optimization of relaxation factor for simple solver

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

1


“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

2


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

3


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


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

5


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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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:

7


Convergence criteria

SIMPLE{ nNonOrthogonalCorrectors 0; residualControl // convergence criteria { "(p|U|k|epsilon|omega)" 2e-‐3; }}

system/fvSolution:

8


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

9


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

10


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

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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


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)


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

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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]


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

14


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)

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Any Questions?

16

optimization of relaxation factor for simple solver

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