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Define terms in flux equation for depletion docs

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Paul Romano 2022-08-16 22:18:55 -05:00
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16
docs/source/usersguide/depletion.rst
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@ -319,16 +319,18 @@ normalizing reaction rates:
.. math::
\phi = \frac{P}{V \cdot \sum\limits_i (Q_i \cdot \sigma^f_i \cdot n_i)}
\phi = \frac{P}{\sum\limits_i (Q_i \sigma^f_i n_i)}
where :math:`\sum_i` is the sum over all nuclides :math:`i`. This equation
makes the same assumptions and issues as discussed in
:ref:`energy-deposition`. Unfortunately, the proposed solution in that
where :math:`P` is the power, :math:`Q_i` is the fission Q value for nuclide
:math:`i`, :math:`\sigma_i^f` is the microscopic fission cross section for
nuclide :math:`i`, and :math:`N_i` is the number of atoms of nuclide
:math:`i`. This equation makes the same assumptions and issues as discussed
in :ref:`energy-deposition`. Unfortunately, the proposed solution in that
section does not apply here since we are decoupled from transport code.
However, there is a method to converge to a more accurate value for flux by
using substeps during time integration.
`This paper <https://doi.org/10.1016/j.anucene.2016.05.031>`_ provides a
good discussion of this method.
using substeps during time integration. `This paper
<https://doi.org/10.1016/j.anucene.2016.05.031>`_ provides a good discussion
of this method.
.. warning::