M CARLO BURN UP CODE CCELERATION USING THE … · using the Correlated Sampling method 1. Monte...
Transcript of M CARLO BURN UP CODE CCELERATION USING THE … · using the Correlated Sampling method 1. Monte...
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MONTE CARLO BURN-UP CODE ACCELERATIONUSING THE CORRELATED SAMPLING METHOD
EXEMPLE WITH TRIPOLI-4-D®
Ph.D. Advisor : CHEICK DIOPPh.D. Advisor : ÉRIC DUMONTEILPh.D. Student : CYRIL DIEUDONNÉ
1Cyril DieudonnéCEA SaclayDEN/DANS/DM2S/SERMA/LTSD
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2Cyril Dieudonné
SUMMARY
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
I. Monte Carlo Burn-up code Accelerationusing the Correlated Sampling method1. Monte Carlo burn-up code principle and TRIPOLI-4-D®
2. The correlated sampling method3. Application to burn-up simulations
II. Concrete Algorithm and Code Development1. Development of a post-treatment module : TRIPOLI-4-RT2. Linking TRIPOLI-4-RT with TRIPOLI-4-D®
3. Basic scheme implementation of the method in TRIPOLI-4-D®
III. First Results1. Test case presentation2. Validation of method3. Performance analysis
IV.Conclusion and Further work
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Cyril Dieudonné 3
IMONTE CARLO BURN-UP CODE ACCELERATIONUSING THE CORRELATED SAMPLING METHOD
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
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Cyril Dieudonné 4
MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
1. Monte Carlo burn-up code principle and TRIPOLI-4-D®
Monte Carlo Burn-up codeDeterministic
Solver
Burn-up
Monte Carlocode
Transport
DeterministicSolver
Burn-up
Monte Carlocode
Transport
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Cyril Dieudonné 5
MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
1. Monte Carlo burn-up code principle and TRIPOLI-4-D®
TRIPOLI-4-D®
Mendel®
Burn-up
TRIPOLI-4®
Transport
Mendel®
Burn-up
TRIPOLI-4®
Transport
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Cyril Dieudonné 6
MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
1. Monte Carlo burn-up code principle and TRIPOLI-4-D®
TRIPOLI-4-D®
Advantages : Complex 3D geometries Punctual energies
Drawback : Prohibitive computation time
Mendel®
Burn-up
TRIPOLI-4®
Transport
Mendel®
Burn-up
TRIPOLI-4®
Transport
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Cyril Dieudonné 7CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. The correlated sampling method
Principle of the correlated sampling method :
We simulate events in a system …… but we score their contributions to an other one
MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD
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Cyril Dieudonné 8CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. The correlated sampling method
Principle of the correlated sampling method :
We simulate events in a system …… but we score their contributions to an other one
Initial medium
Perturbated medium n°1
Perturbated medium n°2
…
MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD
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Cyril Dieudonné 9CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. The correlated sampling method
Principle of the correlated sampling method :
( )0
0
0 ( )MM
E X xp x dx= ∫
( )1
1
1( )MM
E X xp x dx= ∫
MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD
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Cyril Dieudonné 10CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. The correlated sampling method
Principle of the correlated sampling method :
( )0
0
0 ( )MM
E X xp x dx= ∫
( )1
1
1
0
1
00
0
1( )( )
(
( )
( )
() )
MM
M
M
cs
E X xp x dx
x p x dx
x p
p
x
xp
x dx
x
ω
=
=
=
∫
∫
∫
MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD
1
0
( )( )( )
cs p xxp x
ω =
Correction weight due to correlated sampling method :
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Cyril Dieudonné 11CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. The correlated sampling method
Principle of the correlated sampling method :
( )0
0
0 ( )MM
E X xp x dx= ∫
( )1
1
1
0
0
1
*0*
0
*0
1
0*
0
( )( )
(
( )
( )
( )( )
( ) )) (cs
MM
M
M
p xp x
E X xp x dx
x p x dx
x p x dx
p xp x
x xω ω
=
=
=
∫
∫
∫
MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD
1
0
( )( )( )
cs p xxp x
ω =
* 00 *
0
( )( )( )
p xxp x
ω =
Correction weight due to correlated sampling method :
Correction weight due to biaising technique :
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Cyril Dieudonné 12CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. The correlated sampling method
Principle of the correlated sampling method :
( )0
0
0 ( )MM
E X xp x dx= ∫
( )1
1
1
0
0
1
*0*
0
*0
1
0*
0
( )( )
(
( )
( )
( )( )
( ) )) (cs
MM
M
M
p xp x
E X xp x dx
x p x dx
x p x dx
p xp x
x xω ω
=
=
=
∫
∫
∫
( )*, 1 , 1 1
* * *1 1 1
11 1 1
t i t i i idcs i i i ii i
i i i i
T C N eT C N
ω + + → +− Σ −Σ→ + + +→ +
→ + + +
= =
MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD
1
0
( )( )( )
cs p xxp x
ω =
* 00 *
0
( )( )( )
p xxp x
ω =
Correction weight due to correlated sampling method :
Correction weight due to biaising technique :
Weight modification given by this equation :
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Cyril Dieudonné 13CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
3. Application to burn-up simulations
Monte Carlo simulations
Simulation n°1
Simulation n°N
Application of the correlated sampling methodto Monte Carlo burn-up codes :
MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD
time step 1
timestep N
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Cyril Dieudonné 14CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
3. Application to burn-up simulations
Monte Carlo simulations
Simulation n°1
Simulation n°N
Application of the correlated sampling methodto Monte Carlo burn-up codes :
MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD
Monte Carlo simulations
Simulation n°1
Simulation n°1 perturbated
time step 1
timestep N
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Cyril Dieudonné 15CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
3. Application to burn-up simulations
This method has several advantages : The calculation is correct : no systematic error No need to generate random number No need to perform a new tracking
We hope a gain in computation time
But the variance is deterioratedduring the burn-up !
MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD
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Cyril Dieudonné 16CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
3. Application to burn-up simulations
MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD
How does this compromise betweenVariance and Calculation Time scalealong the different burnup steps ?
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Cyril Dieudonné 17
IICONCRETE ALGORITHM
AND CODE DEVELOPMENT
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
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TRIPOLI-4-D®
Burn-upTransportBurn-up
Cyril Dieudonné 18CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
1. Development of a post-treatment module : TRIPOLI-4-RT
CONCRETE ALGORITHM AND CODE DEVELOPMENT
Transport
tracks.root
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TRIPOLI-4-D®
Burn-upTransportBurn-up
Cyril Dieudonné 19CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
1. Development of a post-treatment module : TRIPOLI-4-RT
CONCRETE ALGORITHM AND CODE DEVELOPMENT
CorrelatedSampling
tracks.root
Post-Treatment
TRIPOLI-4-RT
Transport
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TRIPOLI-4-D®
Burn-upTransportBurn-up
Post-Treatment
TRIPOLI-4-RT
Cyril Dieudonné 20CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. Linking TRIPOLI-4-RT with TRIPOLI-4-D®
CONCRETE ALGORITHM AND CODE DEVELOPMENT
Burn-up Burn-upCorrelatedSampling
CorrelatedSampling
tracks.root
Post-Treatment
TRIPOLI-4-RT
Transport
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Post-Treatment
TRIPOLI-4-RT
Cyril Dieudonné 21CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
3. Basic scheme implementation of the method in TRIPOLI-4-D®
CONCRETE ALGORITHM AND CODE DEVELOPMENT
Burn-up
Burn-up Burn-upCorrelatedSampling
CorrelatedSampling
tracks.root
TransportBurn-upTransport
Post-Treatment
TRIPOLI-4-RT
TRIPOLI-4-D®
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Cyril Dieudonné 22
IIIFIRST RESULTS
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
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Cyril Dieudonné 23
FIRST RESULT
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
1. Test case presentation
UO2 pin cell : UOx pin cell with U235, U238 and O16
6 rings Evolution chain of 155 isotopes Flux scored on a 11000 groups
energy mesh
How do we compare burn-upsimulations between them ?
2
1. . .F O Mt
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Post-Treatment
TRIPOLI-4-RT
Cyril Dieudonné 24CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
1. Test case presentation
FIRST RESULTS
Burn-up
Burn-up Burn-upCorrelatedSampling
CorrelatedSampling
tracks.root
TransportBurn-upTransport
Post-Treatment
TRIPOLI-4-RT
TRIPOLI-4-D®
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Post-Treatment
TRIPOLI-4-RT
Cyril Dieudonné 25CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
1. Test case presentation
FIRST RESULTS
Burn-up
Burn-up Burn-upCorrelatedSampling
CorrelatedSampling
tracks.root
TransportBurn-upTransport
Post-Treatment
TRIPOLI-4-RT
TRIPOLI-4-D®
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Cyril Dieudonné 26
FIRST RESULT
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. Validation of method
U235 perturbated concentrationis compatible to the referenceeven over many time step
There is no huge varianceincrease over those time steps
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Cyril Dieudonné 27
FIRST RESULT
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. Validation of method
After 40 GWd/t :systematic error
How to correct it ?
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Cyril Dieudonné 28
FIRST RESULT
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. Validation of method
More simulator does not work
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Cyril Dieudonné 29
FIRST RESULT
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. Validation of method
More neutron does work !
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Cyril Dieudonné 30
FIRST RESULT
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. Validation of method
Importance of a good representationof all possible events to ensure
the smallest statistical and systematic error possiblealong the different time steps !
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Cyril Dieudonné 31
FIRST RESULT
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
3. Performance analysis
Improvement of F.O.M. : 1.5 (even rigth now without optimization)This factor can go up to 3 with optimization
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Cyril Dieudonné 32
FIRST RESULT
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
3. Performance analysis
Improvement of F.O.M. : 1.5 (even rigth now without optimization)This factor can go up to 3 with optimization
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Cyril Dieudonné 33
FIRST RESULT
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
3. Performance analysis
Hope to gain an order of magnitude on the F.O.M.
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Cyril Dieudonné 34CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
4. Optimization and development
FIRST RESULT
TRIPOLI-4-D®
T B T B T B T B
CSP-T
BCSP-T
BCSP-T
T B
BCSP-T
How to define the best calculation scheme ?
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Cyril Dieudonné 35CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
4. Optimization and development
FIRST RESULT
T B T B T B B
CSP-T
B CSP-T
B CSP-T
T B
B CSP-T
T
How to define the best calculation scheme ? Generate several tracks files
TRIPOLI-4-D®
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Cyril Dieudonné 36CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
4. Optimization and development
FIRST RESULT
T B T B T B B
CSP-T
B CSP-T
B CSP-T
T B
B CSP-T
T
How to define the best calculation scheme ? Generate several tracks files Using optimized set of concentration TRIPOLI-4-D®
? T ? T
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Cyril Dieudonné 37
IVCONCLUSION AND FURTHER WORK
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
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Cyril Dieudonné 38
CONCLUSION
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
Development of a new acceleration technique for Monte Carlo burn-up simulations
Implementation in TRIPOLI-4-D®
First results validates the method
Preliminary results for acceleration seems promising! « as is » implementation reveals ≈ factor 1.5 in F.O.M.
improvement step-by-step F.O.M. give hope for an order of magnitude
in acceleration (see further work)
The method can be generalized to other perturbation techniques (eg Taylors series)
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Cyril Dieudonné 39
FURTHER WORK
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
Computing optimization : Acceleration of nuclear data reading Tracks keeping in RAM
Optimization of the calculation scheme : Variance reduction technique (based either on Monte
Carlo or deterministic pre-calculations) :Choice of a best initial set of tracks
Calculation scheme based either on :• full Correlated Sampling• successive sequence between Monte Carlo and Correlated Sampling• insertion in pre-existing scheme like predictor/corrector
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Cyril Dieudonné 40
THANK YOU FOR YOUR ATTENTION
[1] M. Moriwaki, « Multi-Assembly Analysis with an AdvanceCorrelated Sampling Method », J. Nucl. Sci. Technol., 40[7], 905 (2003)
[2] M. Moriwaki, M. Aoyama, « Improvement of Monte Carlo Lattice Burnup Calculation Performance with the Correlated Sampling Method », J. Nucl. Sci. Technol., 39[6], 587, (2002)
[3] H. Rief, « Generalized Monte Carlo Perturbation Algorithms for Correlated Sampling and Second-OrderTaylor Series Approach », Ann. Nucl. Energy, 11[9], 455 (1984)
[4] B. Su, T. He, « Enhanced Correlated Sampling by Source Biaising for Pin Diversion Analysis », Trans. of the ANS, 102 (2010)
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
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Cyril Dieudonné 41CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
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Cyril Dieudonné 42
ANNAXE ITHEORETICAL ANALYZES
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
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Cyril Dieudonné 43
THEORETICAL ANALYZES
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
1. Test case description
Hypothesis : Infinite, homogeneous and isotropic volume N isotope(s) Monokinetic transport Initial simulation without biasing
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Cyril Dieudonné - MIPEGE 44
FIRST RESULTS
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. Theoretical analyze of correlated sampling
Theoretical mean :
Theoretical variance :
Correction of weigth :
11
1 1
1t m
m
mm mit m
m i t
S e dx dx p p
2
2 22 2 1
11 1
1t m
m
mm mit m
m i t
S S e dx dx p p S
1 01
0, t t n
n
cs tn
t
n e
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Cyril Dieudonné 45CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
3. First theoretical results
THEORETICAL ANALYZES
N1 / N0 N1 / N0
N1
N1
N0
N0
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Cyril Dieudonné 46CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
3. First theoretical results
THEORETICAL ANALYZES
N1 / N0
p
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Cyril Dieudonné 47CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
3. First theoretical results
THEORETICAL ANALYZES
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Cyril Dieudonné 48
ANNAXE IIROOT-TOOLS DEVELOPMENT
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
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Cyril Dieudonné 49CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
1. Development of Tripoli-4-RT library
ROOT-TOOLS DEVELOPMENT
CorrelatedSampling
Tripoli-4
Transport
tracks.root
Post-Treatment
Tripoli-4-RT
Developments : ::T4_NuclearDataList( file.ace )
Reading ACE nuclear data ::T4_Geometry( file.root )
Reading geometry ::T4_Response( reaction_rate, … )
New responses available
::T4_ScoreList( … )Simultaneous computation of scores
::T4_CSMethod( … )ROOT tracks perturbation
…
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Cyril Dieudonné - MIPEGE 50
ROOT-TOOLS DEVELOPMENT
CEA SaclayDEN/DANS/DM2S/SERMA/LTSD
2. Study of realistic cases
Unique qualification factor :
2
1. . .F O Mt