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diff --git a/doc/IGE335/Section3.04_bivac.tex b/doc/IGE335/Section3.04_bivac.tex new file mode 100644 index 0000000..5b66c03 --- /dev/null +++ b/doc/IGE335/Section3.04_bivac.tex @@ -0,0 +1,157 @@ +\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 |
