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Added theory on reflective surfaces to docs. Updated description of surfaces.

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Paul Romano 2011-09-08 22:54:10 -04:00
parent 645149a917
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docs/source/methods/index.rst
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@ -7,3 +7,22 @@ Methodology
The OpenMC code solves the neutron transport equation using the Monte Carlo
method whereby particles are tracked as they randomly move through a geometry,
undergoing collisions, and creating secondary particles.
-------------------
Reflective Surfaces
-------------------
In general, a surface can be written in the form :math:`f(x,y,z) = 0`. If a
neutron is traveling in direction :math:`\vec{v}` and crosses a reflective
surface of the above form, it can be shown that the velocity vector will then
become
.. math::
\mathbf{v'} = \mathbf{v} - 2 (\mathbf{v} \cdot \hat{\mathbf{n}})
\hat{\mathbf{n}}
where :math:`\hat{\mathbf{n}}` is a unit vector normal to the surface at the
point of the surface crossing. The direction of the surface normal will be the
gradient to the surface at the point of crossing, i.e. :math:`\mathbf{n} =
\nabla f(x,y,z)`.