M CARLO BURN UP CODE CCELERATION USING THE … · using the Correlated Sampling method 1. Monte...

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

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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IMONTE CARLO BURN-UP CODE ACCELERATIONUSING THE CORRELATED SAMPLING METHOD

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MONTE CARLO BURN-UP CODE USING THE CORRELATED SAMPLING METHOD

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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TRIPOLI-4-D®

Mendel®

Burn-up

TRIPOLI-4®

Transport

Mendel®

Burn-up

TRIPOLI-4®

Transport

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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

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

Initial medium

Perturbated medium n°1

Perturbated medium n°2

0 ( )MM

E X xp x dx= ∫

1( )MM

E X xp x dx= ∫

0 ( )MM

E X xp x dx= ∫

1( )( )

E X xp x dx

x p x dx

( )( )( )

cs p xxp x

Correction weight due to correlated sampling method :

0 ( )MM

E X xp x dx= ∫

( )( )

( ) )) (cs

p xp x

E X xp x dx

x p x dx

p xp x

x xω ω

( )( )( )

cs p xxp x

* 00 *

( )( )( )

p xxp x

Correction weight due to biaising technique :

0 ( )MM

E X xp x dx= ∫

( )( )

( ) )) (cs

p xp x

E X xp 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→ + + +→ +

→ + + +

( )( )( )

cs p xxp x

* 00 *

( )( )( )

p xxp x

Correction weight due to biaising technique :

Weight modification given by this equation :

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 :

time step 1

timestep N

Simulation n°1

Simulation n°N

Application of the correlated sampling methodto Monte Carlo burn-up codes :

Simulation n°1

Simulation n°1 perturbated

time step 1

timestep N

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 !

How does this compromise betweenVariance and Calculation Time scalealong the different burnup steps ?

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IICONCRETE ALGORITHM

AND CODE DEVELOPMENT

TRIPOLI-4-D®

Burn-upTransportBurn-up

1. Development of a post-treatment module : TRIPOLI-4-RT

CONCRETE ALGORITHM AND CODE DEVELOPMENT

Transport

tracks.root

TRIPOLI-4-D®

1. Development of a post-treatment module : TRIPOLI-4-RT

CorrelatedSampling

tracks.root

Post-Treatment

TRIPOLI-4-RT

Transport

TRIPOLI-4-D®

Post-Treatment

TRIPOLI-4-RT

2. Linking TRIPOLI-4-RT with TRIPOLI-4-D®

Burn-up Burn-upCorrelatedSampling

CorrelatedSampling

tracks.root

Post-Treatment

TRIPOLI-4-RT

Transport

Post-Treatment

TRIPOLI-4-RT

3. Basic scheme implementation of the method in TRIPOLI-4-D®

Burn-up

CorrelatedSampling

tracks.root

TransportBurn-upTransport

Post-Treatment

TRIPOLI-4-RT

TRIPOLI-4-D®

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IIIFIRST RESULTS

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FIRST RESULT

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 ?

1. . .F O Mt

Post-Treatment

TRIPOLI-4-RT

FIRST RESULTS

Burn-up

CorrelatedSampling

tracks.root

Post-Treatment

TRIPOLI-4-RT

TRIPOLI-4-D®

Post-Treatment

TRIPOLI-4-RT

FIRST RESULTS

Burn-up

CorrelatedSampling

tracks.root

Post-Treatment

TRIPOLI-4-RT

TRIPOLI-4-D®

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FIRST RESULT

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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FIRST RESULT

After 40 GWd/t :systematic error

How to correct it ?

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FIRST RESULT

More simulator does not work

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FIRST RESULT

More neutron does work !

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FIRST RESULT

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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FIRST RESULT

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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FIRST RESULT

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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FIRST RESULT

Hope to gain an order of magnitude on the F.O.M.

4. Optimization and development

FIRST RESULT

TRIPOLI-4-D®

T B T B T B T B

BCSP-T

How to define the best calculation scheme ?

FIRST RESULT

T B T B T B B

B CSP-T

How to define the best calculation scheme ? Generate several tracks files

TRIPOLI-4-D®

FIRST RESULT

T B T B T B B

B CSP-T

How to define the best calculation scheme ? Generate several tracks files Using optimized set of concentration TRIPOLI-4-D®

? T ? T

Cyril Dieudonné 37

IVCONCLUSION AND FURTHER WORK

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CONCLUSION

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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FURTHER WORK

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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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)

Cyril Dieudonné 42

ANNAXE ITHEORETICAL ANALYZES

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THEORETICAL ANALYZES

1. Test case description

Hypothesis : Infinite, homogeneous and isotropic volume N isotope(s) Monokinetic transport Initial simulation without biasing

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FIRST RESULTS

2. Theoretical analyze of correlated sampling

Theoretical mean :

Theoretical variance :

Correction of weigth :

mm mit m

S e dx dx p p

2 22 2 1

mm mit m

S S e dx dx p p S

0, t t n

3. First theoretical results

N1 / N0 N1 / N0

N1 / N0

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ANNAXE IIROOT-TOOLS DEVELOPMENT

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

Cyril Dieudonné - MIPEGE 50

ROOT-TOOLS DEVELOPMENT

2. Study of realistic cases

Unique qualification factor :

1. . .F O Mt

M CARLO BURN UP CODE CCELERATION USING THE … · using the Correlated Sampling method 1. Monte...

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