diff options
author | knarf <knarf@9c56c927-b35f-42c5-a3f6-df2e9f55b230> | 2010-01-12 20:51:22 +0000 |
---|---|---|
committer | knarf <knarf@9c56c927-b35f-42c5-a3f6-df2e9f55b230> | 2010-01-12 20:51:22 +0000 |
commit | a32568b88b98dd4cc8642cde6c9da957cd7ac7e1 (patch) | |
tree | 5e85bee6a0278d8902a5927f990c55f65e95c161 /doc | |
parent | 585d8889fb03daee0e1092bad5b6c9c21ad3a3df (diff) |
move development of EOS_Polytrope and EOS_Hybrid from Whisky to Cactus
git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinEOS/EOS_Hybrid/trunk@2 9c56c927-b35f-42c5-a3f6-df2e9f55b230
Diffstat (limited to 'doc')
-rw-r--r-- | doc/documentation.tex | 185 |
1 files changed, 185 insertions, 0 deletions
diff --git a/doc/documentation.tex b/doc/documentation.tex new file mode 100644 index 0000000..04ced87 --- /dev/null +++ b/doc/documentation.tex @@ -0,0 +1,185 @@ +% *======================================================================* +% Cactus Thorn template for ThornGuide documentation +% Author: Ian Kelley +% Date: Sun Jun 02, 2002 +% +% Thorn documentation in the latex file doc/documentation.tex +% will be included in ThornGuides built with the Cactus make system. +% The scripts employed by the make system automatically include +% pages about variables, parameters and scheduling parsed from the +% relevent thorn CCL files. +% +% This template contains guidelines which help to assure that your +% documentation will be correctly added to ThornGuides. More +% information is available in the Cactus UsersGuide. +% +% Guidelines: +% - Do not change anything before the line +% % START CACTUS THORNGUIDE", +% except for filling in the title, author, date etc. fields. +% - Each of these fields should only be on ONE line. +% - Author names should be sparated with a \\ or a comma +% - You can define your own macros are OK, but they must appear after +% the START CACTUS THORNGUIDE line, and do not redefine standard +% latex commands. +% - To avoid name clashes with other thorns, 'labels', 'citations', +% 'references', and 'image' names should conform to the following +% convention: +% ARRANGEMENT_THORN_LABEL +% For example, an image wave.eps in the arrangement CactusWave and +% thorn WaveToyC should be renamed to CactusWave_WaveToyC_wave.eps +% - Graphics should only be included using the graphix package. +% More specifically, with the "includegraphics" command. Do +% not specify any graphic file extensions in your .tex file. This +% will allow us (later) to create a PDF version of the ThornGuide +% via pdflatex. | +% - References should be included with the latex "bibitem" command. +% - use \begin{abstract}...\end{abstract} instead of \abstract{...} +% - For the benefit of our Perl scripts, and for future extensions, +% please use simple latex. +% +% *======================================================================* +% +% Example of including a graphic image: +% \begin{figure}[ht] +% \begin{center} +% \includegraphics[width=6cm]{MyArrangement_MyThorn_MyFigure} +% \end{center} +% \caption{Illustration of this and that} +% \label{MyArrangement_MyThorn_MyLabel} +% \end{figure} +% +% Example of using a label: +% \label{MyArrangement_MyThorn_MyLabel} +% +% Example of a citation: +% \cite{MyArrangement_MyThorn_Author99} +% +% Example of including a reference +% \bibitem{MyArrangement_MyThorn_Author99} +% {J. Author, {\em The Title of the Book, Journal, or periodical}, 1 (1999), +% 1--16. {\tt http://www.nowhere.com/}} +% +% *======================================================================* + +\documentclass{article} + +% Use the Cactus ThornGuide style file +% (Automatically used from Cactus distribution, if you have a +% thorn without the Cactus Flesh download this from the Cactus +% homepage at www.cactuscode.org) +\usepackage{../../../../doc/ThornGuide/cactus} + +\begin{document} + +% The author of the documentation +\author{Harry Dimmelmeier, Ian Hawke, Christian Ott} + +% The title of the document (not necessarily the name of the Thorn) +\title{EOS\_Hybrid} + +% the date your document was last changed, if your document is in CVS, +% please use: +\date{$ $Date$ $} + +\maketitle + +% Do not delete next line +% START CACTUS THORNGUIDE + +% Add all definitions used in this documentation here +% \def\mydef etc + +% Add an abstract for this thorn's documentation +\begin{abstract} + EOS\_Hybrid. The equation of state used for ``simple'' core + collapse simulations. +\end{abstract} + +% The following sections are suggestive only. +% Remove them or add your own. + +\section{The equations} +\label{sec:eqn} + +This equation provides the hybrid polytropic / ideal gas equation of +state used by Dimmelmeier et al.~\cite{Dimm05} for supernova collapse. A thorn +wanting to use this needs to use the CactusEOS interface found in +EOS\_Base. + +The equations are +\begin{eqnarray} + \label{eq:eosformulas} + P & = & P_{\textrm{poly}} + P_{\textrm{th}} \\ + \frac{\partial P}{\partial \rho} & = & \frac{\partial + P_{\textrm{poly}}}{\partial \rho} + \frac{\partial + P_{\textrm{th}_1}}{\partial \rho} + \frac{\partial + P_{\textrm{th}_2}}{\partial \rho} \\ + \frac{\partial P}{\partial \epsilon} & = & (\gamma_{\textrm{th}} - 1) + \rho, +\end{eqnarray} +where +\begin{eqnarray} + \label{eq:eostemps} + P_{\textrm{poly}} & = & K \rho^{\gamma} \\ + P_{\textrm{th}} & = & -K \frac{\gamma_{\textrm{th}} - 1}{\gamma - 1} + \rho^{\gamma} + (\gamma_{\textrm{th}} - 1) \rho \epsilon - + (\gamma_{\textrm{th}} - 1) \frac{\gamma - \gamma_1}{\gamma_2 - 1} K + \rho_{\textrm{nuc}}^{\gamma_1 - 1} \rho \\ + \frac{\partial P_{\textrm{poly}}}{\partial \rho} & = & \gamma K + \rho^{\gamma - 1} \\ + \frac{\partial P_{\textrm{th}_1}}{\partial \rho} & = & - \gamma K + \frac{\gamma_{\textrm{th}} - 1}{\gamma - 1} \rho^{\gamma -1} \\ + \frac{\partial P_{\textrm{th}_2}}{\partial \rho} & = & (\gamma - 1) + \epsilon - (\gamma_{\textrm{th}} - 1) \frac{\gamma - + \gamma_1}{(\gamma_1 - 1)(\gamma_2 - 1)} K \rho_{\textrm{nuc}} + (\gamma_1 - 1). +\end{eqnarray} +These expressions do not include the conversions between cgs and +Cactus units that are necessary inside the code. + +For more details, a recent paper to start with would +be~\cite{Dimm05}. + +% \section{Introduction} + +% \section{Physical System} + +% \section{Numerical Implementation} + +% \section{Using This Thorn} + +% \subsection{Obtaining This Thorn} + +% \subsection{Basic Usage} + +% \subsection{Special Behaviour} + +% \subsection{Interaction With Other Thorns} + +% \subsection{Support and Feedback} + +% \section{History} + +% \subsection{Thorn Source Code} + +% \subsection{Thorn Documentation} + +% \subsection{Acknowledgements} + + +\begin{thebibliography}{9} + +\bibitem{Dimm05} +H. Dimmelmeier, J. Novak, A. Font, J.~M. Ibanez, E. Mueller +\newblock +Combining spectral and shock-capturing methods: A new numerical approach +for 3D relativistic core collapse simulations +\newblock Phys. Rev. D71 064023 (2005) + +\end{thebibliography} + +% Do not delete next line +% END CACTUS THORNGUIDE + +\end{document} |