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https://github.com/openmc-dev/openmc.git
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commit
399419f978
9 changed files with 51 additions and 39 deletions
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@ -23,7 +23,7 @@ sys.path.insert(0, os.path.abspath('../sphinxext'))
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# Add any Sphinx extension module names here, as strings. They can be extensions
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# coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
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extensions = ['sphinx.ext.pngmath', 'sphinxcontrib.tikz']
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extensions = ['sphinx.ext.pngmath', 'sphinxcontrib.tikz', 'sphinx.ext.numfig']
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# Add any paths that contain templates here, relative to this directory.
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templates_path = ['_templates']
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@ -196,11 +196,12 @@ latex_elements = {
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\setlistdepth{9}
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\usepackage{tikz}
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\usetikzlibrary{shapes,snakes,shadows,arrows,calc,decorations.markings,patterns,fit,matrix,spy}
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\usepackage{fixltx2e}
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\hypersetup{bookmarksdepth=3}
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%\renewcommand{\thechapter}{\Roman{chapter}}
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\setcounter{tocdepth}{2}
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\numberwithin{equation}{section}
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"""
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""",
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'printindex': r""
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}
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# The name of an image file (relative to this directory) to place at the top of
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@ -18,9 +18,11 @@ free to send a message to the User's Group `mailing list`_.
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.. _Massachusetts Institute of Technology: http://web.mit.edu
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.. _mailing list: https://groups.google.com/forum/?fromgroups=#!forum/openmc-users
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--------
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Contents
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--------
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.. only:: html
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--------
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Contents
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--------
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.. toctree::
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:maxdepth: 1
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@ -439,7 +439,7 @@ by the user. Once all diffusion parameters are calculated, CMFD matrices are
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formed where energy groups are the inner most iteration index. In OpenMC,
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compressed row storage sparse matrices are used due to the sparsity of CMFD
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operators. An example of this sparsity is shown for the 3-D BEAVRS model in
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figures :ref:`fig_loss` and :ref:`fig_prod` [BEAVRS]_. These matrices represent
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figures :num:`fig-loss` and :num:`fig-prod` [BEAVRS]_. These matrices represent
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an assembly radial mesh, 24 cell mesh in the axial direction and two energy
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groups. The loss matrix is 99.92% sparse and the production matrix is 99.99%
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sparse. Although the loss matrix looks like it is tridiagonal, it is really a
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@ -473,14 +473,14 @@ no fission neutrons appear with energies in the thermal group.
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| \ :math:`\left\langle\overline{J}^{u,g}_{l\pm 1/2,m,n}\Delta_m^v\Delta_n^w\right\rangle` | current | mesh, energy |
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+--------------------------------------------------------------------------------------------+----------------+---------------------------+
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.. _fig_loss:
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.. _fig-loss:
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.. figure:: ../_images/loss.png
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:scale: 50
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Sparsity of Neutron Loss Operator
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.. _fig_prod:
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.. _fig-prod:
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.. figure:: ../_images/prod.png
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:scale: 50
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@ -525,9 +525,9 @@ Once weight adjustment factors were calculated, each neutron's statistical
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weight in the source bank was modified according to its location and energy.
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Examples of CMFD simulations using OpenMC can be found in [HermanThesis]_.
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----------
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References
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----------
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.. only:: html
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.. rubric:: References
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.. [BEAVRS] Nick Horelik, Bryan Herman. *Benchmark for Evaluation And Verification of Reactor
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Simulations*. Massachusetts Institute of Technology, http://crpg.mit.edu/pub/beavrs
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@ -63,9 +63,9 @@ Other Methods
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A good survey of other energy grid techniques, including unionized energy grids,
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can be found in a paper by Leppanen_.
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----------
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References
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----------
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.. only:: html
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.. rubric:: References
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.. [Brown] Forrest B. Brown, "New Hash-based Energy Lookup Algorithm for Monte
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Carlo codes," LA-UR-14-24530, Los Alamos National Laboratory (2014).
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@ -42,9 +42,11 @@ One can confirm that any point inside this sphere will correspond to
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In OpenMC, every surface defined by the user is assigned an integer to uniquely
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identify it. We can then refer to either of the two half-spaces created by a
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surface by a combination of the unique ID of the surface and a positive/negative
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sign. The following illustration shows an example of an ellipse with unique ID 1
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sign. Figure :num:`fig-halfspace` shows an example of an ellipse with unique ID 1
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dividing space into two half-spaces.
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.. _fig-halfspace:
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.. figure:: ../_images/halfspace.*
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:align: center
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:figclass: align-center
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@ -57,9 +59,11 @@ to be defined by intersections, unions, and differences or half-spaces, OpenMC
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is currently limited to cells defined only as intersections of
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half-spaces. Thus, the specification of the cell must include a list of
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half-space references whose intersection defines the region. The region is then
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assigned a material defined elsewhere. The following illustration shows an
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assigned a material defined elsewhere. Figure :num:`fig-union` shows an
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example of a cell defined as the intersection of an ellipse and two planes.
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.. _fig-union:
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.. figure:: ../_images/union.*
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:align: center
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:figclass: align-center
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@ -399,10 +403,12 @@ Rectilinear Lattice Indexing
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----------------------------
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Indices are assigned to tiles in a rectilinear lattice based on the tile's
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position along the :math:`x`, :math:`y`, and :math:`z` axes. The figure below
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maps the indices for a 2D lattice. The indices, (1, 1), map to the
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lower-left tile. (5, 1) and (5, 5) map to the lower-right and upper-right
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tiles, respectively.
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position along the :math:`x`, :math:`y`, and :math:`z` axes. Figure
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:num:`fig-rect-lat` maps the indices for a 2D lattice. The indices, (1, 1),
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map to the lower-left tile. (5, 1) and (5, 5) map to the lower-right and
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upper-right tiles, respectively.
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.. _fig-rect-lat:
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.. figure:: ../_images/rect_lat.*
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:align: center
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@ -431,12 +437,15 @@ corner of the lattice, and :math:`p_0, p_1, p_2` are the pitches along the
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Hexagonal Lattice Indexing
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--------------------------
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A skewed coordinate system is used for indexing hexagonal lattice tiles. Rather
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than a :math:`y`-axis, another axis is used that is rotated 30 degrees
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A skewed coordinate system is used for indexing hexagonal lattice tiles.
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Rather than a :math:`y`-axis, another axis is used that is rotated 30 degrees
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counter-clockwise from the :math:`y`-axis. This axis is referred to as the
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:math:`\alpha`-axis. The figure below shows how 2D hexagonal tiles are mapped
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with the :math:`(x, \alpha)` basis. In this system, (0, 0) maps to the center
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tile, (0, 2) to the top tile, and (2, -1) to the middle tile on the right side.
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:math:`\alpha`-axis. Figure :num:`fig-hex-lat` shows how 2D hexagonal tiles
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are mapped with the :math:`(x, \alpha)` basis. In this system, (0, 0) maps to
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the center tile, (0, 2) to the top tile, and (2, -1) to the middle tile on the
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right side.
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.. _fig-hex-lat:
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.. figure:: ../_images/hex_lat.*
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:align: center
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@ -599,9 +599,9 @@ is actually independent of the number of nodes:
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E \left [ \Lambda_{j_{\text{max}}} \right ] = \sqrt{ \frac{N\sigma^2}{2\pi
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k^2}}.
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----------
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References
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----------
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.. only:: html
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.. rubric:: References
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.. [Troubetzkoy] E. Troubetzkoy, H. Steinberg, and M. Kalos, "Monte Carlo
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Radiation Penetration Calculations on a Parallel Computer,"
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@ -1552,9 +1552,9 @@ default, the cutoff weight in OpenMC is :math:`w_c = 0.25` and the survival
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weight is :math:`w_s = 1.0`. These parameters vary from one Monte Carlo code to
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another.
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----------
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References
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----------
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.. only:: html
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.. rubric:: References
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.. [Doyas] Richard J. Doyas and Sterrett T. Perkins, "Interpolation of Tabular
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Secondary Neutron and Photon Energy Distributions," *Nucl. Sci. Eng.*,
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@ -62,9 +62,9 @@ Note that :eq:`lcg-skipahead` has the same general form as \eqref{eq:lcg}, so
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the idea is to determine the new multiplicative and additive constants in
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:math:`O(\log_2 N)` operations.
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----------
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References
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----------
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.. only:: html
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.. rubric:: References
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.. [LEcuyer] P. L’Ecuyer, "Tables of Linear Congruential Generators of
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Different Sizes and Good Lattice Structures," *Math. Comput.*, **68**, 249
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@ -475,9 +475,9 @@ normal distribution, we use an `unpublished rational approximation`_. After
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using the rational approximation, one iteration of Newton's method is applied to
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improve the estimate of the percentile.
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----------
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References
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----------
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.. only:: html
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.. rubric:: References
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.. [George] E. E. Olusegun George and Meenakshi Sivaram, "A modification of the
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Fisher-Cornish approximation for the student t percentiles," Communication
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