Mesh Generation and Automated Simulation

Part II: Issues in Applied Mesh GenerationJohn R. Chawner

Pointwise, Inc.

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Revelations• Meshing is the dirty little

secret of CAE practitioners.

• Pre-processing consumes the vast majority of man-hours for any analysis (75-90%).

• There is no silver bullet.

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Applied Meshing• Interfacing to CAD• Mesh Types & Algorithms• Mesh Quality• Automatic vs. Manual• Software Aspects

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CAD Issues• Interoperability • Geometry

Representations • Poor Geometric Quality

1999 report: CAD interoperabilityproblems cost US automotive industry$1 billion per year

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CAD Interoperability:Plug-in

CADmesher

•Pros:•no translation or conversion errors, •CAD GUI familiar to users

•Cons: •analyst must have access to and be trained for CAD system

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CAD Interoperability:common kernel

mesher CAD

geometrykernel

•Parasolid•ACIS•Open CASCADE•Nlib•Etc.•Pros:

•Portable•Cons

•Limits CAD choice or…•Requires multi-kernel approach

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CAD Interoperability:direct access

CADmesher direct access•CAD Services (www.omg.org)•CADScript (ITI?)•CGM (Sandia)•CAPRI (MIT)•CAD Native API (e.g. Pro/TOOLKIT)•Pros:

•Direct access to CAD data•No need to understand CAD GUI

•Cons:•Neutral interfaces limited to least common denominator•May require CAD license

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CAD Interoperability:indirect access

CADmesherfile

transfer

•Neutral files: IGES, STEP•Native files: CATIA, Pro/E, etc.

•Pros:•No CAD license, no CAD familiarity•Portable

•Cons:•Possible translation errors

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CAD Interoperability:Other Issues

• Level of interoperability– Geometry

(aka “dumb” geometry)– Features

• Bi-directional?

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CAD: Representations• Solids

– Manifold vs. Non-manifold– Solid vs. Partial Solid vs. No

Solids– B-Rep vs. CSG

• NURBs and/or analytics• Discrete

– Faceted data– Sub-division surfaces

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CAD: Quality Issues

• Missing components

• Too much detail• Gaps & overlaps• Slivers• Improper

trimming (tolerances)

• Translation errors

• IGES is the whipping boy - undeservedly

• 70% of CAD files don’t conform to the company’s internal drafting standards

unavoidable

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CAD: Dealing with Poor Quality

• Repair/heal the geometry

– CADfix, DEXCenter (ITI)

– TransMagic– ACIS Healing– CADIQ– PrescientQA– Services,

services, services

• Fault tolerance– Is repair an

inherently unsolvable problem?

• Most successful near-term solution:

– Change process: man in the loop to bridge CAD and CAE

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CAD: Other Issues• Defeaturing• Adding geometry

– outer boundaries– missing pieces (e.g.

windscreens)

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Applied Meshing• Interfacing to CAD• Mesh Types & Algorithms• Mesh Quality• Automatic vs. Manual• Software Aspects

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Importance of the Mesh

• Mesh Quality– Almost any

solver can compute a good solution on a good mesh.

– A poor mesh will yield a poor solution from all but the most robust solver.

• Mesh Density– Given enough

mesh points, any solver can compute a good solution.

– Use too few points in critical locations and no solver will compute a good solution.

You have the most influence over the solution via the mesh.

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Mesh Type• Largely out of your control

– Limited by your solver’s capabilities

• Primary issues– Analysis goals– Accuracy– Turnaround time

• Secondary issues– Cell type(s)– Linear vs. polynomial elements– Boundary conforming or not

structured

unstructured

hybrid

cartesian

Unstr. hex

Images courtesy of Iowa State, JPL, Centaursoft, NASA, NUMECA

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Structured Grid(hex)

• Pro: Structured solvers are very efficient.

• Pro: Good control over hex cell quality including stretching.

• Pro: Methods are mature.• Con: Structured grids take a

long time to generate because of topology.

• Application: CFD

structured

Grid courtesy of Raytheon.

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Unstructured Mesh(tet)

• Pro: High degree of automation

• Pro: Tet meshers are “commodity” items

• Con: hard to make stretched tets

• Application: linear CSM, CEM, inviscid CFD

unstructured

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Hybrid Mesh(hex/pyramid/prism/tet)

• Pro: Balances automation (tet) & structure (hex, prism).

• Con: (Semi)structured mesh is near complex geometry.

• Application: CFDhybrid

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Hexahedral Mesh(hex)

• Pro: Automation (semi-automation?)

• Con: Difficult• Application: CSM

Unstr. hex

Hinge mesh courtesy of Simulation Works

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Cartesian(hex/?)

• Pro: Vast majority of mesh trivial.

• Con: Boundaries may be “stair stepped” –or-

• Con: Complex cells near boundary

• Application: CFD

cartesian

F-16 solution courtesy of Lockheed-Martin Aeronautics

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Mesh Type Relative Merits

• Structured vs. Unstructured

– Unstructured provides more opportunities for automation

– Structured solvers are more efficient

• Hex vs. Tet– Hex: Fewer hex

cells for same volumetric coverage

– Hex: cells easier to stretch

– Hex/Tet: Which is better?

– Tet: Automation!

F-15 solution and mesh courtesy of Cobalt Solutions and USAF.

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Mesh Type by Application

• Linear FEA– Unstructured

tets• Non-linear FEA

– Hex (str or unstr)

• Viscous CFD– Structured

Grid– Hybrid Mesh

• Inviscid CFD– Unstructured

Tets

• If algorithm is sensitive to number of cells (e.g. CEM which is n3), consider higher order elements.

Femur implant mesh courtesy of Cornell Univ. and TrueGrid.

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Mesh Algorithm

• It just doesn’t matter.• All that matters is the

resulting mesh, not how it was generated.

• Unlike solvers, there aren’t any underlying meshing principles.

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Applied Meshing• Interfacing to CAD• Mesh Types & Algorithms• Mesh Quality• Automatic vs. Manual• Software Aspects

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Effects of Poor Mesh Quality

• Solution accuracy decreases– Discretization error increases

with element distortion

• Solution convergence rate decreases– Iterations increase as

minimum included angle increases

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Signs of Poor Mesh Quality

• Large jumps in mesh size• Twisted cells• Cells with one or more

very short edges• Problem: no agreed upon

standard for mesh quality– How to measure and

compare?

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Improving Mesh Quality

• Know your solver’s mesh quality criteria

• Exploit your mesher’s solver controls

• Case study: 20 min. of mesh smoothing reduces run time by 4 hours.

• Adaptive meshing

– Adjust mesh as dictated by solution

• Point insertion

• Point movement

Grids courtesty of Nabla Ltd., EPFL,

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Applications• Interfacing to CAD• Mesh Types & Algorithms• Mesh Quality• Automatic vs. Manual• Software Aspects

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Automatic• Be aware of what automatic

means.– au-to-ma-tic (adj.): without human

intervention– automatic: better than we’re

currently doing• Example: an automatic mesher

that didn’t work half the time and never let you view the mesh

• Be aware of conditions required for automation

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Applied Meshing• Interfacing to CAD • Mesh Types & Algorithms• Mesh Quality• Automatic vs. Manual• Software Aspects

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Software Aspects• Good news! Most (all?) CAE

software comes with its own mesher.

• Bad news! You’ll have to make a business case to buy something else.

• Why would you want to use something else?

– Meshing offers the best opportunities for CAE process improvement.

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Things to Consider• Is your meshing software

contributing toward your primary goals?– Accurate and timely CAE

• Are you using a different mesher for each CAE application?

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Resources

• International Meshing Roundtable– www.IMR.sandia.gov

• Meshing Research Corner (Steve Owen)– www.andrew.cmu.edu/user/sowen/mesh.html

• Mesh generation on the web (Robert Schneiders)

– www-users.informatik.rwth-aachen.de/~roberts/meshgeneration.html

• Geometry in Action (David Eppstein)– http://www.ics.uci.edu/~eppstein/gina/meshgen.html

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Resources cont’

• International Society of Grid Generation– www.ISGG.org

• CFD-Online– www.CFD-Online.com

• CFD Review– www.CFDReview.com