Fixes to documentation

This commit is contained in:
Paul Romano 2015-02-16 20:08:35 -05:00
parent efb3ca0406
commit dab1c2aef3
6 changed files with 52 additions and 2391 deletions

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@ -28,7 +28,7 @@ directions. An example of this is shown in the following expression:
:label: not1
\sum\limits_{u\in(x,y,z)}\left\langle\overline{J}^{u,g}_{l+1/2,m,n}
\Delta_m^v\Delta_n^w\right\rangle
\Delta_m^v\Delta_n^w\right\rangle
Here, :math:`u` takes on each direction one at a time. The parameter :math:`J`
is surface area-averaged over the transverse indices :math:`m` and :math:`n`
@ -142,7 +142,7 @@ defined from MC tallies as follows:
{\left\langle\overline{\overline\phi}_{l,m,n}^h
\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle}
and
and
.. math::
:label: xs3
@ -306,7 +306,7 @@ interior cell,
+ \left(\tilde{D}_{l-1/2,m,n}^{u,g} +
\tilde{D}_{l+1/2,m,n}^{u,g} - \hat{D}_{l-1/2,m,n}^{u,g} +
\hat{D}_{l+1/2,m,n}^{u,g}\right)\overline{\overline{\phi}}_{l,m,n}^g
\\ +
\\ +
\left. \left(-\tilde{D}_{l+1/2,m,n}^{u,g} +
\hat{D}_{l+1/2,m,n}^{u,g}\right)\overline{\overline{\phi}}_{l+1,m,n}^g
\right] +
@ -318,7 +318,7 @@ interior cell,
It should be noted that before substitution, eq. :eq:`eq_neut_bal` was divided
by the volume of the cell, :math:`\Delta_l^u\Delta_m^v\Delta_n^w`. Equation
:eq:`eq_cmfd_sys` can be represented in operator form as
:eq:`eq_cmfd_sys` can be represented in operator form as
.. math::
:label: eq_CMFDopers
@ -349,7 +349,7 @@ and energy group. This is represented as
p_{l,m,n}^g =
\frac{\sum_{h=1}^{G}\overline{\overline{\nu_f\Sigma}}^{h\rightarrow
g}_{f_{l,m,n}}\overline{\overline{\phi}}_{l,m,n}^h\Delta_l^u\Delta_m^v
\Delta_n^w}{\sum_n\sum_m\sum_l\sum_{h=1}^{G}\overline{
\Delta_n^w}{\sum_n\sum_m\sum_l\sum_{h=1}^{G}\overline{
\overline{\nu_f\Sigma}}^{h\rightarrow
g}_{f_{l,m,n}}\overline{\overline{\phi}}_{l,m,n}^h\Delta_l^u\Delta_m^v
\Delta_n^w}.
@ -478,14 +478,14 @@ no fission neutrons appear with energies in the thermal group.
.. figure:: ../_images/loss.png
:scale: 50
Sparsity of Neutron Loss Operator
Sparsity of Neutron Loss Operator
.. _fig_prod:
.. figure:: ../_images/prod.png
:scale: 50
Sparsity of Neutron Production Operator
Sparsity of Neutron Production Operator
To solve the eigenvalue problem with these matrices, different source iteration
and linear solvers can be used. The most common source iteration solver used is
@ -511,7 +511,7 @@ implemented to obtain eigenvalue and multigroup fluxes as described in [Gill]_
and [Knoll]_. This method is not the primary one used, but has gotten recent
attention due to its coupling advantages to other physics such as thermal
hydraulics. Once multigroup fluxes are obtained, a normalized fission source is
calculated in the code using eq. :eq:`eq_cmfd_psrc` directly.
calculated in the code using eq. :eq:`eq_cmfd_psrc` directly.
The next step in the process is to compute weight adjustment factors. These are
calculated by taking the ratio of the expected number of neutrons from the CMFD
@ -523,7 +523,7 @@ the current MC source, OpenMC sums the statistical
weights of neutrons from the source bank on a given spatial and energy mesh.
Once weight adjustment factors were calculated, each neutron's statistical
weight in the source bank was modified according to its location and energy.
Examples of CMFD simulations using OpenMC can be found in [Herman_Thesis]_.
Examples of CMFD simulations using OpenMC can be found in [HermanThesis]_.
----------
References
@ -536,23 +536,23 @@ References
.. [Gill] Daniel F. Gill. *Newton-Krylov methods for the solution of the k-eigenvalue problem in
multigroup neutronics calculations*. Ph.D. thesis, Pennsylvania State University, 2010.
.. [Hebert] Alain Hebert. *Applied reactor physics*. Presses Internationales Polytechnique,
.. [Hebert] Alain Hebert. *Applied reactor physics*. Presses Internationales Polytechnique,
Montreal, 2009.
.. [Herman] Bryan R. Herman, Benoit Forget, Kord Smith, and Brian N. Aviles. Improved
diffusion coefficients generated from Monte Carlo codes. In *Proceedings of M&C
2013*, Sun Valley, ID, USA, May 5 - 9, 2013.
.. [Herman_Thesis] Bryan R. Herman. *Monte Carlo and Thermal Hydraulic Coupling using
Low-Order Nonlinear Diffusion Acceleration*. Sc.D. thesis,
Massachusetts Institute of Technology, 2014.
.. [HermanThesis] Bryan R. Herman. *Monte Carlo and Thermal Hydraulic Coupling using
Low-Order Nonlinear Diffusion Acceleration*. Sc.D. thesis,
Massachusetts Institute of Technology, 2014.
.. [Knoll] D.A. Knoll, H. Park, and C. Newman. *Acceleration of k-eigenvalue/criticality
calculations using the Jacobian-free Newton-Krylov method*. Nuclear Science and
Engineering, 167:133140, 2011.
.. [Park] H. Park, D.A. Knoll, and C.K. Newman. *Nonlinear acceleration of transport
criticality problems*. Nuclear Science and Engineering, 172:5265, 2012.
criticality problems*. Nuclear Science and Engineering, 172:5265, 2012.
.. [Rhodes] Joel Rhodes and Malte Edenius. *CASMO-4 --- A Fuel Assembly Burnup Program.
Users Manual*. Studsvik of America, ssp-09/443-u rev 0, proprietary edition, 2001.