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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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19
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)`.

48
docs/source/usersguide/input.rst
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@ -50,40 +50,40 @@ Geometry Specification -- geometry.xml
Types of surfaces:
x-plane
A plane perpendicular to the x axis, i.e. a surface of the form x - x0
= 0. The coefficients specified are "x0".
``x-plane``
A plane perpendicular to the x axis, i.e. a surface of the form :math:`x - x_0
= 0`. The coefficients specified are ":math:`x_0`".
y-plane
A plane perpendicular to the y axis, i.e. a surface of the form y - y0
= 0. The coefficients specified are "y0".
``y-plane``
A plane perpendicular to the y axis, i.e. a surface of the form :math:`y - y_0
= 0`. The coefficients specified are ":math:`y_0`".
z-plane
A plane perpendicular to the z axis, i.e. a surface of the form z - z0
= 0. The coefficients specified are "z0".
``z-plane``
A plane perpendicular to the z axis, i.e. a surface of the form :math:`z - z_0
= 0`. The coefficients specified are ":math:`z_0`".
plane
An arbitrary plane of the form A*x + B*y + C*z = D. The coefficients
specified are "A B C D".
``plane``
An arbitrary plane of the form :math:`Ax + By + Cz = D`. The coefficients
specified are ":math:`A \: B \: C \: D`".
x-cylinder
``x-cylinder``
An infinite cylinder whose length is paralle to the x-axis. This is a
quadratic surface of the form (y - y0)^2 + (z - z0)^2 = R^2. The coefficients
specified are "y0 z0 R".
quadratic surface of the form :math:`(y - y_0)^2 + (z - z_0)^2 = R^2`. The
coefficients specified are ":math:`y_0 \: z_0 \: R`".
y-cylinder
``y-cylinder``
An infinite cylinder whose length is paralle to the y-axis. This is a
quadratic surface of the form (x - x0)^2 + (z - z0)^2 = R^2. The coefficients
specified are "x0 z0 R".
quadratic surface of the form :math:`(x - x_0)^2 + (z - z_0)^2 = R^2`. The
coefficients specified are ":math:`x_0 \: z_0 \: R`".
z-cylinder
``z-cylinder``
An infinite cylinder whose length is paralle to the z-axis. This is a
quadratic surface of the form (x - x0)^2 + (y - y0)^2 = R^2. The coefficients
specified are "x0 y0 R".
quadratic surface of the form :math:`(x - x_0)^2 + (y - y_0)^2 = R^2`. The
coefficients specified are ":math:`x_0 \: y_0 \: R`".
sphere
A sphere of the form (x - x0)^2 + (y - y0)^2 + (z - z0)^2 = R^2. The
coefficients specified are "x0 y0 z0 R".
``sphere``
A sphere of the form :math:`(x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 =
R^2`. The coefficients specified are ":math:`x_0 \: y_0 \: z_0 \: R`".
----------------------------------------
Materials Specification -- materials.xml