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Added description of filters and scores methodology.

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Paul Romano 2012-08-03 11:43:19 -04:00
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docs/source/methods/tallies.rst
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@ -8,10 +8,56 @@ Tallies
Filters and Scores
------------------
The tally capability in OpenMC takes a similar philosophy as that employed in
the MC21_ Monte Carlo code to give maximum flexibility in specifying tallies
while still maintaining scalability. Any tally in a Monte Carlo simulation can
be written in the following form:
.. math::
:label: tally-integral
X = \underbrace{\int d\mathbf{r} \int d\mathbf{\Omega} \int
dE}_{\text{filters}} \underbrace{f(\mathbf{r}, \mathbf{\Omega},
E)}_{\text{scores}} \psi (\mathbf{r}, \mathbf{\Omega}, E)
A user can specify one or more filters which identify which regions of phase
space should score to a given tally (the limits of integration as shown in
equation :eq:`tally-integral`) as well as the scoring function (:math:`f` in
equation :eq:`tally-integral`). For example, if the desired tally was the
:math:`(n,\gamma)` reaction rate in a fuel pin, the filter would specify the
cell which contains the fuel pin and the scoring function would be the radiative
capture macroscopic cross section. The following quantities can be scored in
OpenMC: flux, total reaction rate, scattering reaction rate, neutron production
from scattering, higher scattering moments, (n,xn) reaction rates, absorption
reaction rate, fission reaction rate, neutron production rate from fission, and
surface currents. The following variables can be used as filters: universe,
material, cell, birth cell, surface, mesh, pre-collision energy, and
post-collision energy.
With filters for pre- and post-collision energy and scoring functions for
scattering and fission production, it is possible to use OpenMC to generate
cross sections with user-defined group structures. These multigroup cross
sections can subsequently be used in deterministic solvers such as coarse-mesh
finite difference (CMFD) diffusion.
------------------------------
Using Maps for Filter-Matching
------------------------------
Some Monte Carlo codes suffer severe performance penalties when tallying a large
number of quantities. Care must be taken to ensure that a tally system scales
well with the total number of tally bins. In OpenMC, a mapping technique is used
that allows for a fast determination of what tally/bin combinations need to be
scored to a given particle's phase space coordinates. For each discrete filter
variable, a list is stored that contains the tally/bin combinations that could
be scored to for each value of the filter variable. If a particle is in cell
:math:`n`, the mapping would identify what tally/bin combinations specify cell
:math:`n` for the cell filter variable. In this manner, it is not necessary to
check the phase space variables against each tally. Note that this technique
only applies to discrete filter variables and cannot be applied to energy
bins. For energy filters, it is necessary to perform a binary search on the
specified energy grid.
-----------------------------------------
Volume-Integrated Flux and Reaction Rates
@ -22,7 +68,6 @@ simulation is the flux or a reaction rate integrated over a finite volume. The
volume may be a particular cell, a collection of cells, or the entire
geometry. There are various methods by which we can estimate reaction rates
----------------
Analog Estimator
----------------
@ -44,7 +89,6 @@ and :math:`w_i` is the pre-collision weight of the particle as it enters event
volume-integrated so if we want a volume-averaged quantity, we need to divided
by the volume of the region of integration.
-------------------
Collision Estimator
-------------------
@ -88,7 +132,6 @@ equation :eq:`analog-estimator`, we see that the collision estimate will result
in a tally with a larger number of events that score to it with smaller
contributions (since we have multiplied it by :math:`\Sigma_x / \Sigma_t`).
----------------------
Track-length Estimator
----------------------
@ -157,3 +200,5 @@ had a collision at every event. Thus, for tallies with outgoing-energy filters
---------------
Surface Current
---------------
.. _MC21: http://www.osti.gov/bridge/servlets/purl/903083-HT5p1o/903083.pdf