optimization of relaxation factor for simple solver
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Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
Masashi Imano (OCAEL Co.Ltd.)
Optimization of relaxation factorfor simple solver
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Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
“Guidebook for Practical Applications of CFDto Pedestrian Wind
Environment around Buildings”
Working Group in Architectural Institute of Japan
Web site (in Japanese and English)( in Japanese)
Akashi Mochida, Yoshihide Tominaga, et al.
Guideline for Practical Applications
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Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
Case A(2:1:1 shape)
Case B(4:4:1 shape)
Case C(Simple blocks)
Case D(High-rise bldg.)
Case E(Niigata)
Case F(Shinjuku, Tokyo)
Benchmark tests
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Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
Mesh Cartesian mesh(snappyHexMesh)
Inflow Interpolate from wind tunnel results
Top & Sidewall Zero gradient
Ground and bldg. wall
Generalized log lawfor a smooth wall
Turbulencemodel Standard k-epsilon
Advectionscheme Upwind
Algorithm SIMPLE (simpleFoam)
Wind direction NNE
Building complexes with simple building shape in actual urban area (Niigata)
Case E - Calculation condition
4
Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
Case E - Validation
RMSE(Root Mean Square Error)
Code O(Overlapping structured grid)0.24
OpenFOAM (Unstructured grid)0.22
NNE
Code OExperiment Code O OpenFOAM
Nor
mal
ized
velo
city
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Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
Test cluster condition
• Project XL server @ Hokkaido University• Hardware: HITACH BladeSymphony BS 2000• CPU: Intel Xeon E7-8870 2.4GHz, 10 cores• Node: 4CPUs (40 cores)• Memory: 128GB/node• HDD: 2TB/node• OS: Any OS (root account is available)• Rental fee: 21,000 yen/month• Other project server: ✓ L server: 10 cores(1CPU), 5,250 yen/month
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Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
Accelerate simple solver
• Relaxation parameters for pressure and velocity are important for steady state incompressible flows (solver: simpleFoam)
relaxationFactors // 0 < relaxationFactors <= 1{ p 0.3; // for pressure (important) U 0.5; // for velocity vectors (important) k 0.5; // for turbulence kinetic energy epsilon 0.5; // for turbulence kinetic energy // dissipation rate}
system/fvSolution:
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Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
Convergence criteria
SIMPLE{ nNonOrthogonalCorrectors 0; residualControl // convergence criteria { "(p|U|k|epsilon|omega)" 2e-‐3; }}
system/fvSolution:
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Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
Results of speedup in SIMPLE 1
0
0.5
1
1.5
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.75 0.8 0.85 0.9Spee
dup
ratio
(bas
e αU
=0.5
, αp=
0.8)
Relaxation factor for velocity (αU)
0.1 0.2 0.3 0.4 0.5 0.6 0.70.8 0.9
Relaxation factor for pressure (αP)
αP=0.1
αP=0.2
αP=0.3
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Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
Results of speedup in SIMPLE 2
0.9
1
1.1
1.2
1.3
1.4
1.5
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.75 0.8 0.85 0.9Spee
dup
ratio
(bas
e αU
=0.5
, αp=
0.8)
Relaxation factor for velocity (αU)
0.1 0.2 0.3 0.4 0.5 0.6 0.70.8 0.9
Relaxation factor for pressure (αP)
αP=0.1
αP=0.2
αP=0.3αP=0.4αP=0.5
αP=0.6
αP=0.7αP=0.8
αP=0.9
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Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
Results of speedup in SIMPLEC
0
125
250
375
500
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Itera
tion
num
ber
Relaxation factor for pressure (αU)
0.1 0.2 0.3 0.4 0.5 0.60.7 0.8 0.9 SIMPLEC
Relaxation factor for velocity (αP)
αP=0.8αP=0.9 αP=0.7
αP=0.6αP=0.5
αP=0.4αP=0.3
αP=0.2αP=0.1
SIMPLEC is almost equivalanceto SIMPLE when αU+αP=1
11
Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
Execution time per iteration
0
600
1200
1800
2400
3000
3600
4200
4800
0 600 1200 1800 2400 3000
Exec
tion
time
[s]
Number of iteration
SIMPLE SIMPLEC
12
Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
Results of speedup in SIMPLEC 2
0
0.5
1
1.5
2
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Spee
dup
ratio
(bas
e αU
=0.5
, αp=
0.8)
Relaxation factor for pressure (αU)
0.1 0.2 0.3 0.4 0.5 0.60.7 0.8 0.9 SIMPLEC
Relaxation factor for velocity (αP)
αO=0.8αP=0.9 αP=0.7 αP=0.6
αP=0.5
αP=0.4αP=0.3
αP=0.2αP=0.1
SIMPLEC is almost equivalanceto SIMPLE when αU+αP=1
13
Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
0
0.5
1
1.5
2
2.5
3
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Max
imum
of v
eloc
ity re
new
al [m
/s]
Relaxation factor for pressure (αU)
Ux Uy Uz
Maximum of velocity renewal 1When solution is converged
(i.e Initial residual for p and U are smaller than criteria)
Inlet velocity atpedestrian level is about 3 m/s.
Maximum of velocity renewalshould be smaller than about10% of 3 m/s, i.e. 0.3 m/s.
0.3 m/s
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Aug. 26th 2012 OpenFOAM Study Meeting for beginner @ Kanto Masashi Imano (OCAEL Co. Ltd.)
0
0.5
1
1.5
2
2.5
3
0 1 2 3 4 5 6 7 8 9 Max
imum
of v
eloc
ity re
new
al [m
/s]
Virtual time step (E=αU /(1-αU)
Ux Uy Uz
Maximum of velocity renewal 2When solution is converged
(i.e Initial residual for p and U are smaller than criteria)
15
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