From 7dfcc480ba1e19bd3232349fc733caef94034292 Mon Sep 17 00:00:00 2001
From: stainer_t <thomas.stainer@oecd-nea.org>
Date: Mon, 8 Sep 2025 13:48:49 +0200
Subject: Initial commit from Polytechnique Montreal

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+\subsubsection{The {\tt BIVACT:} tracking module}\label{sect:BIVACData}
+
+The {\tt BIVACT:} module provides an implementation of the diffusion or simplified $P_n$ method. The {\tt BIVACT:} module can only process
+1D/2D regular geometries of type \moc{CAR1D}, \moc{CAR2D} and \moc{HEX}. The geometry is analyzed and
+a LCM object with signature {\tt L\_BIVAC} is created with the tracking information.
+
+\vskip 0.2cm
+
+The calling specification for this module is:
+
+\begin{DataStructure}{Structure \dstr{BIVACT:}}
+\dusa{TRKNAM}
+\moc{:=} \moc{BIVACT:} $[$ \dusa{TRKNAM} $]$ 
+\dusa{GEONAM} \moc{::}  \dstr{desctrack} \dstr{descbivac}
+\end{DataStructure}
+
+\noindent  where
+\begin{ListeDeDescription}{mmmmmmm}
+
+\item[\dusa{TRKNAM}] {\tt character*12} name of the \dds{tracking} data
+structure that will contain region volume and surface area vectors in
+addition to region identification pointers and other tracking information.
+If \dusa{TRKNAM} also appears on the RHS, the previous tracking 
+parameters will be applied by default on the current geometry.
+
+\item[\dusa{GEONAM}] {\tt character*12} name of the \dds{geometry} data
+structure.
+
+\item[\dstr{desctrack}] structure describing the general tracking data (see
+\Sect{TRKData})
+
+\item[\dstr{descbivac}] structure describing the transport tracking data
+specific to \moc{BIVACT:}.
+
+\end{ListeDeDescription}
+
+\vskip 0.2cm
+
+The \moc{BIVACT:} specific tracking data in \dstr{descbivac} is defined as
+
+\begin{DataStructure}{Structure \dstr{descbivac}}
+$[$ $\{$ \moc{PRIM} $[$ \dusa{ielem} \dusa{icol} $]$ \\
+~~~~$|$ \moc{DUAL} $[$ \dusa{ielem} \dusa{icol} $]$ \\
+~~~~$|$ \moc{MCFD} $\}~]$ \\
+$[~\{$ \moc{PN} $|$ \moc{SPN} $\}$ $[$ \moc{DIFF} $]$ \dusa{nlf} $[$ \moc{SCAT} \dusa{iscat} $]~[$ \moc{VOID} \dusa{nvd}~$]~]$ \\
+{\tt ;}
+\end{DataStructure}
+
+\noindent where
+
+\begin{ListeDeDescription}{mmmmmmm}
+
+\item[\dstr{desctrack}] structure describing the general tracking data (see
+\Sect{TRKData})
+
+\item[\moc{PRIM}] keyword to set a primal finite element (classical)
+discretization.
+
+\item[\moc{DUAL}] keyword to set a mixed-dual finite element discretization. If the
+geometry is hexagonal, a Thomas-Raviart-Schneider method is used.
+
+\item[\moc{MCFD}] keyword to set a mesh-centered finite difference discretization
+in hexagonal geometry.
+
+\item[\dusa{ielem}] order of the finite element representation.  The values
+permitted are: 1 (linear polynomials), 2 (parabolic polynomials), 3 (cubic
+polynomials) or 4 (quartic polynomials). By default \dusa{ielem}=1.
+
+\item[\dusa{icol}] type of quadrature used to integrate the mass matrices. The
+values permitted are: 1 (analytical integration), 2  (Gauss-Lobatto quadrature)
+or 3 (Gauss-Legendre quadrature). By default \dusa{icol}=2. The analytical
+integration corresponds to classical finite elements; the Gauss-Lobatto
+quadrature corresponds to a variational or nodal type collocation and the
+Gauss-Legendre quadrature corresponds to superconvergent finite elements.
+
+\item[\moc{PN}] keyword to set a spherical harmonics ($P_n$) expansion of the flux.\cite{nse2005} This option is currently limited to 1D
+and 2D Cartesian geometries.
+
+\item[\moc{SPN}] keyword to set a simplified spherical harmonics ($SP_n$) expansion
+of the flux.\cite{nse2005,ane10a} This option is currently available with 1D and 2D Cartesian geometries
+and with 2D hexagonal geometries.
+
+\item[\moc{DIFF}] keyword to force using $1/3D^{g}$ as $\Sigma_1^{g}-\Sigma_{{\rm s}1}^{g}$ cross sections. A $P_1$ or $SP_1$ method
+will therefore behave as diffusion theory.
+
+\item[\dusa{nlf}] order of the $P_n$ or $SP_n$ expansion (odd number). Set to zero for diffusion theory (default value).
+
+\item[\moc{SCAT}] keyword to limit the anisotropy of scattering sources.
+
+\item[\dusa{iscat}] number of terms in the scattering sources. \dusa{iscat} $=1$ is used for
+isotropic scattering in the laboratory system. \dusa{iscat} $=2$ is used for
+linearly anisotropic scattering in the laboratory system. The default value is set to $n+1$
+in $P_n$ or $SP_n$ case.
+
+\item[\moc{VOID}] key word to set the number of base points in the Gauss-Legendre quadrature used to integrate
+void boundary conditions if \dusa{icol} $=3$ and \dusa{n} $\ne 0$.
+
+\item[\dusa{nvd}] type of quadrature. The values
+permitted are: 0 (use a (\dusa{n}$+2$)--point quadrature consistent with $P_{{\rm n}}$ theory),
+1 (use a (\dusa{n}$+1$)--point quadrature consistent with $S_{{\rm n}+1}$ theory),
+2 (use an analytical integration of the void boundary conditions). By default \dusa{nvd}=0.
+
+\end{ListeDeDescription}
+
+Various finite element approximations can be obtained by combining different
+values of \dusa{ielem} and \dusa{icol}:
+
+\begin{itemize}
+
+\item {\tt PRIM 1 1~:} Linear finite elements;
+
+\item {\tt PRIM 1 2~:} Mesh corner finite differences;
+
+\item {\tt PRIM 1 3~:} Linear superconvergent finite elements;
+
+\item {\tt PRIM 2 1~:} Quadratic finite elements;
+
+\item {\tt PRIM 2 2~:} Quadratic variational collocation method;
+
+\item {\tt PRIM 2 3~:} Quadratic superconvergent finite elements;
+
+\item {\tt PRIM 3 1~:} Cubic finite elements;
+
+\item {\tt PRIM 3 2~:} Cubic variational collocation method;
+
+\item {\tt PRIM 3 3~:} Cubic superconvergent finite elements;
+
+\item {\tt PRIM 4 2~:} Quartic variational collocation method;
+
+\item {\tt DUAL 1 1~:} Mixed-dual linear finite elements;
+
+\item {\tt DUAL 1 2~:} Mesh centered finite differences;
+
+\item {\tt DUAL 1 3~:} Mixed-dual linear superconvergent finite elements
+
+(numerically equivalent to {\tt PRIM~1~3});
+
+\item {\tt DUAL 2 1~:} Mixed-dual quadratic finite elements;
+
+\item {\tt DUAL 2 2~:} Quadratic nodal collocation method;
+
+\item {\tt DUAL 2 3~:} Mixed-dual quadratic superconvergent finite elements
+
+(numerically equivalent to {\tt PRIM~2~3});
+
+\item {\tt DUAL 3 1~:} Mixed-dual cubic finite elements;
+
+\item {\tt DUAL 3 2~:} Cubic nodal collocation method;
+
+\item {\tt DUAL 3 3~:} Mixed-dual cubic superconvergent finite elements
+
+(numerically equivalent to {\tt PRIM~3~3});
+
+\item {\tt DUAL 4 2~:} Quartic nodal collocation method;
+
+\end{itemize}
+\eject
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