From 17a3aadfa5c9c781a71a4cb944dd6c710d1b5306 Mon Sep 17 00:00:00 2001 From: Paul Romano Date: Mon, 20 Apr 2020 11:50:34 -0500 Subject: [PATCH] Fix placement of normalization factor. Fix link in depletion methods --- docs/source/methods/depletion.rst | 13 ++++++------- docs/source/usersguide/tallies.rst | 10 ++++++---- 2 files changed, 12 insertions(+), 11 deletions(-) diff --git a/docs/source/methods/depletion.rst b/docs/source/methods/depletion.rst index 903d3e5af5..ebd238eaa6 100644 --- a/docs/source/methods/depletion.rst +++ b/docs/source/methods/depletion.rst @@ -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 `_, `2 `_), to evaluate matrix exponentials. In -particular, OpenMC utilizes an `incomplete partial fraction `_ (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 +`_ (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 `_ contains a -typo): +original description of the algorithm presented by `Pusa +`_ 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 ------------------- diff --git a/docs/source/usersguide/tallies.rst b/docs/source/usersguide/tallies.rst index 4856bad01f..75ca142ba4 100644 --- a/docs/source/usersguide/tallies.rst +++ b/docs/source/usersguide/tallies.rst @@ -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: