Difference between revisions of "Delta- and surface-tracking"

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(Transport algorithm in Monte Carlo simulation)
(Transport algorithm in Monte Carlo simulation)
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Tracking is most typically carried out in a [[Constructive solid geometry type|constructive solid geometry (CSG)]], composed of homogeneous material cells, which are defined by combinations of elementary and derived surface types. Serpent 2 also has two advanced geometry types, based on [[CAD-based geometry type|STL format CAD models]] and an [[Unstructured mesh-based geometry type|unstructured polyhedral mesh]]. 
 
Tracking is most typically carried out in a [[Constructive solid geometry type|constructive solid geometry (CSG)]], composed of homogeneous material cells, which are defined by combinations of elementary and derived surface types. Serpent 2 also has two advanced geometry types, based on [[CAD-based geometry type|STL format CAD models]] and an [[Unstructured mesh-based geometry type|unstructured polyhedral mesh]]. 
  
The transport simulation follows a random walk from one interaction to the next, using a simple procedure:
+
The transport simulation follows a random walk from one interaction to the next. The procedure can be described as follows:
 
#Sample path length (distance to next collision)
 
#Sample path length (distance to next collision)
 
#Transport neutron to the collision point
 
#Transport neutron to the collision point
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If the sampled interaction is scattering, the procedure restarts from beginning by sampling the
 
If the sampled interaction is scattering, the procedure restarts from beginning by sampling the
 
distance to the next collision. The direction and energy are changed in the scattering event.
 
distance to the next collision. The direction and energy are changed in the scattering event.
 +
 
The fact that the particle may cross the boundary between two material regions means that the
 
The fact that the particle may cross the boundary between two material regions means that the
 
interaction probability changes along the sampled path. This must be taken into account by
 
interaction probability changes along the sampled path. This must be taken into account by
 
stopping the track at the boundary crossing and sampling a new path length according to the new
 
stopping the track at the boundary crossing and sampling a new path length according to the new
interaction probability.14
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interaction probability.
The different steps of the simulated random walk are covered in the following
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+
 
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<math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>
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== Surface- and delta-tracking ==
 
== Surface- and delta-tracking ==

Revision as of 15:39, 19 November 2015

This a brief description on the delta-tracking based transport routine used in Serpent. The method is also used by other Monte Carlo codes, most notably in the HOLE geometry package in MONK and MCBEND. The original delta-tracking algorithm was introduced by Woodcock in 1965,[1] and a mathematical verification was derived by Coleman in 1968.[2] Delta-tracking is well described in a text book by Lux and Koblinger,[3] and a description of the methodology used in Serpent is found in an article in Annals of Nuclear Energy from 2010.[4]

The input parameters related to delta-tracking are:

  • set dt - sets the probability threshold used for selecting between surface- and delta-tracking
  • set forcedt - enforces the use of delta-tracking in a given list of materials
  • set blockdt - enforces the use of surface-tracking in a given list of materials
  • set minxs - definse the mean-free-path of collisions used to score the collision flux estimator

The output parameters are:

  • TODO


Transport algorithm in Monte Carlo simulation

The Monte Carlo simulation consists of a large number particle histories, in which the random walk of an individual particle is followed, or tracked, through the geometry from its birth to eventual absorption or escape. Tracking is most typically carried out in a constructive solid geometry (CSG), composed of homogeneous material cells, which are defined by combinations of elementary and derived surface types. Serpent 2 also has two advanced geometry types, based on STL format CAD models and an unstructured polyhedral mesh

The transport simulation follows a random walk from one interaction to the next. The procedure can be described as follows:

  1. Sample path length (distance to next collision)
  2. Transport neutron to the collision point
  3. Sample interaction

If the sampled interaction is scattering, the procedure restarts from beginning by sampling the distance to the next collision. The direction and energy are changed in the scattering event.

The fact that the particle may cross the boundary between two material regions means that the interaction probability changes along the sampled path. This must be taken into account by stopping the track at the boundary crossing and sampling a new path length according to the new interaction probability.

Surface- and delta-tracking

Hybrid method used in Serpent

Advantages and limitations

References

  1. ^ Woodcock, E. R., Murphy, T., Hemmings, P. J., and Longworth, T. C. "Techniques used in the GEM code for Monte Carlo neutronics calculations in reactors and other systems of complex geometry." ANL-7050, Argonne National Laboratory, 1965.
  2. ^ Coleman, W. A. "Mathematical verification of a certain Monte Carlo sampling technique and applications of the technique to radiation transport problems." Nucl. Sci. Eng., 31 (1968) 76–81.
  3. ^ Lux, I. and Koblinger, L. "Monte Carlo Particle Transport Methods: Neutron and Photon Calculations." CRC Press, Inc. (1991).
  4. ^ Leppänen, J. "Performance of Woodcock delta-tracking in lattice physics applications using the Serpent Monte Carlo reactor physics burnup calculation code." Ann. Nucl. Energy 37 (2010) 715–722.