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8 changed files with 1221 additions and 3 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']
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extensions = ['sphinx.ext.pngmath', 'sphinxcontrib.tikz']
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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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@ -188,7 +188,14 @@ latex_documents = [
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u'Massachusetts Institute of Technology', 'manual'),
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]
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latex_elements = {'preamble': '\\usepackage{enumitem}\\setlistdepth{9}'}
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latex_elements = {
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'preamble': '''
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\usepackage{enumitem}
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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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'''
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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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# the title page.
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561
docs/source/methods/cmfd.rst
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@ -0,0 +1,561 @@
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.. _methods_cmfd:
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================================================================
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Nonlinear Diffusion Acceleration - Coarse Mesh Finite Difference
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================================================================
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This page section discusses how nonlinear diffusion acceleration (NDA) using
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coarse mesh finite difference (CMFD) is implemented into OpenMC. Before we get
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into the theory, general notation for this section is discussed.
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--------
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Notation
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--------
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Before deriving NDA relationships, notation is explained. If a parameter has a
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:math:`\overline{\cdot}`, it is surface area-averaged and if it has a
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:math:`\overline{\overline\cdot}`, it is volume-averaged. When describing a
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specific cell in the geometry, indices :math:`(i,j,k)` are used which correspond
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to directions :math:`(x,y,z)`. In most cases, the same operation is performed in
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all three directions. To compactly write this, an arbitrary direction set
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:math:`(u,v,w)` that corresponds to cell indices :math:`(l,m,n)` is used. Note
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that :math:`u` and :math:`l` do not have to correspond to :math:`x` and
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:math:`i`. However, if :math:`u` and :math:`l` correspond to :math:`y` and
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:math:`j`, :math:`v` and :math:`w` correspond to :math:`x` and :math:`z`
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directions. An example of this is shown in the following expression:
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.. math::
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:label: not1
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\sum\limits_{u\in(x,y,z)}\left\langle\overline{J}^{u,g}_{l+1/2,m,n}
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\Delta_m^v\Delta_n^w\right\rangle
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Here, :math:`u` takes on each direction one at a time. The parameter :math:`J`
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is surface area-averaged over the transverse indices :math:`m` and :math:`n`
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located at :math:`l+1/2`. Usually, spatial indices are listed as subscripts and
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the direction as a superscript. Energy group indices represented by :math:`g`
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and :math:`h` are also listed as superscripts here. The group :math:`g` is the
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group of interest and, if present, :math:`h` is all groups. Finally, any
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parameter surrounded by :math:`\left\langle\cdot\right\rangle` represents a
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tally quantity that can be edited from a Monte Carlo (MC) solution.
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------
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Theory
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------
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NDA is a diffusion model that has equivalent physics to a transport model. There
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are many different methods that can be classified as NDA. The CMFD method is a
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type of NDA that represents second order multigroup diffusion equations on a
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coarse spatial mesh. Whether a transport model or diffusion model is used to
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represent the distribution of neutrons, these models must satisfy the *neutron
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balance equation*. This balance is represented by the following formula for a
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specific energy group :math:`g` in cell :math:`(l,m,n)`:
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.. math::
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:label: eq_neut_bal
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\sum\limits_{u\in(x,y,z)}\left(\left\langle\overline{J}^{u,g}_{l+1/2,m,n}
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\Delta_m^v\Delta_n^w\right\rangle -
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\left\langle\overline{J}^{u,g}_{l-1/2,m,n}
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\Delta_m^v\Delta_n^w\right\rangle\right)
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+
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\left\langle\overline{\overline\Sigma}_{t_{l,m,n}}^g
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\overline{\overline\phi}_{l,m,n}^g\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle
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= \\
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\sum\limits_{h=1}^G\left\langle
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\overline{\overline{\nu_s\Sigma}}_{s_{l,m,n}}^{h\rightarrow
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g}\overline{\overline\phi}_{l,m,n}^h\Delta_l^u\Delta_m^v\Delta_n^w
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\right\rangle
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+
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\frac{1}{k_{eff}}\sum\limits_{h=1}^G
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\left\langle\overline{\overline{\nu_f\Sigma}}_{f_{l,m,n}}^{h\rightarrow
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g}\overline{\overline\phi}_{l,m,n}^h
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\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle.
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|
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In eq. :eq:`eq_neut_bal` the parameters are defined as:
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|
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* :math:`\left\langle\overline{J}^{u,g}_{l\pm
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1/2,m,n}\Delta_m^v\Delta_n^w\right\rangle` --- surface area-integrated net
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current over surface :math:`(l\pm 1/2,m,n)` with surface normal in direction
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:math:`u` in energy group :math:`g`. By dividing this quantity by the transverse
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area, :math:`\Delta_m^v\Delta_n^w`, the surface area-averaged net current can
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be computed.
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* :math:`\left\langle\overline{\overline\Sigma}_{t_{l,m,n}}^g
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\overline{\overline\phi}_{l,m,n}^g\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle`
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--- volume-integrated total reaction rate over energy group :math:`g`.
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* :math:`\left\langle\overline{\overline{\nu_s\Sigma}}_{s_{l,m,n}}^{h\rightarrow
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g}
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\overline{\overline\phi}_{l,m,n}^h\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle`
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--- volume-integrated scattering production rate of neutrons that begin with
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energy in group :math:`h` and exit reaction in group :math:`g`. This reaction
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rate also includes the energy transfer of reactions (except fission) that
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produce multiple neutrons such as (n, 2n); hence, the need for :math:`\nu_s`
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to represent neutron multiplicity.
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* :math:`k_{eff}` --- core multiplication factor.
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* :math:`\left\langle\overline{\overline{\nu_f\Sigma}}_{f_{l,m,n}}^{h\rightarrow
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g}\overline{\overline\phi}_{l,m,n}^h\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle`
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--- volume-integrated fission production rate of neutrons from fissions in
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group :math:`h` that exit in group :math:`g`.
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|
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Each quantity in :math:`\left\langle\cdot\right\rangle` represents a scalar value that
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is obtained from an MC tally. A good verification step when using an MC code is
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to make sure that tallies satisfy this balance equation within statistics. No
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NDA acceleration can be performed if the balance equation is not satisfied.
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|
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There are three major steps to consider when performing NDA: (1) calculation of
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macroscopic cross sections and nonlinear parameters, (2) solving an eigenvalue
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problem with a system of linear equations, and (3) modifying MC source
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distribution to align with the NDA solution on a chosen mesh. This process is
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illustrated as a flow chart below. After a batch of neutrons
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is simulated, NDA can take place. Each of the steps described above is described
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in detail in the following sections.
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.. tikz:: Flow chart of NDA process. Note "XS" is used for cross section and
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"DC" is used for diffusion coefficient.
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:libs: shapes, snakes, shadows, arrows, calc, decorations.markings, patterns, fit, matrix, spy
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||||
:include: cmfd_tikz/cmfd_flow.tikz
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|
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Calculation of Macroscopic Cross Sections
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-----------------------------------------
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|
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A diffusion model needs macroscopic cross sections and diffusion coefficients to
|
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solve for multigroup fluxes. Cross sections are derived by conserving reaction
|
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rates predicted by MC tallies. From Eq. :eq:`eq_neut_bal`, total, scattering
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production and fission production macroscopic cross sections are needed. They are
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defined from MC tallies as follows:
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.. math::
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:label: xs1
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\overline{\overline\Sigma}_{t_{l,m,n}}^g \equiv
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\frac{\left\langle\overline{\overline\Sigma}_{t_{l,m,n}}^g
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\overline{\overline\phi}_{l,m,n}^g\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle}
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{\left\langle\overline{\overline\phi}_{l,m,n}^g
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\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle},
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.. math::
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:label: xs2
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\overline{\overline{\nu_s\Sigma}}_{s_{l,m,n}}^{h\rightarrow g} \equiv
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\frac{\left\langle\overline{\overline{\nu_s\Sigma}}_{s_{l,m,n}}^{h\rightarrow
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g}\overline{\overline\phi}_{l,m,n}^h\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle}
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{\left\langle\overline{\overline\phi}_{l,m,n}^h
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\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle}
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and
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.. math::
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:label: xs3
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\overline{\overline{\nu_f\Sigma}}_{f_{l,m,n}}^{h\rightarrow g} \equiv
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\frac{\left\langle\overline{\overline{\nu_f\Sigma}}_{f_{l,m,n}}^{h\rightarrow
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g}\overline{\overline\phi}_{l,m,n}^h\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle}
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{\left\langle\overline{\overline\phi}_{l,m,n}^h\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle}.
|
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|
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In order to fully conserve neutron balance, leakage rates also need to be
|
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preserved. In standard diffusion theory, leakage rates are represented by
|
||||
diffusion coefficients. Unfortunately, it is not easy in MC to calculate a
|
||||
single diffusion coefficient for a cell that describes leakage out of each
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surface. Luckily, it does not matter what definition of diffusion coefficient is
|
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used because nonlinear equivalence parameters will correct for this
|
||||
inconsistency. However, depending on the diffusion coefficient definition
|
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chosen, different convergence properties of NDA equations are observed.
|
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Here, we introduce a diffusion coefficient that is derived for a coarse energy
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transport reaction rate. This definition can easily be constructed from
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MC tallies provided that angular moments of scattering reaction rates can
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be obtained. The diffusion coefficient is defined as follows:
|
||||
|
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.. math::
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||||
:label: eq_transD
|
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|
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\overline{\overline D}_{l,m,n}^g =
|
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\frac{\left\langle\overline{\overline\phi}_{l,m,n}^g
|
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\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle}{3
|
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\left\langle\overline{\overline\Sigma}_{tr_{l,m,n}}^g
|
||||
\overline{\overline\phi}_{l,m,n}^g
|
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\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle},
|
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|
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where
|
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|
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.. math::
|
||||
:label: xs4
|
||||
|
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\left\langle\overline{\overline\Sigma}_{tr_{l,m,n}}^g
|
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\overline{\overline\phi}_{l,m,n}^g\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle
|
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=
|
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\left\langle\overline{\overline\Sigma}_{t_{l,m,n}}^g
|
||||
\overline{\overline\phi}_{l,m,n}^g\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle
|
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\\ -
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\left\langle\overline{\overline{\nu_s\Sigma}}_{s1_{l,m,n}}^g
|
||||
\overline{\overline\phi}_{l,m,n}^g\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle.
|
||||
|
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Note that the transport reaction rate is calculated from the total reaction rate
|
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reduced by the :math:`P_1` scattering production reaction rate. Equation :eq:`eq_transD`
|
||||
does not represent the best definition of diffusion coefficients from MC;
|
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however, it is very simple and usually fits into MC tally frameworks
|
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easily. Different methods to calculate more accurate diffusion coefficients can
|
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found in [Herman]_.
|
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|
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CMFD Equations
|
||||
--------------
|
||||
|
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The first part of this section is devoted to discussing second-order finite
|
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volume discretization of multigroup diffusion equations. This will be followed
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up by the formulation of CMFD equations that are used in this NDA
|
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scheme. When performing second-order finite volume discretization of the
|
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diffusion equation, we need information that relates current to flux. In this
|
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numerical scheme, each cell is coupled only to its direct neighbors. Therefore,
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only two types of coupling exist: (1) cell-to-cell coupling and (2)
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cell-to-boundary coupling. The derivation of this procedure is referred to as
|
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finite difference diffusion equations and can be found in literature such
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as [Hebert]_. These current/flux relationships are as follows:
|
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|
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* cell-to-cell coupling
|
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.. math::
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:label: eq_cell_cell
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\overline{J}^{u,g}_{l\pm1/2,m,n} = -\frac{2\overline{\overline
|
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D}_{l\pm1,m,n}^g\overline{\overline
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D}_{l,m,n}^g}{\overline{\overline D}_{l\pm1,m,n}^g\Delta_l^u +
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\overline{\overline
|
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D}_{l,m,n}^g\Delta_{l\pm1}^u}
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\left(\pm\overline{\overline{\phi}}_{l\pm1,m,n}^g\mp
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\overline{\overline{\phi}}_{l,m,n}^g\right),
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|
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* cell-to-boundary coupling
|
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|
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.. math::
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:label: eq_cell_bound
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|
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\overline{J}^{u,g}_{l\pm1/2,m,n} = \pm\frac{2\overline{\overline
|
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D}_{l,m,n}^g\left(1 -
|
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\beta_{l\pm1/2,m,n}^{u,g}\right)}{4\overline{\overline
|
||||
D}_{l,m,n}^g\left(1 + \beta_{l\pm1/2,m,n}^{u,g}\right) + \left(1 -
|
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\beta_{l\pm1/2,m,n}^{u,g}\right)\Delta_l^u}\overline{\overline{\phi}}_{l,m,n}^{g}.
|
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|
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In Eqs. :eq:`eq_cell_cell` and :eq:`eq_cell_bound`, the :math:`\pm` refers to
|
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left (:math:`-x`) or right (:math:`+x`) surface in the :math:`x` direction,
|
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back (:math:`-y`) or front (:math:`+y`) surface in the :math:`y` direction and
|
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bottom (:math:`-z`) or top (:math:`+z`) surface in the :math:`z` direction. For
|
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cell-to-boundary coupling, a general albedo, :math:`\beta_{l\pm1/2,m,n}^{u,g}`,
|
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is used. The albedo is defined as the ratio of incoming (:math:`-` superscript)
|
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to outgoing (:math:`+` superscript) partial current on any surface represented
|
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as
|
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|
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.. math::
|
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:label: eq_albedo
|
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|
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\beta_{l\pm1/2,m,n}^{u,g} =
|
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\frac{\overline{J}^{u,g-}_{l\pm1/2,m,n}}{\overline{J}^{u,g+}_{l\pm1/2,m,n}}.
|
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|
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Common boundary conditions are: vacuum (:math:`\beta=0`), reflective
|
||||
(:math:`\beta=1`) and zero flux (:math:`\beta=-1`). Both eq. :eq:`eq_cell_cell`
|
||||
and eq. :eq:`eq_cell_bound` can be written in this generic form,
|
||||
|
||||
.. math::
|
||||
:label: eq_dtilde
|
||||
|
||||
\overline{J}^{u,g}_{l\pm1/2,m,n} = \widetilde{D}_{l,m,n}^{u,g} \left(\dots\right).
|
||||
|
||||
The parameter :math:`\widetilde{D}_{l,m,n}^{u,g}` represents the linear
|
||||
coupling term between current and flux. These current relationships can be
|
||||
sustituted into eq. :eq:`eq_neut_bal` to produce a linear system of multigroup
|
||||
diffusion equations for each spatial cell and energy group. However, a solution
|
||||
to these equations is not consistent with a higher order transport solution
|
||||
unless equivalence factors are present. This is because both the diffusion
|
||||
approximation, governed by Fick's Law, and spatial trunction error will produce
|
||||
differences. Therefore, a nonlinear parameter,
|
||||
:math:`\widehat{D}_{l,m,n}^{u,g}`, is added to eqs. :eq:`eq_cell_cell` and
|
||||
:eq:`eq_cell_bound`. These equations are, respectively,
|
||||
|
||||
.. math::
|
||||
:label: eq_dhat_cell
|
||||
|
||||
\overline{J}^{u,g}_{l\pm1/2,m,n} = -\widetilde{D}_{l,m,n}^{u,g}
|
||||
\left(\pm\overline{\overline{\phi}}_{l\pm1,m,n}^g\mp
|
||||
\overline{\overline{\phi}}_{l,m,n}^g\right) + \widehat{D}_{l,m,n}^{u,g}
|
||||
\left(\overline{\overline{\phi}}_{l\pm1,m,n}^g +
|
||||
\overline{\overline{\phi}}_{l,m,n}^g\right)
|
||||
|
||||
and
|
||||
|
||||
.. math::
|
||||
:label: eq_dhat_bound
|
||||
|
||||
\overline{J}^{u,g}_{l\pm1/2,m,n} = \pm\widetilde{D}_{l,m,n}^{u,g}
|
||||
\overline{\overline{\phi}}_{l,m,n}^{g} + \widehat{D}_{l,m,n}^{u,g}
|
||||
\overline{\overline{\phi}}_{l,m,n}^{g}.
|
||||
|
||||
The only unknown in each of these equations is the equivalence parameter. The
|
||||
current, linear coupling term and flux can either be obtained or derived from
|
||||
MC tallies. Thus, it is called nonlinear because it is dependent on the flux
|
||||
which is updated on the next iteration.
|
||||
|
||||
Equations :eq:`eq_dhat_cell` and :eq:`eq_dhat_bound` can be substituted into
|
||||
eq. :eq:`eq_neut_bal` to create a linear system of equations that is consistent
|
||||
with transport physics. One example of this equation is written for an
|
||||
interior cell,
|
||||
|
||||
.. math::
|
||||
:label: eq_cmfd_sys
|
||||
|
||||
\sum_{u\in
|
||||
x,y,x}\frac{1}{\Delta_l^u}\left[\left(-\tilde{D}_{l-1/2,m,n}^{u,g} -
|
||||
\hat{D}_{l-1/2,m,n}^{u,g}\right)\overline{\overline{\phi}}_{l-1,m,n}^g\right.
|
||||
+ \left(\tilde{D}_{l-1/2,m,n}^{u,g} +
|
||||
\tilde{D}_{l+1/2,m,n}^{u,g} - \hat{D}_{l-1/2,m,n}^{u,g} +
|
||||
\hat{D}_{l+1/2,m,n}^{u,g}\right)\overline{\overline{\phi}}_{l,m,n}^g
|
||||
\\ +
|
||||
\left. \left(-\tilde{D}_{l+1/2,m,n}^{u,g} +
|
||||
\hat{D}_{l+1/2,m,n}^{u,g}\right)\overline{\overline{\phi}}_{l+1,m,n}^g
|
||||
\right] +
|
||||
\overline{\overline\Sigma}_{t_{l,m,n}}^g\overline{\overline{\phi}}_{l,m,n}^g
|
||||
- \sum\limits_{h=1}^G\overline{\overline{\nu_s\Sigma}}^{h\rightarrow
|
||||
g}_{s_{l,m,n}}\overline{\overline{\phi}}_{l,m,n}^h =
|
||||
\frac{1}{k}\sum\limits_{h=1}^G\overline{\overline{\nu_f\Sigma}}^{h\rightarrow
|
||||
g}_{f_{l,m,n}}\overline{\overline{\phi}}_{l,m,n}^h.
|
||||
|
||||
It should be noted that before substitution, eq. :eq:`eq_neut_bal` was divided
|
||||
by the volume of the cell, :math:`\Delta_l^u\Delta_m^v\Delta_n^w`. Equation
|
||||
:eq:`eq_cmfd_sys` can be represented in operator form as
|
||||
|
||||
.. math::
|
||||
:label: eq_CMFDopers
|
||||
|
||||
\mathbb{M}\mathbf{\Phi} = \frac{1}{k}\mathbb{F}\mathbf{\Phi},
|
||||
|
||||
where :math:`\mathbb{M}` is the neutron loss matrix operator,
|
||||
:math:`\mathbb{F}` is the neutron production matrix operator,
|
||||
:math:`\mathbf{\Phi}` is the multigroup flux vector and :math:`k` is the
|
||||
eigenvalue. This generalized eigenvalue problem is solved to obtain fundamental
|
||||
mode multigroup fluxes and eigenvalue. In order to produce consistent results
|
||||
with transport theory from these equations, the neutron balance equation must
|
||||
have been satisfied by MC tallies. The desire is that CMFD equations will
|
||||
produce a more accurate source than MC after each fission source generation.
|
||||
|
||||
CMFD Feedback
|
||||
-------------
|
||||
|
||||
Now that a more accurate representation of the expected source distribution is
|
||||
estimated from CMFD, it needs to be communicated back to MC. The first step
|
||||
in this process is to generate a probability mass function that provides
|
||||
information about how probable it is for a neutron to be born in a given cell
|
||||
and energy group. This is represented as
|
||||
|
||||
.. math::
|
||||
:label: eq_cmfd_psrc
|
||||
|
||||
p_{l,m,n}^g =
|
||||
\frac{\sum_{h=1}^{G}\overline{\overline{\nu_f\Sigma}}^{h\rightarrow
|
||||
g}_{f_{l,m,n}}\overline{\overline{\phi}}_{l,m,n}^h\Delta_l^u\Delta_m^v
|
||||
\Delta_n^w}{\sum_n\sum_m\sum_l\sum_{h=1}^{G}\overline{
|
||||
\overline{\nu_f\Sigma}}^{h\rightarrow
|
||||
g}_{f_{l,m,n}}\overline{\overline{\phi}}_{l,m,n}^h\Delta_l^u\Delta_m^v
|
||||
\Delta_n^w}.
|
||||
|
||||
This equation can be multiplied by the number of source neutrons to obtain an
|
||||
estimate of the expected number of neutrons to be born in a given cell and
|
||||
energy group. This distribution can be compared to the MC source distribution
|
||||
to generate weight adjusted factors defined as
|
||||
|
||||
.. math::
|
||||
:label: eq_waf
|
||||
|
||||
f_{l,m,n}^g = \frac{Np_{l,m,n}^g}{\sum\limits_s w_s};\quad s\in
|
||||
\left(g,l,m,n\right).
|
||||
|
||||
The MC source distribution is represented on the same coarse mesh as
|
||||
CMFD by summing all neutrons' weights, :math:`w_s`, in a given cell and
|
||||
energy group. MC source weights can then be modified by this weight
|
||||
adjustment factor so that it matches the CMFD solution on the coarse
|
||||
mesh,
|
||||
|
||||
.. math::
|
||||
:label: src_mod
|
||||
|
||||
w^\prime_s = w_s\times f_{l,m,n}^g;\quad s\in \left(g,l,m,n\right).
|
||||
|
||||
It should be noted that heterogeneous information about local coordinates and
|
||||
energy remain constant throughout this modification process.
|
||||
|
||||
------------------------
|
||||
Implementation in OpenMC
|
||||
------------------------
|
||||
|
||||
The section describes how CMFD was implemented in OpenMC. Before the simulation
|
||||
begins, a user sets up a CMFD input file that contains the following basic
|
||||
information:
|
||||
|
||||
* CMFD mesh (space and energy),
|
||||
* boundary conditions at edge of mesh (albedos),
|
||||
* acceleration region (subset of mesh, optional),
|
||||
* fission source generation (FSG)/batch that CMFD should begin, and
|
||||
* whether CMFD feedback should be applied.
|
||||
|
||||
It should be noted that for more difficult simulations (e.g., light water
|
||||
reactors), there are other options available to users such as tally resetting
|
||||
parameters, effective down-scatter usage, tally estimator, etc. For more
|
||||
information please see :ref:`usersguide_cmfd`.
|
||||
|
||||
Of the options described above, the optional acceleration subset region is an
|
||||
uncommon feature. Because OpenMC only has a structured Cartesian mesh, mesh
|
||||
cells may overlay regions that don't contain fissionable material and may be so
|
||||
far from the core that the neutron flux is very low. If these regions were
|
||||
included in the CMFD solution, bad estimates of diffusion parameters may result
|
||||
and affect CMFD feedback. To deal with this, a user can carve out an active
|
||||
acceleration region from their structured Cartesian mesh. This is illustrated
|
||||
in diagram below. When placing a CMFD mesh over a geometry, the boundary
|
||||
conditions must be known at the global edges of the mesh. If the geometry is
|
||||
complex like the one below, one may have to cover the whole geometry including
|
||||
the reactor pressure vessel because we know that there is a zero incoming
|
||||
current boundary condition at the outer edge of the pressure vessel. This is
|
||||
not viable in practice because neutrons in simulations may not reach mesh cells
|
||||
that are near the pressure vessel. To circumvent this, one can shrink the mesh
|
||||
to cover just the core region as shown in the diagram. However, one must still
|
||||
estimate the boundary conditions at the global boundaries, but at these
|
||||
locations, they are not readily known. In OpenMC, one can carve out the active
|
||||
core region from the entire structured Cartesian mesh. This is shown in the
|
||||
diagram below by the darkened region over the core. The albedo boundary
|
||||
conditions at the active core/reflector boundary can be tallied indirectly
|
||||
during the MC simulation with incoming and outgoing partial currents. This
|
||||
allows the user to not have to worry about neutrons producing adequate tallies
|
||||
in mesh cells far away from the core.
|
||||
|
||||
.. tikz:: Diagram of CMFD acceleration mesh
|
||||
:libs: shapes, snakes, shadows, arrows, calc, decorations.markings, patterns, fit, matrix, spy
|
||||
:include: cmfd_tikz/meshfig.tikz
|
||||
|
||||
During an MC simulation, CMFD tallies are accumulated. The basic tallies needed
|
||||
are listed in Table :ref:`tab_tally`. Each tally is performed on a spatial and
|
||||
energy mesh basis. The surface area-integrated net current is tallied on every
|
||||
surface of the mesh. OpenMC tally objects are created by the CMFD code
|
||||
internally, and cross sections are calculated at each CMFD feedback iteration.
|
||||
The first CMFD iteration, controlled by the user, occurs just after tallies are
|
||||
communicated to the master processor. Once tallies are collapsed, cross
|
||||
sections, diffusion coefficients and equivalence parameters are calculated. This
|
||||
is performed only on the acceleration region if that option has been activated
|
||||
by the user. Once all diffusion parameters are calculated, CMFD matrices are
|
||||
formed where energy groups are the inner most iteration index. In OpenMC,
|
||||
compressed row storage sparse matrices are used due to the sparsity of CMFD
|
||||
operators. An example of this sparsity is shown for the 3-D BEAVRS model in
|
||||
figures :ref:`fig_loss` and :ref:`fig_prod` [BEAVRS]_. These matrices represent
|
||||
an assembly radial mesh, 24 cell mesh in the axial direction and two energy
|
||||
groups. The loss matrix is 99.92% sparse and the production matrix is 99.99%
|
||||
sparse. Although the loss matrix looks like it is tridiagonal, it is really a
|
||||
seven banded matrix with a block diagonal matrix for scattering. The production
|
||||
matrix is a :math:`2\times 2` block diagonal; however, zeros are present because
|
||||
no fission neutrons appear with energies in the thermal group.
|
||||
|
||||
.. _tab_tally:
|
||||
|
||||
.. table:: OpenMC CMFD tally list
|
||||
|
||||
+--------------------------------------------------------------------------------------------+----------------+---------------------------+
|
||||
+--------------------------------------------------------------------------------------------+----------------+---------------------------+
|
||||
| tally | score | filter |
|
||||
+============================================================================================+================+===========================+
|
||||
| \ :math:`\left\langle\overline{\overline\phi}_{l,m,n}^g | flux | mesh, energy |
|
||||
| \Delta_l^u\Delta_m^v\Delta_n^w\right\rangle` | | |
|
||||
+--------------------------------------------------------------------------------------------+----------------+---------------------------+
|
||||
| \ :math:`\left\langle\overline{\overline\Sigma}_{t_{l,m,n}}^g | total | mesh, energy |
|
||||
| \overline{\overline\phi}_{l,m,n}^g\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle` | | |
|
||||
+--------------------------------------------------------------------------------------------+----------------+---------------------------+
|
||||
| \ :math:`\left\langle\overline{\overline{\nu_s\Sigma}}_{s1_{l,m,n}}^g | nu-scatter-1 | mesh, energy |
|
||||
| \overline{\overline\phi}_{l,m,n}^g\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle` | | |
|
||||
+--------------------------------------------------------------------------------------------+----------------+---------------------------+
|
||||
| \ :math:`\left\langle\overline{\overline{\nu_s\Sigma}}_{s_{l,m,n}}^{h\rightarrow g} | nu-scatter | mesh, energy, energyout |
|
||||
| \overline{\overline\phi}_{l,m,n}^h\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle` | | |
|
||||
+--------------------------------------------------------------------------------------------+----------------+---------------------------+
|
||||
| \ :math:`\left\langle\overline{\overline{\nu_f\Sigma}}_{f_{l,m,n}}^{h\rightarrow g} | nu-fission | mesh, energy, energyout |
|
||||
| \overline{\overline\phi}_{l,m,n}^h\Delta_l^u\Delta_m^v\Delta_n^w\right\rangle` | | |
|
||||
+--------------------------------------------------------------------------------------------+----------------+---------------------------+
|
||||
| \ :math:`\left\langle\overline{J}^{u,g}_{l\pm 1/2,m,n}\Delta_m^v\Delta_n^w\right\rangle` | current | mesh, energy |
|
||||
+--------------------------------------------------------------------------------------------+----------------+---------------------------+
|
||||
|
||||
.. _fig_loss:
|
||||
|
||||
.. figure:: ../_images/loss.png
|
||||
:scale: 50
|
||||
|
||||
Sparsity of Neutron Loss Operator
|
||||
|
||||
.. _fig_prod:
|
||||
|
||||
.. figure:: ../_images/prod.png
|
||||
:scale: 50
|
||||
|
||||
Sparsity of Neutron Production Operator
|
||||
|
||||
To solve the eigenvalue problem with these matrices, different source iteration
|
||||
and linear solvers can be used. The most common source iteration solver used is
|
||||
standard power iteration as described in [Gill]_. To accelerate these source
|
||||
iterations, a Wielandt shift scheme can be used as discussed in [Park]_. PETSc
|
||||
solvers were first implemented to perform the linear solution in parallel that
|
||||
occurs once per source iteration. When using PETSc, different types of parallel
|
||||
linear solvers and preconditioners can be used. By default, OpenMC uses an
|
||||
incomplete LU preconditioner and a GMRES Krylov solver. After some initial
|
||||
studies of parallelization with PETSc, it was observed that because CMFD
|
||||
matrices are very sparse, solution times do not scale well. An additional
|
||||
Gauss-Seidel linear solver with Chebyshev acceleration was added that is
|
||||
similar to the one used for CMFD in CASMO [Rhodes]_ and [Smith]_. This solver
|
||||
was implemented with a custom section for two energy groups. Because energy
|
||||
group is the inner most index, a block diagonal is formed when using more than
|
||||
one group. For two groups, it is easy to invert this diagonal analytically
|
||||
inside the Gauss-Seidel iterative solver. For more than two groups, this
|
||||
analytic inversion can still be performed, but with more computational effort.
|
||||
A standard Gauss-Seidel solver is used for more than two groups.
|
||||
|
||||
Besides a power iteration, a Jacobian-free Newton-Krylov method was also
|
||||
implemented to obtain eigenvalue and multigroup fluxes as described in [Gill]_
|
||||
and [Knoll]_. This method is not the primary one used, but has gotten recent
|
||||
attention due to its coupling advantages to other physics such as thermal
|
||||
hydraulics. Once multigroup fluxes are obtained, a normalized fission source is
|
||||
calculated in the code using eq. :eq:`eq_cmfd_psrc` directly.
|
||||
|
||||
The next step in the process is to compute weight adjustment factors. These are
|
||||
calculated by taking the ratio of the expected number of neutrons from the CMFD
|
||||
source distribution to the current number of neutrons in each mesh. It is
|
||||
straightforward to compute the CMFD number of neutrons because it is the
|
||||
product between the total starting initial weight of neutrons and the CMFD
|
||||
normalized fission source distribution. To compute the number of neutrons from
|
||||
the current MC source, OpenMC sums the statistical
|
||||
weights of neutrons from the source bank on a given spatial and energy mesh.
|
||||
Once weight adjustment factors were calculated, each neutron's statistical
|
||||
weight in the source bank was modified according to its location and energy.
|
||||
Examples of CMFD simulations using OpenMC can be found in [Herman_Thesis]_.
|
||||
|
||||
----------
|
||||
References
|
||||
----------
|
||||
|
||||
.. [BEAVRS] Nick Horelik, Bryan Herman. *Benchmark for Evaluation And Verification of Reactor
|
||||
Simulations*. Massachusetts Institute of Technology, http://crpg.mit.edu/pub/beavrs
|
||||
, 2013.
|
||||
|
||||
.. [Gill] Daniel F. Gill. *Newton-Krylov methods for the solution of the k-eigenvalue problem in
|
||||
multigroup neutronics calculations*. Ph.D. thesis, Pennsylvania State University, 2010.
|
||||
|
||||
.. [Hebert] Alain Hebert. *Applied reactor physics*. Presses Internationales Polytechnique,
|
||||
Montreal, 2009.
|
||||
|
||||
.. [Herman] Bryan R. Herman, Benoit Forget, Kord Smith, and Brian N. Aviles. Improved
|
||||
diffusion coefficients generated from Monte Carlo codes. In *Proceedings of M&C
|
||||
2013*, Sun Valley, ID, USA, May 5 - 9, 2013.
|
||||
|
||||
.. [Herman_Thesis] Bryan R. Herman. *Monte Carlo and Thermal Hydraulic Coupling using
|
||||
Low-Order Nonlinear Diffusion Acceleration*. Sc.D. thesis,
|
||||
Massachusetts Institute of Technology, 2014.
|
||||
|
||||
.. [Knoll] D.A. Knoll, H. Park, and C. Newman. *Acceleration of k-eigenvalue/criticality
|
||||
calculations using the Jacobian-free Newton-Krylov method*. Nuclear Science and
|
||||
Engineering, 167:133–140, 2011.
|
||||
|
||||
.. [Park] H. Park, D.A. Knoll, and C.K. Newman. *Nonlinear acceleration of transport
|
||||
criticality problems*. Nuclear Science and Engineering, 172:52–65, 2012.
|
||||
|
||||
.. [Rhodes] Joel Rhodes and Malte Edenius. *CASMO-4 --- A Fuel Assembly Burnup Program.
|
||||
User’s Manual*. Studsvik of America, ssp-09/443-u rev 0, proprietary edition, 2001.
|
||||
|
||||
.. [Smith] Kord S Smith and Joel D Rhodes III. *Full-core, 2-D, LWR core calculations with
|
||||
CASMO-4E*. In Proceedings of PHYSOR 2002, Seoul, Korea, October 7 - 10, 2002.
|
||||
19
docs/source/methods/cmfd_tikz/cmfd_flow.tikz
Normal file
19
docs/source/methods/cmfd_tikz/cmfd_flow.tikz
Normal file
|
|
@ -0,0 +1,19 @@
|
|||
\begin{tikzpicture}
|
||||
\matrix[every node/.style={draw, thick, minimum width=3cm, minimum height=1cm, align=center}, column sep=2cm, row sep=1cm] (m) {
|
||||
\node[draw, fill=red!40] (start) {Batch $i$ \\ tally NDA}; & \\
|
||||
\node[draw, diamond, aspect=2, fill=green!40] (cmfd) {Run NDA?}; & \node[draw, fill=red!40] (end) {Batch $i + 1$ \\ tally NDA}; \\
|
||||
\node[draw, fill=blue!40] (xs) {Calculate XS \& DC}; & \node[draw, fill=blue!40] (modify) {Modify MC Source}; \\
|
||||
\node[draw, fill=blue!40] (nonlinear) {Calculate Equivalence}; & \node[draw, fill=blue!40] (eqs) {Solve NDA eqs.};\\
|
||||
};
|
||||
|
||||
\begin{scope}[every path/.style={->,very thick,draw}]
|
||||
\draw (start.south) -- (cmfd.north);
|
||||
\draw (cmfd.east) -- node[above] {no} (end.west);
|
||||
\draw (cmfd.south) -- node[right] {yes} (xs.north);
|
||||
\draw (xs.south) -- (nonlinear.north);
|
||||
\draw (nonlinear.east) -- (eqs.west);
|
||||
\draw (eqs.north) -- (modify.south);
|
||||
\draw (modify.north) -- (end.south);
|
||||
\end{scope}
|
||||
|
||||
\end{tikzpicture}
|
||||
628
docs/source/methods/cmfd_tikz/meshfig.tikz
Normal file
628
docs/source/methods/cmfd_tikz/meshfig.tikz
Normal file
|
|
@ -0,0 +1,628 @@
|
|||
|
||||
% these dimensions are determined in arrow_dimms.ods
|
||||
|
||||
\def\scale{1.0}
|
||||
|
||||
\def\latWidth{0.2808363589*\scale}
|
||||
|
||||
\def\RPVOR{3*\scale}
|
||||
\def\rectW{0.75*\scale}
|
||||
\def\RPVIR{2.8694005485*\scale}
|
||||
\def\BarrelIR{2.4547472901*\scale}
|
||||
\def\BarrelOR{2.5293848766*\scale}
|
||||
\def\ShieldOR{2.6040224631*\scale}
|
||||
|
||||
\def\bafCIRx{0.9829272561*\scale}
|
||||
\def\bafCIRy{2.1062726917*\scale}
|
||||
\def\bafCORx{1.0119529842*\scale}
|
||||
\def\bafCORy{2.1352984197*\scale}
|
||||
\def\bafMIRx{1.8254363328*\scale}
|
||||
\def\bafMIRy{1.5445999739*\scale}
|
||||
\def\bafMORx{1.8544620609*\scale}
|
||||
\def\bafMORy{1.573625702*\scale}
|
||||
|
||||
\tikzset{Assembly/.style={
|
||||
inner sep=0pt,
|
||||
text width=\latWidth in,
|
||||
minimum size=\latWidth in,
|
||||
draw=black,
|
||||
align=center
|
||||
}
|
||||
}
|
||||
|
||||
\def\tkzRPV{(0,0) circle (\RPVIR) (0,0) circle (\RPVOR)}
|
||||
\def\tkzBarrel{(0,0) circle (\BarrelIR) (0,0) circle (\BarrelOR)}
|
||||
\def\tkzShields{(0,0) circle (\BarrelOR) (0,0) circle (\ShieldOR)}
|
||||
|
||||
\def\tkzBaffCOR{(-\bafCORx, -\bafCORy) rectangle (\bafCORx, \bafCORy)}
|
||||
\def\tkzBaffCIR{(-\bafCIRx, -\bafCIRy) rectangle (\bafCIRx, \bafCIRy)}
|
||||
\def\tkzBaffMOR{(-\bafMORx, -\bafMORy) rectangle (\bafMORx, \bafMORy)}
|
||||
\def\tkzBaffMIR{(-\bafMIRx, -\bafMIRy) rectangle (\bafMIRx, \bafMIRy) }
|
||||
\def\tkzBaffleC{ \tkzBaffCIR \tkzBaffCOR }
|
||||
\def\tkzBaffleM{ \tkzBaffMIR \tkzBaffMOR }
|
||||
|
||||
\def\tkzBaffCClip{\tkzBaffCIR (-\RPVOR, -\RPVOR) rectangle (\RPVOR, \RPVOR)}
|
||||
\def\tkzBaffMClip{\tkzBaffMIR (-\RPVOR, -\RPVOR) rectangle (\RPVOR, \RPVOR)}
|
||||
|
||||
\def\highenr{blue!50}
|
||||
\def\midenr{yellow!50}
|
||||
\def\lowenr{red!50}
|
||||
\def\lightgray{black!25}
|
||||
\def\darkgray{black!80}
|
||||
|
||||
\begin{tikzpicture}[x=1in,y=1in, xshift=3in]
|
||||
\scalebox{0.6}{
|
||||
% draw RPV, barrel, and shield panels
|
||||
|
||||
\path[fill=black,even odd rule] \tkzRPV;
|
||||
\path[fill=black,even odd rule] \tkzBarrel;
|
||||
\begin{scope}
|
||||
\clip[rotate around={45:(0,0)}] (-\RPVOR, -\rectW) rectangle (\RPVOR, \rectW) (-\rectW, \RPVOR) rectangle (\rectW, -\RPVOR);
|
||||
\path[fill=black,even odd rule] \tkzShields;
|
||||
\end{scope}
|
||||
|
||||
|
||||
% draw assembly row/column headers
|
||||
|
||||
\draw[red, thick] ($(-7*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {R} -- ($(-7*\latWidth,4*\latWidth)$);
|
||||
\draw[red, thick] ($(-6*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {P} -- ($(-6*\latWidth,6*\latWidth)$);
|
||||
\draw[red, thick] ($(-5*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {N} -- ($(-5*\latWidth,7*\latWidth)$);
|
||||
\draw[red, thick] ($(-4*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {M} -- ($(-4*\latWidth,7*\latWidth)$);
|
||||
\draw[red, thick] ($(-3*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {L} -- ($(-3*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(-2*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {K} -- ($(-2*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(-1*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {J} -- ($(-1*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(-0*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {H} -- ($(-0*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(1*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {G} -- ($(1*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(2*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {F} -- ($(2*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(3*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {E} -- ($(3*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(4*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {D} -- ($(4*\latWidth,7*\latWidth)$);
|
||||
\draw[red, thick] ($(5*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {C} -- ($(5*\latWidth,7*\latWidth)$);
|
||||
\draw[red, thick] ($(6*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {B} -- ($(6*\latWidth,6*\latWidth)$);
|
||||
\draw[red, thick] ($(7*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[above, anchor=south] {A} -- ($(7*\latWidth,4*\latWidth)$);
|
||||
|
||||
\begin{scope}[rotate=90]
|
||||
\draw[red, thick] ($(-7*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {15} -- ($(-7*\latWidth,4*\latWidth)$);
|
||||
\draw[red, thick] ($(-6*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {14} -- ($(-6*\latWidth,6*\latWidth)$);
|
||||
\draw[red, thick] ($(-5*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {13} -- ($(-5*\latWidth,7*\latWidth)$);
|
||||
\draw[red, thick] ($(-4*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {12} -- ($(-4*\latWidth,7*\latWidth)$);
|
||||
\draw[red, thick] ($(-3*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {11} -- ($(-3*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(-2*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {10} -- ($(-2*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(-1*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {9} -- ($(-1*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(-0*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {8} -- ($(-0*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(1*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {7} -- ($(1*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(2*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {6} -- ($(2*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(3*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {5} -- ($(3*\latWidth,8*\latWidth)$);
|
||||
\draw[red, thick] ($(4*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {4} -- ($(4*\latWidth,7*\latWidth)$);
|
||||
\draw[red, thick] ($(5*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {3} -- ($(5*\latWidth,7*\latWidth)$);
|
||||
\draw[red, thick] ($(6*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {2} -- ($(6*\latWidth,6*\latWidth)$);
|
||||
\draw[red, thick] ($(7*\latWidth,\RPVOR/\latWidth*\latWidth)$) node[left, anchor=east] {1} -- ($(7*\latWidth,4*\latWidth)$);
|
||||
\end{scope}
|
||||
|
||||
% draw fuel assembly nodes
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-7*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-6*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-5*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-4*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-3*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-2*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-1*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-0*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 1*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 2*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 3*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 4*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 5*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 6*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 7*\latWidth,8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,8*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-7*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-6*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-5*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-4*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-3*\latWidth,7*\latWidth)$) {}; % L1
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-2*\latWidth,7*\latWidth)$) {6}; % K1
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-1*\latWidth,7*\latWidth)$) {}; % J1
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-0*\latWidth,7*\latWidth)$) {6}; % H1
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 1*\latWidth,7*\latWidth)$) {}; % G1
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 2*\latWidth,7*\latWidth)$) {6}; % F1
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 3*\latWidth,7*\latWidth)$) {}; % E1
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 4*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 5*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 6*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 7*\latWidth,7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,7*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-7*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-6*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-5*\latWidth,6*\latWidth)$) {}; % N2
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-5*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-4*\latWidth,6*\latWidth)$) {}; % M2
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-4*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-3*\latWidth,6*\latWidth)$) {16}; % L2
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-2*\latWidth,6*\latWidth)$) {}; % K2
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-1*\latWidth,6*\latWidth)$) {20}; % J2
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-0*\latWidth,6*\latWidth)$) {}; % H2
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 1*\latWidth,6*\latWidth)$) {20}; % G2
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 2*\latWidth,6*\latWidth)$) {}; % F2
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 3*\latWidth,6*\latWidth)$) {16}; % E2
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 4*\latWidth,6*\latWidth)$) {}; % D2
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 4*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 5*\latWidth,6*\latWidth)$) {}; % C2
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 5*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 6*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 7*\latWidth,6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,6*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-7*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-6*\latWidth,5*\latWidth)$) {}; % P3
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-6*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-5*\latWidth,5*\latWidth)$) {15}; % N3
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-5*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-4*\latWidth,5*\latWidth)$) {16}; % M3
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-4*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-3*\latWidth,5*\latWidth)$) {}; % L3
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-2*\latWidth,5*\latWidth)$) {16}; % K3
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-1*\latWidth,5*\latWidth)$) {}; % J3
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-0*\latWidth,5*\latWidth)$) {16}; % H3
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 1*\latWidth,5*\latWidth)$) {}; % G3
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 2*\latWidth,5*\latWidth)$) {16}; % F3
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 3*\latWidth,5*\latWidth)$) {}; % E3
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 4*\latWidth,5*\latWidth)$) {16}; % D3
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 4*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 5*\latWidth,5*\latWidth)$) {15}; % C3
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 5*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 6*\latWidth,5*\latWidth)$) {}; % B3
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 6*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 7*\latWidth,5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,5*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-7*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-6*\latWidth,4*\latWidth)$) {}; % P4
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-6*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-5*\latWidth,4*\latWidth)$) {16}; % N4
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-5*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-4*\latWidth,4*\latWidth)$) {}; % M4
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-4*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-3*\latWidth,4*\latWidth)$) {16}; % L4
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-2*\latWidth,4*\latWidth)$) {}; % K4
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-1*\latWidth,4*\latWidth)$) {12}; % J4
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-0*\latWidth,4*\latWidth)$) {}; % H4
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 1*\latWidth,4*\latWidth)$) {12}; % G4
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 2*\latWidth,4*\latWidth)$) {}; % F4
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 3*\latWidth,4*\latWidth)$) {16}; % E4
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 4*\latWidth,4*\latWidth)$) {}; % D4
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 4*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 5*\latWidth,4*\latWidth)$) {16}; % C4
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 5*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 6*\latWidth,4*\latWidth)$) {}; % B4
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 6*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 7*\latWidth,4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,4*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-7*\latWidth,3*\latWidth)$) {}; % R5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-7*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-6*\latWidth,3*\latWidth)$) {16}; % P5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-6*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-5*\latWidth,3*\latWidth)$) {}; % N5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-5*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-4*\latWidth,3*\latWidth)$) {16}; % M5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-4*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-3*\latWidth,3*\latWidth)$) {}; % L5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-2*\latWidth,3*\latWidth)$) {12}; % K5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-1*\latWidth,3*\latWidth)$) {}; % J5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-0*\latWidth,3*\latWidth)$) {12}; % H5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 1*\latWidth,3*\latWidth)$) {}; % G5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 2*\latWidth,3*\latWidth)$) {12}; % F5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 3*\latWidth,3*\latWidth)$) {}; % E5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 4*\latWidth,3*\latWidth)$) {16}; % D5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 4*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 5*\latWidth,3*\latWidth)$) {}; % C5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 5*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 6*\latWidth,3*\latWidth)$) {16}; % B5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 6*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 7*\latWidth,3*\latWidth)$) {}; % A5
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 7*\latWidth,3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,3*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-7*\latWidth,2*\latWidth)$) {6}; % R6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-7*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-6*\latWidth,2*\latWidth)$) {}; % P6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-6*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-5*\latWidth,2*\latWidth)$) {16}; % N6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-5*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-4*\latWidth,2*\latWidth)$) {}; % M6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-4*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-3*\latWidth,2*\latWidth)$) {12}; % L6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-2*\latWidth,2*\latWidth)$) {}; % K6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-1*\latWidth,2*\latWidth)$) {12}; % J6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-0*\latWidth,2*\latWidth)$) {}; % H6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 1*\latWidth,2*\latWidth)$) {12}; % G6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 2*\latWidth,2*\latWidth)$) {}; % F6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 3*\latWidth,2*\latWidth)$) {12}; % E6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 4*\latWidth,2*\latWidth)$) {}; % D6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 4*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 5*\latWidth,2*\latWidth)$) {16}; % C6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 5*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 6*\latWidth,2*\latWidth)$) {}; % B6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 6*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 7*\latWidth,2*\latWidth)$) {6}; % A6
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 7*\latWidth,2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,2*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-7*\latWidth,1*\latWidth)$) {}; % R7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-7*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-6*\latWidth,1*\latWidth)$) {20}; % P7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-6*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-5*\latWidth,1*\latWidth)$) {}; % N7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-5*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-4*\latWidth,1*\latWidth)$) {12}; % M7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-4*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-3*\latWidth,1*\latWidth)$) {}; % L7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-2*\latWidth,1*\latWidth)$) {12}; % K7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-1*\latWidth,1*\latWidth)$) {}; % J7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-0*\latWidth,1*\latWidth)$) {16}; % H7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 1*\latWidth,1*\latWidth)$) {}; % G7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 2*\latWidth,1*\latWidth)$) {12}; % F7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 3*\latWidth,1*\latWidth)$) {}; % E7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 4*\latWidth,1*\latWidth)$) {12}; % D7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 4*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 5*\latWidth,1*\latWidth)$) {}; % C7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 5*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 6*\latWidth,1*\latWidth)$) {20}; % B7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 6*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 7*\latWidth,1*\latWidth)$) {}; % A7
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 7*\latWidth,1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,1*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-7*\latWidth,0*\latWidth)$) {6}; % R8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-7*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-6*\latWidth,0*\latWidth)$) {}; % P8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-6*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-5*\latWidth,0*\latWidth)$) {16}; % N8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-5*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-4*\latWidth,0*\latWidth)$) {}; % M8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-4*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-3*\latWidth,0*\latWidth)$) {12}; % L8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-2*\latWidth,0*\latWidth)$) {}; % K8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-1*\latWidth,0*\latWidth)$) {16}; % J8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-0*\latWidth,0*\latWidth)$) {}; % H8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 1*\latWidth,0*\latWidth)$) {16}; % G8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 2*\latWidth,0*\latWidth)$) {}; % F8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 3*\latWidth,0*\latWidth)$) {12}; % E8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 4*\latWidth,0*\latWidth)$) {}; % D8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 4*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 5*\latWidth,0*\latWidth)$) {16}; % C8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 5*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 6*\latWidth,0*\latWidth)$) {}; % B8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 6*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 7*\latWidth,0*\latWidth)$) {6}; % A8
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 7*\latWidth,0*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,0*\latWidth)$) {};
|
||||
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-7*\latWidth,-1*\latWidth)$) {}; % R9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-7*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-6*\latWidth,-1*\latWidth)$) {20}; % P9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-6*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-5*\latWidth,-1*\latWidth)$) {}; % N9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-5*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-4*\latWidth,-1*\latWidth)$) {12}; % M9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-4*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-3*\latWidth,-1*\latWidth)$) {}; % L9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-2*\latWidth,-1*\latWidth)$) {12}; % K9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-1*\latWidth,-1*\latWidth)$) {}; % J9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-0*\latWidth,-1*\latWidth)$) {16}; % H9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 1*\latWidth,-1*\latWidth)$) {}; % G9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 2*\latWidth,-1*\latWidth)$) {12}; % F9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 3*\latWidth,-1*\latWidth)$) {}; % E9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 4*\latWidth,-1*\latWidth)$) {12}; % D9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 4*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 5*\latWidth,-1*\latWidth)$) {}; % C9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 5*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 6*\latWidth,-1*\latWidth)$) {20}; % B9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 6*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 7*\latWidth,-1*\latWidth)$) {}; % A9
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 7*\latWidth,-1*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,-1*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-7*\latWidth,-2*\latWidth)$) {6}; % R10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-7*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-6*\latWidth,-2*\latWidth)$) {}; % P10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-6*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-5*\latWidth,-2*\latWidth)$) {16}; % N10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-5*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-4*\latWidth,-2*\latWidth)$) {}; % M10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-4*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-3*\latWidth,-2*\latWidth)$) {12}; % L10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-2*\latWidth,-2*\latWidth)$) {}; % K10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-1*\latWidth,-2*\latWidth)$) {12}; % J10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-0*\latWidth,-2*\latWidth)$) {}; % H10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 1*\latWidth,-2*\latWidth)$) {12}; % G10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 2*\latWidth,-2*\latWidth)$) {}; % F10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 3*\latWidth,-2*\latWidth)$) {12}; % E10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 4*\latWidth,-2*\latWidth)$) {}; % D10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 4*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 5*\latWidth,-2*\latWidth)$) {16}; % C10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 5*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 6*\latWidth,-2*\latWidth)$) {}; % B10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 6*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 7*\latWidth,-2*\latWidth)$) {6}; % A10
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 7*\latWidth,-2*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,-2*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-7*\latWidth,-3*\latWidth)$) {}; % R11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-7*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-6*\latWidth,-3*\latWidth)$) {16}; % P11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-6*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-5*\latWidth,-3*\latWidth)$) {}; % N11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-5*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-4*\latWidth,-3*\latWidth)$) {16}; % M11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-4*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-3*\latWidth,-3*\latWidth)$) {}; % L11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-2*\latWidth,-3*\latWidth)$) {12}; % K11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-1*\latWidth,-3*\latWidth)$) {}; % J11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-0*\latWidth,-3*\latWidth)$) {12}; % H11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 1*\latWidth,-3*\latWidth)$) {}; % G11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 2*\latWidth,-3*\latWidth)$) {12}; % F11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 3*\latWidth,-3*\latWidth)$) {}; % E11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 4*\latWidth,-3*\latWidth)$) {16}; % D11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 4*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 5*\latWidth,-3*\latWidth)$) {}; % C11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 5*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 6*\latWidth,-3*\latWidth)$) {16}; % B11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 6*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 7*\latWidth,-3*\latWidth)$) {}; % A11
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 7*\latWidth,-3*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,-3*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-7*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-6*\latWidth,-4*\latWidth)$) {}; % P12
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-6*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-5*\latWidth,-4*\latWidth)$) {16}; % N12
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-5*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-4*\latWidth,-4*\latWidth)$) {}; % M12
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-4*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-3*\latWidth,-4*\latWidth)$) {16}; % L12
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-2*\latWidth,-4*\latWidth)$) {}; % K12
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-1*\latWidth,-4*\latWidth)$) {12}; % J12
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-0*\latWidth,-4*\latWidth)$) {}; % H12
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 1*\latWidth,-4*\latWidth)$) {12}; % G12
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 2*\latWidth,-4*\latWidth)$) {}; % F12
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 3*\latWidth,-4*\latWidth)$) {16}; % E12
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 4*\latWidth,-4*\latWidth)$) {}; % D12
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 4*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 5*\latWidth,-4*\latWidth)$) {16}; % C12
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 5*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 6*\latWidth,-4*\latWidth)$) {}; % B12
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 6*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 7*\latWidth,-4*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,-4*\latWidth)$) {};
|
||||
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-7*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-6*\latWidth,-5*\latWidth)$) {}; % P13
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-6*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-5*\latWidth,-5*\latWidth)$) {15}; % N13
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-5*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-4*\latWidth,-5*\latWidth)$) {16}; % M13
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-4*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-3*\latWidth,-5*\latWidth)$) {}; % L13
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-2*\latWidth,-5*\latWidth)$) {16}; % K13
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-1*\latWidth,-5*\latWidth)$) {}; % J13
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($(-0*\latWidth,-5*\latWidth)$) {16}; % H13
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 1*\latWidth,-5*\latWidth)$) {}; % G13
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 2*\latWidth,-5*\latWidth)$) {16}; % F13
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 3*\latWidth,-5*\latWidth)$) {}; % E13
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\midenr] at ($( 4*\latWidth,-5*\latWidth)$) {16}; % D13
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 4*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 5*\latWidth,-5*\latWidth)$) {15}; % C13
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 5*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 6*\latWidth,-5*\latWidth)$) {}; % B13
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 6*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 7*\latWidth,-5*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,-5*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-7*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-6*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-5*\latWidth,-6*\latWidth)$) {}; % N14
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-5*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-4*\latWidth,-6*\latWidth)$) {}; % M14
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-4*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-3*\latWidth,-6*\latWidth)$) {16}; % L14
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-2*\latWidth,-6*\latWidth)$) {}; % K14
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-1*\latWidth,-6*\latWidth)$) {20}; % J14
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($(-0*\latWidth,-6*\latWidth)$) {}; % H14
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 1*\latWidth,-6*\latWidth)$) {20}; % G14
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lowenr] at ($( 2*\latWidth,-6*\latWidth)$) {}; % F14
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 3*\latWidth,-6*\latWidth)$) {16}; % E14
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 4*\latWidth,-6*\latWidth)$) {}; % D14
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 4*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 5*\latWidth,-6*\latWidth)$) {}; % C14
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 5*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 6*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 7*\latWidth,-6*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,-6*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-7*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-6*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-5*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-4*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-3*\latWidth,-7*\latWidth)$) {}; % L15
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-3*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-2*\latWidth,-7*\latWidth)$) {6}; % K15
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-2*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-1*\latWidth,-7*\latWidth)$) {}; % J15
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-1*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($(-0*\latWidth,-7*\latWidth)$) {6}; % H15
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($(-0*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 1*\latWidth,-7*\latWidth)$) {}; % G15
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 1*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 2*\latWidth,-7*\latWidth)$) {6}; % F15
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 2*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\highenr] at ($( 3*\latWidth,-7*\latWidth)$) {}; % E15
|
||||
\node [Assembly, fill=\darkgray, opacity=0.7] at ($( 3*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 4*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 5*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 6*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 7*\latWidth,-7*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,-7*\latWidth)$) {};
|
||||
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-8*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-7*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-6*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-5*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-4*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-3*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-2*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-1*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($(-0*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 1*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 2*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 3*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 4*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 5*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 6*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 7*\latWidth,-8*\latWidth)$) {};
|
||||
\node [Assembly, fill=\lightgray, opacity=0.3] at ($( 8*\latWidth,-8*\latWidth)$) {};
|
||||
|
||||
% draw baffle north/south
|
||||
|
||||
\begin{scope}[even odd rule]
|
||||
\clip[rotate=90] \tkzBaffMClip;
|
||||
\path[fill=black] \tkzBaffleC;
|
||||
\end{scope}
|
||||
\begin{scope}[even odd rule]
|
||||
\clip \tkzBaffCClip;
|
||||
\clip \tkzBaffMClip;
|
||||
\path[fill=black, rotate=90] \tkzBaffleM;
|
||||
\end{scope}
|
||||
|
||||
% draw baffle east/west
|
||||
|
||||
\begin{scope}[rotate=90]
|
||||
\begin{scope}[even odd rule]
|
||||
\clip[rotate=90] \tkzBaffMClip;
|
||||
\path[fill=black] \tkzBaffleC;
|
||||
\end{scope}
|
||||
\begin{scope}[even odd rule]
|
||||
\clip \tkzBaffCClip;
|
||||
\clip \tkzBaffMClip;
|
||||
\path[fill=black, rotate=90] \tkzBaffleM;
|
||||
\end{scope}
|
||||
\end{scope}}
|
||||
\end{tikzpicture}
|
||||
|
|
@ -16,3 +16,4 @@ Theory and Methodology
|
|||
tallies
|
||||
eigenvalue
|
||||
parallelization
|
||||
cmfd
|
||||
|
|
|
|||
|
|
@ -1301,6 +1301,8 @@ attributes or sub-elements. These are not used in "voxel" plots:
|
|||
|
||||
*Default*: None
|
||||
|
||||
.. _usersguide_cmfd:
|
||||
|
||||
------------------------------
|
||||
CMFD Specification -- cmfd.xml
|
||||
------------------------------
|
||||
|
|
@ -1361,7 +1363,7 @@ It can be turned on with "true" and off with "false".
|
|||
*Default*: false
|
||||
|
||||
``<gauss_seidel_tolerance>`` Element
|
||||
--------------------
|
||||
------------------------------------
|
||||
|
||||
The ``<gauss_seidel_tolerance>`` element specifies two parameters. The first is
|
||||
the absolute inner tolerance for Gauss-Seidel iterations when performing CMFD
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue