Difference between revisions of "Variance reduction"

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Variance reduction in Serpent is based on standard weight-window techniques, described <ref>Lux, I. and Koblinger, L. ''"Monte Carlo Particle Transport Methods: Neutron and Photon Calculations."'' CRC-Press, 1991. [https://gnssn.iaea.org/NSNI/Shared%20Documents/OPEN%20Shared%20Files/MonteCarloParticleTransportMethodsNeutronAndPhotonCalculations.pdf (available on-line]).</ref>
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Variance reduction in Serpent is based on standard weight-window techniques.<ref>Lux, I. and Koblinger, L. ''"Monte Carlo Particle Transport Methods: Neutron and Photon Calculations."'' CRC-Press, 1991. [https://gnssn.iaea.org/NSNI/Shared%20Documents/OPEN%20Shared%20Files/MonteCarloParticleTransportMethodsNeutronAndPhotonCalculations.pdf (available on-line]).</ref> The weight window mesh and additional parameters are defined using the [[Input syntax manual#wwin (weight window mesh definition)|wwin card]]. Serpent supports two mesh types:
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*Weight-window mesh generated using the built-in response matrix method-based solver (see the [[Input syntax manual#wwgen (response matrix based importance map solver)|wgen card]]).
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*MCNP WWINP format weight window-mesh.<ref> D. Pelowitz (ed.), ''“MCNP6 User’s Manual: Appendix C Mesh-Based WWINP, WWOUT, and WWONE File Format,”'' LA-CP-13-00634, Los Alamos National Laboratory (2013).</ref>
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This tutorial demonstrates the basic functionality of the built-in solver. The methodology is described in the related publications.<ref>J. Leppänen ''"Response Matrix Method–Based Importance Solver and Variance Reduction Scheme in the Serpent 2 Monte Carlo Code."'' Nucl. Technol. [https://doi.org/10.1080/00295450.2019.1603710 (in press)]</ref><ref>J. Leppänen and M. Jokipii. ''"Global Variance Reduction Scheme with Self-Adaptive Weight-Window Mesh in the Serpent 2 Monte Carlo Code."'' In Proc. M&C2019, Portland, OR, Aug. 25-29, 2019.</ref>
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== Test case ==
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The test case is comprised of an isotropic, point-wise, low-energy neutron source, enclosed inside two cylindrical shields made of steel and concrete. The geometry is in 2D for the sake of simplicity, but the same procedures apply to 3D problems as well. The geometry plot and complete input listing are provided below (click Expand to show).
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[[File:VR_Ref_geom1.png|frameless|200px]]
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<div class="toccolours mw-collapsible mw-collapsed" style="width:60em;">
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'''Completely made-up neutron shielding problem'''
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<div class="mw-collapsible-content">
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  % --- Geometry (nested cylinders)
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surf 1 cyl 0.0 0.0 100.0
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surf 2 cyl 0.0 0.0 120.0
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surf 3 cyl 0.0 0.0 200.0
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surf 4 cyl 0.0 0.0 300.0
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surf 5 sqc 0.0 0.0 400.0
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cell 1 0 air      -1
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cell 2 0 steel    1 -2
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cell 3 0 air      2 -3
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cell 4 0 concrete  3 -4
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cell 5 0 air      4 -5
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cell 6 0 outside  5
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% --- Materials
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mat steel    -8.00000E+00  rgb 100 100 100
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  6000.03c    -4.00000E-04
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14000.03c    -5.00000E-03
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15031.03c    -2.30000E-04
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16000.03c    -1.50000E-04
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24000.03c    -1.90000E-01
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25055.03c    -1.00000E-02
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26000.03c    -7.01730E-01
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28000.03c    -9.25000E-02
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mat air      -1.20500E-03  rgb 255 255 220
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  6000.03c    -1.24000E-04
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  7014.03c    -7.55268E-01
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  8016.03c    -2.31781E-01
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18040.03c    -1.28270E-02
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mat concrete -2.30000E+00  rgb 180 180 180
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  1001.03c    -1.00000E-02
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  8016.03c    -5.32000E-01
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11023.03c    -2.90000E-02
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13027.03c    -3.40000E-02
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14000.03c    -3.37000E-01
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20000.03c    -4.40000E-02
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26000.03c    -1.40000E-02
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% --- Source
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src 1 sp 0 0 0 se 1E-6    % Isotropic 1 eV point source
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set srcrate 1              % Normalize to unit source rate
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% --- Run parameters
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set nps 200000 50
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set gcu -1                % Group constant generation off
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% --- Geometry plot:
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plot 3 500 500
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% --- Mesh plot (flux)
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det F1                    % Flux detector
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mesh 8 -4 F1 3 500 500    % Plot detector scores
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% --- Detectors
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det d1 dc 3                % Flux in airspace between walls
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surf s2 cyl 0.0 160.0 5.0 
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det d2 dtl s2              % Flux at y = 160 (between the walls)
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surf s3 cyl 0.0 350.0 5.0 
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det d3 dtl s3              % Flux at y = 350 (outside the concrete wall)
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</div>
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</div>
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== References ==
 
== References ==

Revision as of 14:16, 4 October 2019

Variance reduction in Serpent is based on standard weight-window techniques.[1] The weight window mesh and additional parameters are defined using the wwin card. Serpent supports two mesh types:

  • Weight-window mesh generated using the built-in response matrix method-based solver (see the wgen card).
  • MCNP WWINP format weight window-mesh.[2]

This tutorial demonstrates the basic functionality of the built-in solver. The methodology is described in the related publications.[3][4]


Test case

The test case is comprised of an isotropic, point-wise, low-energy neutron source, enclosed inside two cylindrical shields made of steel and concrete. The geometry is in 2D for the sake of simplicity, but the same procedures apply to 3D problems as well. The geometry plot and complete input listing are provided below (click Expand to show).

VR Ref geom1.png

Completely made-up neutron shielding problem 

 % --- Geometry (nested cylinders)

surf 1 cyl 0.0 0.0 100.0
surf 2 cyl 0.0 0.0 120.0
surf 3 cyl 0.0 0.0 200.0
surf 4 cyl 0.0 0.0 300.0
surf 5 sqc 0.0 0.0 400.0

cell 1 0 air      -1
cell 2 0 steel     1 -2
cell 3 0 air       2 -3
cell 4 0 concrete  3 -4
cell 5 0 air       4 -5
cell 6 0 outside   5

% --- Materials

mat steel    -8.00000E+00  rgb 100 100 100

 6000.03c    -4.00000E-04
14000.03c    -5.00000E-03
15031.03c    -2.30000E-04
16000.03c    -1.50000E-04
24000.03c    -1.90000E-01
25055.03c    -1.00000E-02
26000.03c    -7.01730E-01
28000.03c    -9.25000E-02

mat air      -1.20500E-03  rgb 255 255 220

 6000.03c    -1.24000E-04
 7014.03c    -7.55268E-01
 8016.03c    -2.31781E-01
18040.03c    -1.28270E-02

mat concrete -2.30000E+00  rgb 180 180 180

 1001.03c    -1.00000E-02
 8016.03c    -5.32000E-01
11023.03c    -2.90000E-02
13027.03c    -3.40000E-02
14000.03c    -3.37000E-01
20000.03c    -4.40000E-02
26000.03c    -1.40000E-02

% --- Source 

src 1 sp 0 0 0 se 1E-6     % Isotropic 1 eV point source
set srcrate 1              % Normalize to unit source rate

% --- Run parameters

set nps 200000 50
set gcu -1                 % Group constant generation off

% --- Geometry plot:

plot 3 500 500

% --- Mesh plot (flux)

det F1                     % Flux detector
mesh 8 -4 F1 3 500 500     % Plot detector scores

% --- Detectors

det d1 dc 3                % Flux in airspace between walls

surf s2 cyl 0.0 160.0 5.0  
det d2 dtl s2              % Flux at y = 160 (between the walls)

surf s3 cyl 0.0 350.0 5.0  
det d3 dtl s3              % Flux at y = 350 (outside the concrete wall)


References

  1. ^ Lux, I. and Koblinger, L. "Monte Carlo Particle Transport Methods: Neutron and Photon Calculations." CRC-Press, 1991. (available on-line).
  2. ^ D. Pelowitz (ed.), “MCNP6 User’s Manual: Appendix C Mesh-Based WWINP, WWOUT, and WWONE File Format,” LA-CP-13-00634, Los Alamos National Laboratory (2013).
  3. ^ J. Leppänen "Response Matrix Method–Based Importance Solver and Variance Reduction Scheme in the Serpent 2 Monte Carlo Code." Nucl. Technol. (in press)
  4. ^ J. Leppänen and M. Jokipii. "Global Variance Reduction Scheme with Self-Adaptive Weight-Window Mesh in the Serpent 2 Monte Carlo Code." In Proc. M&C2019, Portland, OR, Aug. 25-29, 2019.
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