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Merge pull request #1547 from paulromano/more-doc-fixes

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Fix placement of normalization factor. Fix link in depletion methods
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Andrew Johnson 2020-04-20 19:07:01 -04:00 • committed by GitHub
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2 changed files with 12 additions and 11 deletions
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13
docs/source/methods/depletion.rst
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@ -132,9 +132,10 @@ more matrix exponentials. OpenMC uses the Chebyshev rational approximation
method (CRAM), which was introduced in a series of papers by Pusa (`1
<https://doi.org/10.13182/NSE09-14>`_, `2
<https://doi.org/10.13182/NSE10-81>`_), to evaluate matrix exponentials. In
particular, OpenMC utilizes an `incomplete partial fraction <cram_ipf>`_ (IPF)
form of CRAM that provides a good balance of numerical stability and efficiency.
In this representation the matrix exponential is approximated as
particular, OpenMC utilizes an `incomplete partial fraction
<https://doi.org/10.13182/NSE15-26>`_ (IPF) form of CRAM that provides a good
balance of numerical stability and efficiency. In this representation the matrix
exponential is approximated as
.. math::
@ -147,8 +148,8 @@ where :math:`k` is the order of the approximation and :math:`\alpha_0`,
have been tabulated for orders up to :math:`k=48`. Rather than computing the
full approximation and then multiplying it by a vector, the following algorithm
is used to incrementally apply the terms within the product (note that the
original description of the algorithm presented by `Pusa <cram_ipf>`_ contains a
typo):
original description of the algorithm presented by `Pusa
<https://doi.org/10.13182/NSE15-26>`_ contains a typo):
1. :math:`\mathbf{n} \gets \mathbf{n_0}`
2. For :math:`\ell = 1, 2, \dots, k/2`
@ -162,8 +163,6 @@ The :math:`k`\ th order approximation for CRAM requires solving :math:`k/2`
sparse linear systems. OpenMC relies on functionality from
:mod:`scipy.sparse.linalg` for solving the linear systems.
.. _cram_ipf: https://doi.org/10.13182/NSE15-26
-------------------
Data Considerations
-------------------

10
docs/source/usersguide/tallies.rst
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@ -348,13 +348,15 @@ factor that can be applied to other tallies:
f = \frac{P}{H'} = \frac{[\text{J}/\text{s}]}{[\text{J}/\text{source}]} =
\left [ \frac{\text{source}}{\text{s}} \right ].
With this normalization factor, we can then get the flux in typical units:
Multiplying by the normalization factor and dividing by volume, we can then get
the flux in typical units:
.. math::
\phi' = \frac{\phi}{fV} = \frac{[\text{particle-cm}/\text{source}]}
{[\text{source}/\text{s}][\text{cm}^3]} = \left [
\frac{\text{particle}}{\text{cm}^2\cdot\text{s}} \right ]
\phi' = \frac{f\phi}{V} =
\frac{[\text{source}/\text{s}][\text{particle-cm}/\text{source}]}
{[\text{cm}^3]} = \left [\frac{\text{particle}}{\text{cm}^2\cdot\text{s}}
\right ]
There are several slight variations on this procedure: