From 7c567e197a14159a8a687180a7a440e88df5382e Mon Sep 17 00:00:00 2001
From: Bryan Herman <bherman@mit.edu>
Date: Wed, 10 Sep 2014 15:06:21 -0400
Subject: [PATCH] added cmfd section to theory which includes notation section

---
 docs/source/methods/cmfd.rst  | 38 +++++++++++++++++++++++++++++++++++
 docs/source/methods/index.rst |  1 +
 2 files changed, 39 insertions(+)
 create mode 100644 docs/source/methods/cmfd.rst

diff --git a/docs/source/methods/cmfd.rst b/docs/source/methods/cmfd.rst
new file mode 100644
index 0000000000..d837048f37
--- /dev/null
+++ b/docs/source/methods/cmfd.rst
@@ -0,0 +1,38 @@
+.. _methods_cmfd:
+
+================================================================
+Nonlinear Diffusion Acceleration - Coarse Mesh Finite Difference
+================================================================
+
+This page section discusses how nonlinear diffusion acceleration (NDA) using coarse mesh finite difference (CMFD) is implemented into OpenMC. Before we get into the theory, general notation for this section is discussed.
+
+--------
+Notation
+--------
+
+Before deriving NDA relationships, notation is explained. If a parameter has a
+:math:`\overline{\cdot}`, it is surface area-averaged and if it has a
+:math:`\overline{\overline\cdot}`, it is volume-averaged. When describing a
+specific cell in the geometry, indices :math:`(i,j,k)` are used which correspond
+to directions :math:`(x,y,z)`. In most cases, the same operation is performed in
+all three directions. To compactly write this, an arbitrary direction set
+:math:`(u,v,w)` that corresponds to cell indices :math:`(l,m,n)` is used. Note
+that :math:`u` and :math:`l` do not have to correspond to :math:`x` and
+:math:`i`. However, if :math:`u` and :math:`l` correspond to :math:`y` and
+:math:`j`, :math:`v` and :math:`w` correspond to :math:`x` and :math:`z`
+directions. An example of this is shown in the following expression:
+
+.. math::
+    :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 
+
+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`
+located at :math:`l+1/2`.  Usually, spatial indices are listed as subscripts and
+the direction as a superscript. Energy group indices represented by :math:`g`
+and :math:`h` are also listed as superscripts here. The group :math:`g` is the
+group of interest and, if present, :math:`h` is all groups. Finally, any
+parameter surrounded by :math:`\left\langle\cdot\right\rangle` represents a
+tally quantity that can be edited from an MC solution.
diff --git a/docs/source/methods/index.rst b/docs/source/methods/index.rst
index 0ff4fb1988..1df4f324a3 100644
--- a/docs/source/methods/index.rst
+++ b/docs/source/methods/index.rst
@@ -16,3 +16,4 @@ Theory and Methodology
     tallies
     eigenvalue
     parallelization
+    cmfd