46080542 ansys mesh introduction
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Appendix A
Mesh Quality
A-1ANSYS, Inc. Proprietary
© 2010 ANSYS, Inc. All rights reserved.
Release 12.0
March 2010
Introduction to ANSYS Meshing
Appendix A: Mesh Quality
Training ManualOverview
• Mesh Quality Metrics in ANSYS Meshing– Skewness
– Aspect Ratio
– Worst Element
• Mesh Quality Considerations for the FLUENT Solver– General Considerations– General Considerations
– Impact of Mesh Quality on the Solution
• Mesh Quality Considerations for the CFX Solver
• Factors Affecting Mesh Quality– CAD Issues
– Mesh Resolution and Distribution
– Meshing Method
– Inflation
• Strategies to Improve Mesh Quality– CAD Cleanup
A-2ANSYS, Inc. Proprietary
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– CAD Cleanup
– Virtual Topology
– Pinch Controls
– Sensible Mesh Sizings and Inflation Settings
– General Recommendations
• Workshop A.1 Virtual Topology for an Auto Manifold
• Workshop A.2 FLUENT and CFX Mesh Quality Metrics
Appendix A: Mesh Quality
Training ManualMesh Quality Metrics in ANSYS Meshing
• Mesh Metrics are available under
Mesh Options to set and review
mesh metric information and to
evaluate mesh qualityevaluate mesh quality
• Different physics and different
solvers have different requirements
for mesh quality
• Mesh metrics available in ANSYS
Meshing include:– Element Quality
– Aspect Ratio
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– Aspect Ratio
– Jacobian Ration
– Warping Factor
– Parallel Deviation
– Maximum Corner Angle
– Skewness
Appendix A: Mesh Quality
Training Manual
Skewness
Two methods for determining skewness:
1. Based on the Equilateral Volume deviation:
optimal (equilateral) cell
Mesh Quality Metrics
• Skewness =
• Applies only to triangles and tetrahedra
• Default method for tris and tets
2. Based on the deviation from a Normalized Angle deviation:
−− θθθθmaxθ
optimal cell size cell size
optimal cell size
−
actual cell
circumsphere
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• Skewness =
Where is the equiangular face/cell (60 for tets and tris, and 90 for quads and hexas)
• Applies to all cell and face shapes
• Used for prisms and pyramids
−
−
−
e
mine
e
emax ,180
maxθ
θθ
θ
θθ
minθ
maxθ
eθ
0 1
Perfect Worst
Appendix A: Mesh Quality
Training ManualMesh Quality Metrics
Aspect Ratio
• Aspect for generic triangles and quads is a
function of the ratio of longest side to the
aspect ratio = 1 high-aspect-ratio quad
aspect ratio = 1 high-aspect-ratio triangle
function of the ratio of longest side to the
shortest side of the reconstructed
quadrangles (see User Guide for details)
• Equal to 1 (ideal) for an equilateral triangle
or a square
A-5ANSYS, Inc. Proprietary
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Appendix A: Mesh Quality
Training ManualMesh Quality Statistics in ANSYS Meshing
• The min, max, averaged and standard
deviation for the selected mesh metric
are shown for the surface mesh (after
Preview Surface Mesh generation) and
for the volume mesh (after Preview
Inflation layer or Generate MeshInflation layer or Generate Mesh
generation)
• The worst elements can be highlighted
using the Show Worst Elements under
the Mesh object in the Tree Outline
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Appendix A: Mesh Quality
Training ManualMesh Quality Considerations for FLUENT
• FLUENT requires high quality mesh to avoid numerical diffusion
• Several Mesh Quality Metrics are involved in order to quantify the quality,
however the skewness is the primary metric
• The aspect ratio and cell size change mesh metrics are also very • The aspect ratio and cell size change mesh metrics are also very
important
• In worst scenarios and depending on the solver used (density based or
pressure based) FLUENT can tolerate poor mesh quality. However some
applications may require higher mesh quality, resolution and good mesh
distribution
• The location of poor quality elements helps determine their effect
• Some overall mesh quality metrics may be obtained in Ansys Meshing
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• Some overall mesh quality metrics may be obtained in Ansys Meshing
under the Statistics object
• Additional mesh quality metrics may be retrieved in FLUENT GUI under
Mesh/Info/Quality from the menu, or using the TUI commands
‘mesh/quality’
Appendix A: Mesh Quality
Training ManualMesh Quality Requirements for FLUENT
• The most important mesh metrics for Fluent are:
– Skewness
– Aspect Ratio
– Cell Size Change (not implemented in Ansys – Cell Size Change (not implemented in Ansys
Meshing)
For all/most applications:
• For Skewness:
– For Hexa, Tri and Quad: it should be less than 0.8
– For tetrahedra: it should be less than 0.9
• For Aspect Ratio:
– It should be less than 40, but this depends on
• Poor mesh quality may
lead to inaccurate
solution and/or slow
convergence
• Some applications may
require even lower
skewness than the
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– It should be less than 40, but this depends on
the flow characteristics
– More than 50 may be tolerated at the inflation
layers
• For Cell Size Change:
– It should be between 1 and 2.
skewness than the
suggested value
Appendix A: Mesh Quality
Training ManualSkewness and the Fluent Solver
• High skewness values are not recommended
• Generally try to keep maximum skewness of volume mesh < 0.95.
However this value is strongly related to type of physics and the location
of the cellof the cell
• FLUENT reports negative cell volumes if volume mesh contains
degenerate cells.
• Classification of the mesh quality metrics based on skewness:
•
0-0.25 0.25-0.50 0.50-0.80 0.80-0.95 0.95-0.98 0.98-1.00*
Excellent very good good acceptable bad Inacceptable*
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•
* In some circumstances the pressure based solver in Fluent can handle
meshes containing a small percentage of cells with skewness ~0.98.
Excellent very good good acceptable bad Inacceptable*
Appendix A: Mesh Quality
Training Manual
(max,avg)CSKEW=(0.912,0.291)
(max,avg)CAR=(62.731,7.402)
Impact of the Mesh Quality on the Solution
Example
Me
sh
1
(max,avg)CSKEW=(0.801,0.287)
(max,avg)CAR=(8.153,1.298)
VzMIN≈-90ft/min
VzMAX≈600ft/min
Large cell size changeM
es
h 1
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VzMIN≈-100ft/min
VzMAX≈400ft/min
Me
sh
2
Appendix A: Mesh Quality
Training ManualMesh Quality Considerations for CFX
• Mesh quality requirements are somewhat different for the CFX
solver than for the FLUENT solver due to the difference in the
solver structure for the two codes
– Fluent uses a a cell-centered scheme, in which the fluid flow variables are – Fluent uses a a cell-centered scheme, in which the fluid flow variables are
allocated at the center of the computational cell, and the mesh-element is
the same as the solver-element
– CFX employs a vertex-centered scheme for which the fluid flow variables
are stored at the cell vertex, and the solver-element or control volume is a
“dual” of the mesh-element. This means that the vertex of the mesh-
element is the center of the solver-element
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Appendix A: Mesh Quality
Training ManualMesh Quality Considerations for CFX
• The CFX solver calculates 3 important measures of mesh
quality at the start of a run and updates them each time the
mesh is deformed
– Mesh Orthogonality
– Aspect Ratio
– Expansion Factor
+--------------------------------------------------------------------+
| Mesh Statistics |
+--------------------------------------------------------------------+
Domain Name: Air Duct
Minimum Orthogonality Angle [degrees] = 20.4 ok
Maximum Aspect Ratio = 13.5 OK
Maximum Mesh Expansion Factor = 700.4 !
Domain Name: Water Pipe
Minimum Orthogonality Angle [degrees] = 32.8 ok
Good(OK)
Acceptable
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Minimum Orthogonality Angle [degrees] = 32.8 ok
Maximum Aspect Ratio = 6.4 OK
Maximum Mesh Expansion Factor = 73.5 !
Global Mesh Quality Statistics :
Minimum Orthogonality Angle [degrees] = 20.4 ok
Maximum Aspect Ratio = 13.5 OK
Maximum Mesh Expansion Factor = 700.4 !
Acceptable(ok)
Questionable(!)
Appendix A: Mesh Quality
Training Manual
•Orthogonality measures alignment of:
• ip-face normal vector, n, &
• node-to-node vector, s.
Mesh Orthogonality in CFX
• Orthogonality Factor = n·s, >1/3 desirable
• Orthogonality Angle = 90º-acos(n·s), >20º desirable
• Are these different than Max/Min Face Angles in CFD Post? YES!– Face angles correspond to angles between edges
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– Face angles correspond to angles between edges
– One can have an acceptable Face Angle and an unacceptable Orthogonality
Angle if an element is skewed in two directions…
Appendix A: Mesh Quality
Training ManualMesh Expansion Factor in CFX
Expansion factor measures how
poorly the nodal position corresponds
to the control volume centroidto the control volume centroid
• Mesh Expansion Factor ≈ ratio of largest to smallest elementvolumes surrounding a node,<20 is desirable
• The Mesh Expansion Factor is essentially identical to the Element Volume
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• The Mesh Expansion Factor is essentially identical to the Element Volume Ratio in CFD Post
Appendix A: Mesh Quality
Training ManualMesh Aspect Ratio in CFX
Aspect ratio measures how stretched a
control volume is
• Aspect Ratio = maximum of the ratio of largest to smallest ip-areas for each element surrounding a node,<100 is desirable
• The Aspect Ratio is very similar to the Edge Length Ratio in CFD Post
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Appendix A: Mesh Quality
Training ManualSignificance of Mesh Quality in CFX
• Sources of discretisation error
– non-orthogonality introduces errors in flux approximations
Why is geometrical mesh quality important?
– non-orthogonality introduces errors in flux approximations
– large mesh expansion introduces errors in storage and source
approximations
• Amplification of discretisation error
– corrections to reduce errors caused by non-orthogonality can create
unphysical influences
• Difficulties solving linearised equations
– large aspect ratios require use of more significant digits
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– large aspect ratios require use of more significant digits
(i.e. use of double precision solver)
Appendix A: Mesh Quality
Training ManualFactors Affecting Mesh Quality
• CAD Issues
– Small edges, sharp edges and faces
– Small gaps/passages between edges and faces
– Unconnected geometry entities
CAD issues need to
be fixed to avoid this
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Appendix A: Mesh Quality
Training ManualFactors Affecting Mesh Quality
• Mesh Resolution
and Distribution
– Geometry with
abrupt changes,
discontinuities discontinuities
and/or small gaps
may require more
resolution, and
– Mesh distribution
where appropriate to
be able to predict
physical conditions
Inappropriate
resolution and
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resolution and
distribution may lead
to large cell size
change, aspect ratio
and/or skewness
Appendix A: Mesh Quality
Training ManualFactors Affecting Mesh Quality
• Type of Size Function
– Inappropriate usage (or
no usage at all) of
Advanced Size Functions
(ASF) may lead to poor (ASF) may lead to poor
mesh quality
– Use Curvature ASF for
geometries with
dominant curvature
features
– Use Proximity ASF for
geometries with gaps or
narrow components
– Use Curvature and
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– Use Curvature and
Proximity ASF in
geometries having a
combination of these
features ASF may be used to
avoid this !
Appendix A: Mesh Quality
Training ManualFactors Affecting the Mesh Quality
• Meshing Method
– Inappropriate usage of Meshing Method (Automatic, Tetrahedrons, Sweep, MultiZone
and CFX-Mesh) may lead to large skewness
– The selection of the Meshing Method depends on the geometry and application
– It is a good practice to use Show the Sweepable Bodies under the Mesh object in the – It is a good practice to use Show the Sweepable Bodies under the Mesh object in the
Tree Outline
– Many applications may take advantage of Patch Conforming and Sweep Meshing Method
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A relatively “good” mesh in
terms of max skewness,
however the average and
standard deviation are large
Appendix A: Mesh Quality
Training ManualFactors Affecting Mesh Quality
• Inflation
Inappropriate:
– Surface mesh
quality
– Choice of the – Choice of the
inflation surfaces
– Inflation Option
– Inflation algorithm
(layer compression
or stair-stepping)
– Inflation
parameters
– Advanced Inflation
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– Advanced Inflation
Options
may lead to poor
mesh quality!
Affected Inflation
Appendix A: Mesh Quality
Training ManualStrategies to Improve Mesh Quality
• CAD cleanup
Use CAD or DM to:
– Simplify the geometry
– Merge small edges
After split edge/Project
edge/merge face in DM
– Merge small edges
– Merge the faces in
order to reduce the
number of faces
– Avoid narrow faces
– Keep volume gaps only
where important
– Decompose the
geometry
– Remove unnecessary
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– Remove unnecessary
geometries
– Add geometries
– Repair the geometry
Appendix A: Mesh Quality
Training ManualStrategies to Improve Mesh Quality
• Virtual topology
Use VT in order to
simplify details at
geometry level in AM
After virtual merging of
narrow face with wide face
Can be added under
Model object in the
Tree Outline
Mesh may be
improved by creating
virtual edges/faces
If the resulting
surface mesh is
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surface mesh is
distorted consider
fixing the geometry
issue in DM or CAD
Appendix A: Mesh Quality
Training ManualStrategies to Improve Mesh Quality
• Pinch Controls
– Allow to remove small features (small edges
or narrow faces) at the mesh level
– Intended for Patch-Conforming Tetrahedral Method
– When it is defined the small features are “pinched-
Pinch locations are detected
automatically with Pinch Controls under
Mesh object in the Tree Outline
– When it is defined the small features are “pinched-
out” from the mesh when pinch criteria are met
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Appendix A: Mesh Quality
Training ManualStrategies to Improve Mesh Quality
• Sensible Mesh Sizings and Inflation Settings
The minimal size decreased 2X in order to
fit the narrow geometry. As a result the
mesh quality has been improved. Local
face sizing may also be used
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face sizing may also be used
Appendix A: Mesh Quality
Training Manual
• General Recommendations
– A volume mesh may be considered inacceptable if it satisfies one or more the following conditions:
Strategies to Improve Mesh Quality
• Very high skewness for FLUENT meshes(> 0.98)
• Degenerate cells (skewness ~ 1)
• High aspect ratio cells
• Negative volumes
– Cell Quality can be improved by:
• Improving surface mesh quality
• Moving mesh nodes
• CAD to fix geometric problems such as sharp angles, small edges, merge faces unite
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• CAD to fix geometric problems such as sharp angles, small edges, merge faces unite and/or decompose the geometries
• Clean-up tools in DM to simplify the geometries and their entities
• Different methods, global and local sizings and parameters in the ANSYS Meshing Application
• Pinch Controls in the ANSYS Meshing Application to avoid small features
• Virtual topology in the ANSYS Meshing Application in order to simplify the geometry
Appendix A: Mesh Quality
Training ManualMiscellaneous
• If the model contains multiple
parts or bodies the mesh metric
information can be shown by
highlighting them under the highlighting them under the
Geometry object in the Tree
Outline
• The Body of Influence (BOI)
technique may be used also to
control the mesh quality and
appropriate local resolution
• More advanced mesh statistics
including histograms can be
exhibited by FE Modeler Mesh
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exhibited by FE Modeler Mesh
Metrics in FEM
• Different mesh quality metrics
can also be viewed in CFD Post
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