – Change cell display attributes
� Show Worst Element – Automatically zooms the display to the worst element (based on current settings).
� Update button – Will update values reported in the panel when options are changed.
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Assessing Mesh Quality
� GAMBIT has several methods for assessing mesh quality.
� Aspect Ratio
� Diagonal Ratio
� Edge Ratio
� EquiAngle Skew
EquiSize Skew
5-28 © 2006 Fluent Inc.
� EquiSize Skew
� MidAngle Skew
� Size Change
� Stretch
� Taper
� Volume
� The most important of these quality metrics are EquiAngle Skew and Size Change.
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Mesh Quality – EquiAngle Skew
� The most important mesh quality metric is EquiAngle Skew (QEAS).
θθ−θ
θ−θ−θ
=e
e
e
eEASQ minmax ,
180max
cellor facein angleLargest max
=θ
=θ
maxθ
minθ
maxθ
5-29 © 2006 Fluent Inc.
� Range of EquiAngle Skew values
� QEAS = 0 describes a perfectly orthogonal element
� QEAS = 1 describes a degenerate element
0
(best)
1
(worst)
cellor facer equiangulafor Angle
cellor facein angleSmallest min
=θ
=θ
e
min
minθ
eθ
o60=θeTri/Tet
eθ
o90=θeQuad/Hex
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� Another important mesh quality metric is Size Change (QSC).
Mesh Quality – Size Change
[ ]nSC rrrQ ,,,max 21 K=
j
iri
element neighbor of Volumeor Area
element of Volumeor Area=
iV 1=jV
2=jV
3=jV
5-30 © 2006 Fluent Inc.
� This metric applies only to 3D elements.
� By definition, QSC > 0.
� QSC = 0 describes an element whose neighbor elements have exactly
the same volume as the element of interest (i.e. uniform mesh).
jelement neighbor of Volumeor AreaiV 1=jV3=jV
4=jV
3D Example
QSC,i = Vj=1/Vi since j=1
has largest volume ratio
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Striving for Quality
� A poor quality grid can cause inaccurate solutions and/or slow convergence.
� Minimize EquiAngle Skew:
� Hex, Tri, Quad: Skewness for all/most cells should be less than 0.85.
� Tetrahedral: Skewness for all/most cells should be less than 0.9.
� All elements: Size Change for cells in regions of interest should be less than 2
� Minimize local variations in cell size, such as large jumps in size between
adjacent cells.
5-31 © 2006 Fluent Inc.
adjacent cells.
� If Examine Mesh shows such violations:
� Determine the reason(s) for the violations
� Differences in spacing and grading on adjacent edges
� Geometry with small features or other defects
� Geometric complexity and size
� Mesh that grows too rapidly
� Delete mesh completely or partially.
� Clean and/or decompose geometry, premesh edges and faces or adjust meshing
parameters
� Remesh the domain.
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Appendix
5-32 © 2006 Fluent Inc.
Appendix
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Mesh Quality – Aspect Ratio
� Tri/Tet
� f is a scaling factor
� Quad/Hex
� e is the average length of edges in a
r
RfQAR =
[ ][ ]N
NAR
eee
eeeQ
,,,min
,,,max
21
21
K
K
=
� The Aspect Ratio metric (QAR) applies to tri, tet, quad, and hex elements and is
defined differently for each element type. The definitions are as follows:
5-33 © 2006 Fluent Inc.
� f is a scaling factor
� R and r are radii of circles (tri
elements) or spheres (tet elements)
that inscribe and circumscribe the
mesh element.
� f = 1/2 for tri elements and f = 1/3 for
tet elements.
� ei is the average length of edges in a
coordinate system local to the
element.
� N is the number of coordinate
directions associated with the
element
� N = 2 for quad elements
� N = 3 for hex elements
R
ra
b
c
d 21
cae
+=
22
dbe
+=
Inscribed circle
Circumscribed circle
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Mesh Quality – Diagonal Ratio
� The Diagonal Ratio metric (QDR) applies only to quad and hex elements
and is defined as follows:
� The di are the diagonals of the element.
� N is the total number of diagonals for a given element
[ ][ ]N
NDR
ddd
dddQ
,,,min
,,,max
21
21
K
K
=
5-34 © 2006 Fluent Inc.
� N is the total number of diagonals for a given element
� N = 2 for quad elements
� N = 4 for hex elements.
1d
2d1d
2d
3d
4d
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Mesh Quality – Edge Ratio
� The Edge Ratio quality metric (QER) is defined as follows:
� The si are the edge lengths of the element.
� N is the total number of edges for the element of interest.
[ ][ ]N
NER
sss
sssQ
,,,min
,,,max
21
21
K
K
=
5-35 © 2006 Fluent Inc.
Quad
N = 4
Tri
N = 3
Tet
N = 6
Pyramid
N = 8
Wedge
N = 9
Hex
N = 12
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Mesh Quality – EquiSize Skew
� The EquiSize Skew metric (QEVS) applies only to quad and hex elements
and is defined as follows:
� S is the area (2D) or volume (3D) of the element of interest.
� S is the maximum area (2D) or volume (3D) of an equilateral cell the
eq
eqEVS
S
SSQ
−=
5-36 © 2006 Fluent Inc.
� Seq is the maximum area (2D) or volume (3D) of an equilateral cell the
circumscribing radius of which is identical to that of the mesh element.
Actual element
Area = S
0 < QEVS < 1
Equilateral element
Area = Seq
QEVS = 0
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Mesh Quality – MidAngle Skew
� The MidAngle Skew (QMAS) applies only to quadrilateral and hexahedral
elements.
� Defined by the cosine of the minimum angle formed between the
bisectors of the element edges (quad) or faces (hex).
� For quad elements: θ= cosMASQ
5-37 © 2006 Fluent Inc.
� For hex elements:
Bisectors
θ
[ ]321 cos,cos,cosmax θθθ=MASQ
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Mesh Quality – Stretch
� The Stretch quality metric (QS) applies only to quadrilateral and
hexahedral elements and is defined as follows:
� di is the length of diagonal i
� s is the length of the element edge j,
[ ][ ]n
mS
ddd
sssKQ
,,,max
,,,min1
21
21
K
K
−=
5-38 © 2006 Fluent Inc.
� sj is the length of the element edge j,
� n and m are the total numbers of diagonals and edges, respectively.
� Quad elements: n = 2, m = 4, and K = 2;
� Hex elements: n = 4, m = 12, and K = 3.
� By definition, 0 < QS < 1.
� QS = 0 describes an equilateral element
� QS = 1 describes a completely degenerate element.
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Mesh Quality – Taper
� The Taper quality metric (QT) applies only to quadrilateral and hexahedral mesh elements and is defined as follows:� For any quadrilateral (or hexahedral)
mesh element, it is possible to construct a parallelogram (or parallelepiped) such that the distance between any given corner of the
Bisectors
Cornernode
T T1
T2
5-39 © 2006 Fluent Inc.
between any given corner of the parallelogram (or parallelepiped) and its nearest element corner node is a constant value.
� As a result, any vector, T, constructed from an element corner node to the nearest corner of the parallelogram (or parallelepiped) possesses a magnitude identical to that of all other such vectors.
� Each vector T can be resolved into components, Ti, that are parallel to the bisectors of the mesh element.
� Quad elements: two components
� Hex elements: three components
Element edge
� The Taper quality metric is defined as the normalized maximum of all such components for the element.
� By definition, 0 < QT < 1.� QT = 0 describes an equilateral element
� QT = 2 describes a degenerate element
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Mesh Quality – Volume and Warpage
� Volume
� The Volume quality metric (QV) applies only to 3D elements and represents quality in terms of element volume.
� Warpage
� The Warpage (QW) applies only to quad elements and is defined as follows:
5-40 © 2006 Fluent Inc.
� Z is the deviation from a best-fit plane that contains the element
� a and b are the lengths of the line segments that bisect the edges of the element.
� By definition, 0 < QW < 1
� QW = 0 describes an equilateral element
� QW = 1 describes a degenerate element.
[ ]baZ
QW,min
=
Element edge
Best-fit plane
Bisectors