From 7dfcc480ba1e19bd3232349fc733caef94034292 Mon Sep 17 00:00:00 2001 From: stainer_t Date: Mon, 8 Sep 2025 13:48:49 +0200 Subject: Initial commit from Polytechnique Montreal --- doc/IGE351/SectDasminfo.tex | 342 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 342 insertions(+) create mode 100644 doc/IGE351/SectDasminfo.tex (limited to 'doc/IGE351/SectDasminfo.tex') diff --git a/doc/IGE351/SectDasminfo.tex b/doc/IGE351/SectDasminfo.tex new file mode 100644 index 0000000..445273c --- /dev/null +++ b/doc/IGE351/SectDasminfo.tex @@ -0,0 +1,342 @@ +\section{Contents of a \dir{asminfo} directory}\label{sect:asminfodir} + +This directory contains the multigroup collision probabilities and response matrices +required in the solution of the transport equation. + +\subsection{State vector content for the \dir{asminfo} data structure}\label{sect:asminfostate} + +The dimensioning parameters for this data structure, which are stored in the state vector +$\mathcal{S}^{a}_{i}$, represent: + +\begin{itemize} +\item The type of collision probabilities considered $I_{T}=\mathcal{S}^{a}_{1}$ where + +\begin{displaymath} +I_{T} = \left\{ +\begin{array}{rl} + 1 & \textrm{Scattering reduced collision probability or response matrix}\\ + 2 & \textrm{Direct collision probability or response matrix} \\ + 3 & \textrm{Scattering reduced directional collision probability} \\ + 4 & \textrm{Direct directional collision probability} +\end{array} \right. +\end{displaymath} + +\item The type of collision probability closure relation used $I_{C}=\mathcal{S}^{a}_{2}$ +(see \moc{NORM} keyword in \moc{ASM:} operator input option) + +\begin{displaymath} +I_{C} = \left\{ +\begin{array}{rl} + 0 & \textrm{Total reflection closure relation} \\ + 1 & \textrm{No closure relation used} +\end{array} \right. +\end{displaymath} + +\item A parameter related to the albedo leakage model $I_{\beta}=\mathcal{S}^{a}_{3}$ +(see \moc{ALSB} keyword in \moc{ASM:} operator input option) + +\begin{displaymath} +I_{\beta} = \left\{ +\begin{array}{rl} + 0 & \textrm{Groupwise escape matrices \moc{WIS} are stored} \\ + 1 & \textrm{No information is stored} +\end{array} \right. +\end{displaymath} + +\item $\mathcal{S}^{a}_{4}$ (not used) + +\item The option to indicate whether response matrix or collision probability matrices are stored +on the structure $I_{p}=\mathcal{S}^{a}_{5}$ (see \moc{PIJ} and \moc{ARM} +keyword in \moc{ASM:} operator input option) + +\begin{displaymath} +I_{p} = \left\{ +\begin{array}{rl} + 1 & \textrm{Response matrices will be stored (the \moc{ARM} keyword was +selected)} \\ + 2 & \textrm{Collision probability matrices will be stored (the \moc{PIJ} keyword was +selected)} +\end{array} \right. +\end{displaymath} + +\item The option to indicate the type of streaming model used $I_{k}=\mathcal{S}^{a}_{6}$ (see \moc{PIJK} and \moc{ECCO} +keyword in \moc{ASM:} operator input option) + +\begin{displaymath} +I_{k} = \left\{ +\begin{array}{rl} + 1 & \textrm{No streaming model used (a leakage model may or may not be used)} \\ + 2 & \textrm{Isotropic streaming model used (ECCO model)} \\ + 3 & \textrm{Anisotropic streaming model used (TIB\`ERE model)} +\end{array} \right. +\end{displaymath} + +\item The type of collision probability normalization method used $I_{n}=\mathcal{S}^{a}_{7}$ (see +\moc{PNOR} keyword in \moc{ASM:} operator input option) + +\begin{displaymath} +I_{n} = \left\{ +\begin{array}{rl} + 0 & \textrm{No normalization} \\ + 1 & \textrm{Gelbard normalization algorithm} \\ + 2 & \textrm{Diagonal element normalization} \\ + 3 & \textrm{Non-linear normalization} \\ + 4 & \textrm{Helios type normalization} +\end{array} \right. +\end{displaymath} + +\item Number of energy groups +$G=\mathcal{S}^{a}_{8}$ + +\item Number of unknown in flux system $N_{u}=\mathcal{S}^{a}_{9}$ + +\item Number of mixtures $N_{m}=\mathcal{S}^{a}_{10}$ + +\item Number of Legendre orders of the scattering cross sections used in the +main transport solution. $N_{\rm ans}=\mathcal{S}^{a}_{11}$ + +\item Flag for the availability of diffusion coefficients. $I_{\rm diff}=\mathcal{S}^{a}_{12}$ + +\begin{displaymath} +I_{\rm diff} = \left\{ +\begin{array}{rl} + 0 & \textrm{No diffusion coefficients available;} \\ + 1 & \textrm{Diffusion coefficients are available.} +\end{array} \right. +\end{displaymath} + +\item Type of equation solved. $I_{\rm bfp}=\mathcal{S}^{a}_{13}$ +\begin{displaymath} +\mathcal{S}^{t}_{13} = \left\{ +\begin{array}{rl} + 0 & \textrm{Boltzmann transport equation} \\ + 1 & \textrm{Boltzmann Fokker-Planck equation with Galarkin energy propagation factors} \\ + 2 & \textrm{Boltzmann Fokker-Planck equation with Przybylski and Ligou energy propagation} \\ + & \textrm{factors.} +\end{array} \right. +\end{displaymath} + +\end{itemize} + +\subsection{The main \dir{asminfo} directory}\label{sect:asminfodirmain} + +On its first level, the +following records and sub-directories will be found in the \dir{asminfo} directory: + +\begin{DescriptionEnregistrement}{Main records and sub-directories in \dir{asminfo}}{8.0cm} +\CharEnr + {SIGNATURE\blank{3}}{$*12$} + {Signature of the data structure ($\mathsf{SIGNA}=${\tt L\_PIJ\blank{7}}).} +\CharEnr + {LINK.MACRO\blank{2}}{$*12$} + {Name of the {\sc macrolib} on which the collision probabilities are based.} +\CharEnr + {LINK.TRACK\blank{2}}{$*12$} + {Name of the {\sc tracking} on which the collision probabilities are based.} +\IntEnr + {STATE-VECTOR}{$40$} + {Vector describing the various parameters associated with this data structure $\mathcal{S}^{a}_{i}$, + as defined in \Sect{asminfostate}.} +\CharEnr + {TRACK-TYPE\blank{2}}{$*12$} + {Type of tracking considered ($\mathsf{CDOOR}$). Allowed values are: + {\tt 'EXCELL'}, {\tt 'SYBIL'}, {\tt 'MCCG'}, {\tt 'SN'}, {\tt 'BIVAC'} and {\tt 'TRIVAC'}.} +\DirlEnr + {GROUP\blank{7}}{$\mathcal{S}^{a}_{8}$} + {List of energy-group sub-directories. Each component of the list is a directory containing + the multigroup collision probabilities and response matrices associated with an energy group. + The specification of this directory is given in Sect.~\ref{sect:asminfodhdirgroup} or~\ref{sect:asminfodirgroup} + depending if a double-heterogeneity is present or not. A double-heterogeneity is present if $\mathcal{S}^{t}_{40}=1$ + in the {\sc tracking} object.} +\end{DescriptionEnregistrement} + +\clearpage + +\subsection{The \moc{GROUP} double-heterogeneity group sub-directory}\label{sect:asminfodhdirgroup} + +This directory is containing the following records, corresponding to a single energy group: + +\begin{DescriptionEnregistrement}{Records and sub-directories in \moc{GROUP}}{7.0cm} + +\RealEnr + {DRAGON-TXSC\blank{1}}{$N_{m}+1$}{cm$^{-1}$} + {where $N_{m}=\mathcal{P}_{1}$. The total cross section $\Sigma_{m}^{g}$ for $N_{m}+1$ composite mixtures assuming that the first mixture + represents void ($\Sigma_{m}^{g}=0$). A transport correction may or may not + be included. The first component of this array is always equal to 0.} +\RealEnr + {DRAGON-S0XSC}{$N_{m}+1,N_{\rm ans}$}{cm$^{-1}$} + {The within group scattering cross section $\Sigma_{0,m,w}$ (see \Sect{macrolibdirgroup}) + for $N_{m}+1$ composite mixtures assuming that the first mixture + represents void ($\Sigma_{0,m,w}^{g}=0$). A transport correction may or may not + be included. Many Legendre orders may be given. The first component of this + array, for each Legendre order, is always equal to 0.} +\IntEnr + {NCO\blank{9}}{${\cal M}$} + {where ${\cal M}=\mathcal{P}_{2}-\mathcal{P}_{1}$. Number of composite mixtures in each macro-mixture.} +\OptRealEnr + {RRRR\blank{8}}{${\cal M}$}{$\mathcal{P}_{6}=1,2$}{} + {Group-dependent double-heterogeneity information.} +\OptRealEnr + {QKOLD\blank{7}}{$\mathcal{P}_{4},\mathcal{P}_{5},{\cal M}$}{$\mathcal{P}_{6}=1$}{} + {Group-dependent double-heterogeneity information related to the escape probabilities in the micro-structures.} +\OptRealEnr + {QKDEL\blank{7}}{$\mathcal{P}_{4},\mathcal{P}_{5},{\cal M}$}{$\mathcal{P}_{6}=1,2$}{} + {Group-dependent double-heterogeneity information related to the escape probabilities in the micro-structures.} +\OptRealEnr + {PKL\blank{9}}{$\mathcal{P}_{4},\mathcal{P}_{5},\mathcal{P}_{5},{\cal M}$}{$\mathcal{P}_{6}=1,2$}{} + {Group-dependent double-heterogeneity information related to the collision probabilities in the micro-structures.} +\OptDbleEnr + {COEF\blank{8}}{${\cal F},{\cal F},{\cal M}$}{$\mathcal{P}_{6}=1,2$}{} + {where ${\cal F}=1+\mathcal{P}_{4}\times\mathcal{P}_{5}$. Group-dependent double-heterogeneity information.} +\OptRealEnr + {P1I\blank{9}}{$\mathcal{P}_{4},{\cal M}$}{$\mathcal{P}_{6}=3$}{} + {Group-dependent double-heterogeneity information related to the escape probabilities through the composite.} +\OptRealEnr + {P1DI\blank{8}}{$\mathcal{P}_{4},{\cal M}$}{$\mathcal{P}_{6}=3$}{} + {Group-dependent double-heterogeneity information related to the escape probabilities from the matrix.} +\OptRealEnr + {P1KI\blank{8}}{$\mathcal{P}_{4},\mathcal{P}_{5},{\cal M}$}{$\mathcal{P}_{6}=3$}{} + {Group-dependent double-heterogeneity information related to the escape probabilities from the micro-structures.} +\OptRealEnr + {SIGA1\blank{7}}{$\mathcal{P}_{4},{\cal M}$}{$\mathcal{P}_{6}=3$}{} + {Group-dependent double-heterogeneity information related to the equivalent total cross-section.} +\DirEnr + {BIHET\blank{7}} + {Directory containing collision probability or response matrix information related to the macro-geometry (i.$\,$e., + the geometry with homogenized micro-structures). The specification of this directory is given in \Sect{asminfodirgroup}. + Note that the value of $N_{m}=\mathcal{P}_{2}$ in this object is set to take into account the macro-mixtures. Similarly, + the value $N_{r}=\mathcal{P}_{3}$ is the number of macro-volumes.} +\end{DescriptionEnregistrement} + +\vskip -0.5cm + +\subsection{The \moc{GROUP} or \moc{BIHET} group sub-directory}\label{sect:asminfodirgroup} + +This directory is containing the following records, corresponding to a single energy group: + +\begin{DescriptionEnregistrement}{Records and sub-directories in \moc{GROUP}}{7.0cm} +\OptRealEnr + {ALBEDO\blank{6}}{$\mathcal{S}^{M}_{8}$}{$\mathcal{S}^{M}_{8}>0$}{} + {Surface ordered physical albedos in \moc{GROUP}. The number of physical albedos $\mathcal{S}^{M}_{8}$ is defined + in \Sect{macrolibstate}.} +\OptRealEnr + {ALBEDO-FU\blank{3}}{$\mathcal{S}^{M}_{8}$}{$\mathcal{S}^{M}_{8}>0$}{} + {Surface ordered physical albedo functions in \moc{GROUP}. The number of physical albedos $\mathcal{S}^{M}_{8}$ is defined + in \Sect{macrolibstate}.} +\RealEnr + {DRAGON-TXSC\blank{1}}{$N_{m}+1$}{cm$^{-1}$} + {The total cross section $\Sigma_{m}^{g}$ for $N_{m}+1$ mixtures assuming that the first mixture + represents void ($\Sigma_{m}^{g}=0$). A transport correction may or may not + be included. The first component of this array is always equal to 0.} +\OptRealEnr + {DRAGON-T1XSC}{$N_{m}+1$}{*}{cm$^{-1}$} + {where $N_{m}=\mathcal{P}_{1}$. The current-weighted total cross section $\Sigma_{1,m}^{g}$ for $N_{m}+1$ composite mixtures assuming that the first mixture + represents void ($\Sigma_{1,m}^{g}=0$). The first component of this array is always equal to 0.} +\OptRealEnr + {DRAGON-T2XSC}{$N_{m}+1$}{*}{cm$^{-1}$} + {where $N_{m}=\mathcal{P}_{1}$. The second moment-weighted total cross section $\Sigma_{2,m}^{g}$ for $N_{m}+1$ composite mixtures assuming that the first mixture + represents void ($\Sigma_{2,m}^{g}=0$). The first component of this array is always equal to 0.} +\RealEnr + {DRAGON-S0XSC}{$N_{m}+1,N_{\rm ans}$}{cm$^{-1}$} + {The within group scattering cross section $\Sigma_{0,m,w}$ (see \Sect{macrolibdirgroup}) + for $N_{m}+1$ mixtures assuming that the first mixture + represents void ($\Sigma_{0,m,w}^{g}=0$). A transport correction may or may not + be included. Many Legendre orders may be given. The first component of this + array, for each Legendre order, is always equal to 0.} +\OptRealEnr + {DRAGON-DIFF\blank{1}}{$N_{m}+1$}{$I_{\rm diff}=1$}{cm} + {Diffusion coefficients $D_{m}^{g}$ for $N_{m}+1$ mixtures assuming that the first mixture + represents void ($D_{m}^{g}=1.0\times 10^{10}$). The first component of this array is always equal to $1.0\times 10^{10}$.} +\OptRealEnr + {FUNKNO\$USS\blank{2}}{$N_{U}$}{*}{1} + {Solution of the Livolant-Jeanpierre fine-structure equation. $N_{U}$ is the number of unknowns in each subgroup and each energy group. (*) This information is + present if the flux is computed within module {\tt USS:}.} +\OptDirEnr + {STREAMING\blank{3}}{$I_{k}=2$} + {Directory containing P1 information to be used with the ECCO isotropic + streaming model. This directory uses the same specification as \moc{GROUP} + where P0 information is replaced with P1 information. Cross sections + used in this directory are {\sl not}--transport corrected.} +\end{DescriptionEnregistrement} + +Additional records are provided to support Boltzmann Fokker-Planck (BFP) solutions: + +\begin{DescriptionEnregistrement}{BFP records in \moc{GROUP}}{7.0cm} +\OptRealEnr + {DRAGON-ESTOP}{$N_{m}+1,2$}{$I_{\rm bfp}>0$}{MeV cm$^{-1}$} + {Initial and final stopping power.} +\OptRealEnr + {DRAGON-EMOMT}{$N_{m}+1$}{$I_{\rm bfp}>0$}{cm$^{-1}$} + {Restricted momentum transfer cross section. } +\OptRealEnr + {DRAGON-DELTE}{$1$}{$I_{\rm bfp}>0$}{MeV} + {Energy width of the energy group.} +\OptIntEnr + {DRAGON-ISLG\blank{1}}{$1$}{$I_{\rm bfp}>0$} + {Integer set to 0 in energy groups $< G$ and set to 1 in energy group $G$.} +\end{DescriptionEnregistrement} + +\vskip -0.5cm + +\subsubsection{The \moc{trafict} dependent records on a \moc{GROUP} directory}\label{sect:traficgrpdiringdir} + +If a collision probability method is used, the following records will also be +found on the group sub-directory: + +\begin{DescriptionEnregistrement}{Collision probability records in \moc{GROUP}}{7.0cm} +\OptRealEnr + {DRAGON-PCSCT}{$N_{r},N_{r}$}{$I_{p}=2$}{} + {The scattering-reduced ($I_{T}=1,3$) collision probability matrix ${\bf W}_{g}$ or direct + ($I_{T}=2,4$) collision probability matrix ${\bf p}_{g}$} +\OptRealEnr + {DRAGON1PCSCT}{$N_{r},N_{r}$}{$I_{k}=3$}{} +{The $x-$directed P1 scattering-reduced ($I_{T}=3$) collision probability matrix ${\bf Y}_{x,g}$ + or direct ($I_{T}=4$) collision probability matrix ${\bf p}_{x,g}$} +\OptRealEnr + {DRAGON2PCSCT}{$N_{r},N_{r}$}{$I_{k}=3$}{} + {The $y-$directed P1 scattering-reduced ($I_{T}=3$) collision probability matrix ${\bf Y}_{y,g}$ + or direct ($I_{T}=4$) collision probability matrix ${\bf p}_{y,g}$} +\OptRealEnr + {DRAGON3PCSCT}{$N_{r},N_{r}$}{$I_{k}=3$}{} + {The $z-$directed P1 scattering-reduced ($I_{T}=3$) collision probability matrix ${\bf Y}_{z,g}$ + or direct ($I_{T}=4$) collision probability matrix ${\bf p}_{z,g}$} +\OptRealEnr + {DRAGON1P*SCT}{$N_{r},N_{r}$}{$I_{k}=3$}{} + {The $x-$directed matrix ${\bf p}_g^{-1}{\bf p}_{x,g}^*$} +\OptRealEnr + {DRAGON2P*SCT}{$N_{r},N_{r}$}{$I_{k}=3$}{} + {The $y-$directed matrix ${\bf p}_g^{-1}{\bf p}_{y,g}^*$} +\OptRealEnr + {DRAGON3P*SCT}{$N_{r},N_{r}$}{$I_{k}=3$}{} + {The $z-$directed matrix ${\bf p}_g^{-1}{\bf p}_{z,g}^*$} +\OptRealEnr + {DRAGON-WIS\blank{2}}{$N_{r}$}{$I_{\beta}=1$}{} + {The scattering-reduced leakage matrix $W_{is}^{g}$ } +\end{DescriptionEnregistrement} + +\goodbreak +\noindent where +\begin{itemize} +\item the reduced collision probability matrix is defined as +$${\bf p}_{g}=\{p_{ij,g}\> ;\> \forall i \ {\rm and} \ j \}$$ +\item the reduced directional probability matrix, used in the first +TIB\`ERE equation, is defined as +$${\bf p}_{k,g}^*=\{p_{ij,k,g}^*\> ;\> \forall i \ {\rm and} \ j \} \ \ ; \ \ +k=x, \ y, \ {\rm or } \ z$$ +\item the reduced directional probability matrix, used in the second +TIB\`ERE equation, is defined as +$${\bf p}_{k,g}=\{p_{ij,k,g}\> ;\> \forall i \ {\rm and} \ j \} \ \ ; \ \ +k=x, \ y, \ {\rm or } \ z \ \ \ .$$ +The total cross sections used to compute this matrix are {\sl not}--transport +corrected. +\item the P0 scattering reduced collision probability matrix is defined as +$${\bf W}_{g}=[{\bf I}-{\bf p}_{g} \ {\bf\Sigma}_{{\rm s}0,g\gets g}]^{-1} {\bf p}_{g}$$ +\item the P1 scattering reduced directionnal collision probability matrix is defined as +$${\bf Y}_{k,g}=[{\bf I}-{\bf p}_{k,g} \ {\bf\Sigma}_{{\rm s}1,g\gets g}]^{-1} {\bf p}_{k,g} \ \ ; \ \ +k=x, \ y, \ {\rm or } \ z$$ +\end{itemize} + +\eject + +\input{SectDasmsybil.tex} % Description of Sybil response matrices +\input{SectDasmmccg.tex} % Description of MCCG response matrices -- cgit v1.2.3