Multiphase Modeling in ANSYS CFD - ANSYS - Simulation Driven
epsilon_Mesh_error in ANSYS
-
Upload
aruatscribd -
Category
Documents
-
view
48 -
download
2
description
Transcript of epsilon_Mesh_error in ANSYS
… within Epsilon
… within Epsilon
Twin Cities ANSYS® User Meeting
November 2011
Mesh Discretization Error
Twin Cities ANSYS® User Meeting
November 2011
Mesh Discretization Error
3
… within Epsilon
ANSYS User Meeting
Mesh Discretization Error
1. Mesh Discretization: The “One-sided” Error Source
2. Tet Pregidous
3. Case Study A: Shape-Functions Effect– With and without mid-side nodes
– Stresses & Deflection
4. Case Study B: Mesh Convergence– Node vs. Element (Averaged vs Unaveraged)
– PRERR (SEPC/SMXB)
4
… within Epsilon
ANSYS User Meeting
• Often small compared to load/material property error/scatter
• Ownership of error lands on analyst– Often linked to “credibility” of whole analysis
• True Error analysis would likely show Mesh Discretization is minor issue– And yet... Scrutiny continues
– And rules and criteria abound… (while other scatter goes unmentioned)
Mesh Discretization Error
“It can be measured? Well let’s fixate on it!” “It can be measured? Well let’s fixate on it!”
5
… within Epsilon
ANSYS User Meeting
• A “one-sided” error source*– Predictions are usually lower than actual (not higher)
• Excepting Singularities
– Nagging feeling because of non-conservative nature• Stress is usually underpredicted*
– Upper bound not determinable• Without employing knowledge of materials/loads/element
shape functions – discussed later
Mesh Discretization Error
*Powergraphics results (classic) isn’t so one-sided – discussed later
6
… within Epsilon
ANSYS User Meeting
• Bias Against Tetrahedrons (Tet’s)– Source of grievance?
• Low order Tets (a.k.a “T4”, a.k.a “non-midside noded Tet”)– Too Stiff in bending / large error with 1 element through thickness
• 1st Tet’s (Berkely 1960’s) were high order
• You’d have to work at it to get ANSYS to create T4’s (structural)
– Tets (10 noded) are Less efficient per DOF• Longer solve times
• Shorter meshing times
• Added control allows refinement at location of interest– More efficient than Mapped meshing!
– Less pleasing to the eye (esp. higher aspect ratios)
– Stigmatism is receding over last decade
Tet-Pregidious
7
… within Epsilon
ANSYS User Meeting
• Thick to thin rings with inner pressfit (radial expansion)– Stress gradient related to radius2
• Case Study A, Expansion of Thick/Thin Ring– Actually used 5° wedge
Case Study A
8
… within Epsilon
ANSYS User Meeting
• Case Study A– Peak Stresses have similar convergence patterns/rate
Case Study A
15000
20000
25000
30000
35000
40000
45000
1.5 2 2.5 3
Peak
Str
ess
Ring ID
Low Order Elements
1/thick
4/Thick
5/Thick
15000
20000
25000
30000
35000
40000
45000
50000
1.5 2 2.5 3
Peak
Str
ess
Ring ID
High Order Elements
1/Thick
2/Thick
5/Thick
9
… within Epsilon
ANSYS User Meeting
• Case Study A– Peak Stresses have similar convergence patterns/rate
Case Study A
15000
20000
25000
30000
35000
40000
45000
50000
1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9
Stre
ss
Inner Radius
High & Low Order Elements
Low 1/Thick
Low 2/Thick
Low 5/Thick
High 1/Thick
High 2/Thick
High 5/Thick
10
… within Epsilon
ANSYS User Meeting
• Case Study A– OD Deflections
Case Study A
0.0013
0.0014
0.0015
0.0016
0.0017
0.0018
0.0019
0.002
0.0021
1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9
Def
lect
ions
Inner Radius
High & Low Order Elements
11
… within Epsilon
ANSYS User Meeting
• Case Study A– OD Deflections
Case Study A
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9
Def
lect
ion
Inner Radius
High & Low Order Elements
12
… within Epsilon
ANSYS User Meeting
• Case Study A– Deflections Along Path
Case Study A
1.35E-03
1.45E-03
1.55E-03
1.65E-03
1.75E-03
1.85E-03
1.95E-03
2.05E-03
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Low 1/ThickLow 2/ThickLow 5/ThickHigh 1/ThickHigh 5/Thick
13
… within Epsilon
ANSYS User Meeting
• Case Study A Conclusions– Element Stress Gradient
• Linear for high or low order elements
– Element Displacement Gradient• Linear for low order element
• 2nd order polynomial for high order element
– Thin Rings are well approximated with single element through the thickness
• This extends to beams as well
Case Study A
14
… within Epsilon
ANSYS User Meeting
• Case Study B– Stress along path
– Node vs. Element (Averaged vs Unaveraged)
– PRERR (SEPC/SMXB)
Mesh Discretization Error
15
… within Epsilon
ANSYS User Meeting
• Stress along path– Background stress of 180
– KT =2.0
Case Study B
17
… within Epsilon
ANSYS User Meeting
• Peak Stress– Varying Mesh densities
• WB ‘s adaptive mesh refinement automates this task refining only regions of interest (thanks, paul)
Case Study B
345
350
355
360
365
370
375
0 20 40 60 80 100 120
Stre
ss
Mesh Density
Mesh Convergence
18
… within Epsilon
ANSYS User Meeting
• Stress along path
Case Study B
180
200
220
240
260
280
300
320
340
360
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Stre
ss
Path Length
Very FineFineMediumCoarse
19
… within Epsilon
ANSYS User Meeting
• Stress along path: zoom
Case Study B
240
260
280
300
320
340
360
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
Stre
ss
Path Length
Very FineFineMediumCoarse
20
… within Epsilon
ANSYS User Meeting
• Stress along path: Unaveraged Results
Case Study B
220
240
260
280
300
320
340
360
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Stre
ss
Path Length
Very Fine
Fine
Medium
Coarse
21
… within Epsilon
ANSYS User Meeting
• Case Study B Conclusion:– Discontinuity of stress element-to-element
relates to degree of mesh discretization error
Case Study B
22
… within Epsilon
ANSYS User Meeting
• Discontinuity at element boundaries is key
Error Assessment
Difference at boundary
23
… within Epsilon
ANSYS User Meeting
• Discontinuity at element boundaries is key
Error Assessment
• Energy difference per element• Considers volume/stiffness
24
… within Epsilon
ANSYS User Meeting
• Discontinuity at element boundaries is key
Error Assessment
• Sum it over the model (selected region)
• Normalize it to the whole model energy(includes load magnitude)
Yields a single number!(PRERR, or Percentage error in the energy norm)
25
… within Epsilon
ANSYS User Meeting
• Percentage error in the energy norm (PRERR)
Error Assessment
0.797
4.0
MediumCoarse
1.59
8.95
26
… within Epsilon
ANSYS User Meeting
• Percentage error in the energy norm (PRERR)
Error Assessment
0.32
0.06
Very FineFine
0.56
1.13
27
… within Epsilon
ANSYS User Meeting
• SMXB– Checks all nodes (doesn’t necessarily correspond to the MX
location!)
– Only mentioned once in Help Manual!
– Training Classes refer to it as a “confidence band”…
Error Assessment
Root Mean Square of:(avg. value – element value)for each element sharing node
/EOF
Average stress from contributing elements (what’s plotted)