Ansys Mesh Introduction - Appendix a Mesh Quality

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



Release 12.0

March 2010

– 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


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



Release 12.0

March 2010

– Aspect Ratio

– Jacobian Ration

– Warping Factor

– Parallel Deviation

– Maximum Corner Angle

– Skewness


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



Release 12.0

March 2010

• 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


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



Release 12.0

March 2010


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



Release 12.0

March 2010


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



Release 12.0

March 2010

• 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’


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



Release 12.0

March 2010

– 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


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*



Release 12.0

March 2010

•

* 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*


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



Release 12.0

March 2010

VzMIN≈-100ft/min

VzMAX≈400ft/min

Me

sh

2


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



Release 12.0

March 2010


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


Good(OK)

Acceptable



Release 12.0

March 2010




Global Mesh Quality Statistics :




Acceptable(ok)

Questionable(!)


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



Release 12.0

March 2010

– 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…


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



Release 12.0

March 2010

• The Mesh Expansion Factor is essentially identical to the Element Volume Ratio in CFD Post


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



Release 12.0

March 2010


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



Release 12.0

March 2010

– large aspect ratios require use of more significant digits

(i.e. use of double precision solver)


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



Release 12.0

March 2010



• 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



Release 12.0

March 2010

resolution and

distribution may lead

to large cell size

change, aspect ratio

and/or skewness



• 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



Release 12.0

March 2010

– Use Curvature and

Proximity ASF in

geometries having a

combination of these

features ASF may be used to

avoid this !


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



Release 12.0

March 2010

A relatively “good” mesh in

terms of max skewness,

however the average and

standard deviation are large



• 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



Release 12.0

March 2010

– Advanced Inflation

Options

may lead to poor

mesh quality!

Affected Inflation


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



Release 12.0

March 2010

– Remove unnecessary

geometries

– Add geometries

– Repair the geometry



• 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



Release 12.0

March 2010

surface mesh is

distorted consider

fixing the geometry

issue in DM or CAD



• 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



Release 12.0

March 2010



• 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



Release 12.0

March 2010

face sizing may also be used


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



Release 12.0

March 2010

• 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


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



Release 12.0

March 2010

exhibited by FE Modeler Mesh

Metrics in FEM

• Different mesh quality metrics

can also be viewed in CFD Post

Date post:	30-Nov-2015
Category:	Documents
Upload:	luis-tamayo
View:	490 times
Download:	34 times

Ansys Mesh Introduction - Appendix a Mesh Quality

Documents