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

Cyril Dieudonné 3

IMONTE CARLO BURN-UP CODE ACCELERATIONUSING THE CORRELATED SAMPLING METHOD


Cyril Dieudonné 4

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

Cyril Dieudonné 5




TRIPOLI-4-D®

Mendel®

Burn-up

TRIPOLI-4®

Transport

Mendel®

Burn-up

TRIPOLI-4®

Transport

Cyril Dieudonné 6




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





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

0

0 ( )MM

E X xp x dx= ∫

( )1

1

1( )MM

E X xp x dx= ∫





( )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

=

=

=

∫

∫

∫


1

0

( )( )( )

cs p xxp x

ω =

Correction weight due to 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

0

( )( )( )

cs p xxp x

ω =

* 00 *

0

( )( )( )

p xxp x

ω =


Correction weight due to biaising technique :




( )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→ + + +→ +

→ + + +

= =


1

0

( )( )( )

cs p xxp x

ω =

* 00 *

0

( )( )( )

p xxp x

ω =


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 ?

Cyril Dieudonné 17

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®

Cyril Dieudonné 22

IIIFIRST RESULTS


Cyril Dieudonné 23

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 ?

2

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®

Cyril Dieudonné 26

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

Cyril Dieudonné 27

FIRST RESULT



After 40 GWd/t :systematic error

How to correct it ?

Cyril Dieudonné 28

FIRST RESULT



More simulator does not work

Cyril Dieudonné 29

FIRST RESULT



More neutron does work !

Cyril Dieudonné 30

FIRST RESULT



Importance of a good representationof all possible events to ensure

the smallest statistical and systematic error possiblealong the different time steps !

Cyril Dieudonné 31

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

Cyril Dieudonné 32

FIRST RESULT



Improvement of F.O.M. : 1.5 (even rigth now without optimization)This factor can go up to 3 with optimization

Cyril Dieudonné 33

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

CSP-T

BCSP-T

BCSP-T

T B

BCSP-T

How to define the best calculation scheme ?



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®



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

Cyril Dieudonné 37

IVCONCLUSION AND FURTHER WORK


Cyril Dieudonné 38

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)

Cyril Dieudonné 39

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

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)



Cyril Dieudonné 42

ANNAXE ITHEORETICAL ANALYZES


Cyril Dieudonné 43

THEORETICAL ANALYZES


1. Test case description

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

Cyril Dieudonné - MIPEGE 44

FIRST RESULTS


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


3. First theoretical results


N1 / N0 N1 / N0

N1

N1

N0

N0




N1 / N0

p




Cyril Dieudonné 48

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 :

2

1. . .F O Mt

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