Added overview of program flow in documentation.

docs/source/methods/introduction.rst

@@ -31,6 +31,99 @@ simulate:
 where :math:`\sigma^2` is the variance of the sample mean and :math:`N` is the
 number of realizations.
 
+------------------------
+Overview of Program Flow
+------------------------
+
+OpenMC performs a Monte Carlo simulation one particle at a time -- at no point
+is more than one particle being tracked. Before any particles are tracked, the
+problem must be initialized. This involves the following steps:
+
+  - Read input files and building data structures for the geometry, materials,
+    tallies, and other associated variables.
+
+  - Initialize the pseudorandom number generator.
+
+  - Read ACE format cross-sections specified in the problem.
+
+  - If using a special energy grid treatment such as a union energy grid or
+    lethargy bins, that must be initialized as well.
+
+  - In a fixed source problem, source sites are sampled from the specified
+    source. In a criticality problem, source sites are sampled from some initial
+    source distribution or from a source file. The source sites consist of
+    coordinates, a direction, and an energy.
+
+Once initialization is complete, the actual transport simulation can
+proceed. The life of a single particle will proceed as follows:
+
+  1. The particle's properties are initialized from a source site previously
+     sampled.
+
+  2. Based on the particle's coordinates, the current cell in which the particle
+     resides is determined.
+
+  3. The energy-dependent cross-sections for the material that the particle is
+     currently in are determined. Note that this includes the total
+     cross-section, which is not pre-calculated.
+
+  4. The distance to the nearest boundary of the particle's cell is determined
+     based on the bounding surfaces to the cell.
+
+  5. The distance to the next collision is sampled. If the total material
+     cross-section is :math:`\Sigma_t`, this can be shown to be
+
+     .. math::
+
+         d = -\frac{\ln \xi}{\Sigma_t}
+
+     where :math:`\sigma` is a `pseudorandom number`_ sampled from a uniform
+     distribution on [0,1).
+
+  5. If the distance to the nearest boundary is less than the distance to the next
+     collision, the particle is moved forward to this boundary. Then, the process
+     is repeated from step 2. If the distance to collision is closer than the
+     distance to the nearest boundary, then the particle will undergo a collision.
+
+  6. The material at the collision site may consist of multiple nuclides. First,
+     the nuclide with which the collision will happen is sampled based on the
+     total cross-sections. If the total cross section of material :math:`i` is
+     :math:`\Sigma_{t,i}`, then the probability that any nuclide is sampled is
+
+     .. math::
+
+         P(i) = \frac{\Sigma_{t,i}}{\Sigma_t}
+
+  7. Once the specific nuclide is sampled, the random samples a reaction for
+     that nuclide based on the microscopic cross sections. If the microscopic
+     cross-section for some reaction :math:`x` is :math:`\sigma_x` and the total
+     microscopic cross section for the nuclide is :math:`\sigma_t`, then the
+     probability that reaction :math:`x` will occur is
+
+     .. math::
+
+         P(x) = \frac{\sigma_x}{\sigma_t}
+
+  8. If the sampled reaction is elastic or inelastic scattering, the outgoing
+     energy and angle is sampled from the appropriate distribution.  If the
+     reaction is (n,xn), it's also treated as scattering and the weight of the
+     particle is increased by the multiplicity of the reaction. The particle
+     then continues from step 3. If the reaction is absorption or fission, the
+     particle dies and if necessary, fission sites are created and stored in the
+     fission bank.
+
+After all particles have been simulated, there are a few final tasks that must
+be performed before the run is finished. This include the following:
+
+  - With the accumulated sum and sum of squares for each tally, the sample mean
+    and its variance is calculated.
+
+  - All tallies and other results are written to disk.
+
+  - If requested, a source file is written to disk
+
+  - All allocatable arrays are deallocated.
+
 ---------------------
 Criticality Algorithm
 ---------------------
@@ -38,3 +131,4 @@ Criticality Algorithm
 .. _probability distributions: http://en.wikipedia.org/wiki/Probability_distribution
 .. _Monte Carlo: http://en.wikipedia.org/wiki/Monte_Carlo_method
 .. _central limit theorem: http://en.wikipedia.org/wiki/Central_limit_theorem
+.. _pseudorandom number: http://en.wikipedia.org/wiki/Pseudorandom_number_generator