From 7c7511d577c233d97a5edf7f4403768935bf696b Mon Sep 17 00:00:00 2001 From: knarf Date: Wed, 18 Nov 2009 16:36:37 +0000 Subject: This is a _temporary_ repository to be able to start to work on the code right now. I have put in the public version of Whisky to start from. Everybody with commit rights should get commit messages (and the other way around). It should not be a problem to add people to that list, just ask. I don't want to get into political problems because someone feels excluded, but I also don't want to give everyone access per se. Frank git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinInitialData/GRHydro_InitData/trunk@3 ac85fae7-cede-4708-beff-ae01c7fa1c26 --- doc/documentation.tex | 151 ++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 151 insertions(+) create mode 100644 doc/documentation.tex (limited to 'doc') diff --git a/doc/documentation.tex b/doc/documentation.tex new file mode 100644 index 0000000..968e98a --- /dev/null +++ b/doc/documentation.tex @@ -0,0 +1,151 @@ +\documentclass{article} + +\begin{document} + +\title{Whisky\_Init\_Data} +\author{Luca Baiotti, Ian Hawke, Scott Hawley} +\date{24/07/2008} +\maketitle + +\abstract{Whisky\_Init\_Data - some initial data for {\tt Whisky}} + +\section{Introduction} +\label{sec:intro} + +This thorn generates some initial data for the Whisky code. There are more (and more physically +interesting) initial-data codes in other thorns. As with the Whisky code itself, please feel free to +add, alter or extend any part of this code. However please keep the documentation up to date (even, +or especially, if it's just to say what doesn't work). + +Currently this thorn contains a few tests that should really be test suites, some shock-tube +initial data, +%some (largely untested and unmaintained; please use the TOV initial-data codes in the +%dedicated thorns) TOV initial data solver routines, +a routine to set atmopshere everywhere on the +grid (for tests), a routine to read initial data from files (not very generic, tough) and a routine +to set up the simple-wave initial data . + + +\subsection{Tests} +\label{sec:tests} + +There are tests of the TVD reconstruction routine and of the routines +that convert between conservative and primitive variables. These all +just produce output to the screen or to {\tt fort.*} files. The +reconstruction test outputs the function to be reconstructed and the +boundary-extended values. The conservative-to-primitive test just +outputs the two sets of variables. If you haven't altered the code an if you set +\begin{verbatim} +eos_polytrope::eos_gamma = 2.0 +eos_polytrope::eos_k = 100.0 +\end{verbatim} +(which are the defaults), the output should be +% I checked that in 2008 the number were still right (but one gets them with eos_gamma=2.0 and +% eos_k ~ 0.1865) and committed the new ones for the default eos parameter values. + +\begin{verbatim} + primitive variables: + rho : 1.29047172182043 + velx : 9.902578465178671E-004 + vely : 9.902578465178671E-004 + velz : 9.902578465178671E-004 + eps : 0.374770481293314 + press : 166.531726481819 + w_lor : 1.00000147091915 +\end{verbatim} +The conservative to primitive to conservative test outputs the initial +and final data which should agree. + +\subsection{Shocktube tests} +\label{sec:shock} + +There are three possible shock-tube problems, referred to as {\tt Sod}, +{\tt Simple} and {\tt Blast}, with initial data +\begin{center} + \begin{tabular}[c]{|c|c|c|c|c|c|c|} + \hline Type & $\rho_{_L}$ & $v^i_{_L}$ & $\varepsilon_{_L}$ & $\rho_{_R}$ & $v^i_{_R}$ + & $\varepsilon_{_R}$ \\ \hline + Sod & 1 & 0 & 1.5 & 0.125 & 0 & 0.15 \\ + Simple & 10 & 0 & 20 & 1 & 0 & $10^{-6}$ \\ + Blast & 1 & 0 & 1500 & 1 & 0 & $1.5\cdot 10^{-2}$ \\ \hline + \end{tabular} +\end{center} +The shock shape can be planar (along each axis or along the main diagonal) or spherical and the +position of the plane or of the center of the sphere can be chosen though parameters. +If a diagonal shock is selected, the initial data is set to either the left or right +state depending on where the centre of the cell falls. Cleverer +routines that weight the initial data to avoid ``staircasing'' may be +added if there is demand. For more discussion on shock tubes +see~\cite{livrevsrrfd}. + + +%\subsection{TOV stars} +%\label{sec:tov} +% +%The Tolman-Oppenheimer-Volkoff solution is a spherically symmetric +%fluid ball matched to a Schwarzschild exterior. Typically an +%atmosphere is placed in the exterior to stop the equations of motion +%of the fluid being singular. Given an equation of state, the central +%density $\rho_c$ is specified. Then the solution is found by +%integrating the radial equations +%\begin{eqnarray} +% \label{eq:tov} +% \frac{\partial P(r)}{\partial r} & = & - \frac{(\rho + \rho \epsilon +% + P)(m + 4\pi r^3 P)}{r (r - 2m)} \\ +% \frac{\partial (\log \alpha (r))}{\partial r} & = & \frac{m + 4 \pi +% r^3 P}{r (r - 2m)} \\ +% \frac{\partial m(r)}{\partial r} & = & 4 \pi r^2 (\rho + \rho +% \epsilon) \\ +% \gamma_{rr}(r) & = & \left( 1-\frac{2m(r)}{r} \right)^{-1}, +%\end{eqnarray} +%where $m$ is the mass energy contained in a sphere radius $r$, +%$\gamma_{ij}$ the 3-metric, and $\alpha$ the lapse in standard +%Schwarzschild like coordinates. For more details see~\cite{hydro1}. +% +%The routines here, written by Scott Hawley, use the LSODA library to +%integrate the equations and then interpolate onto the Cartesian +%grid. +% +%This routine is untested and unmaintained: please use other thorns providing TOV initial data. They +%are located in dedicated thorns of this arrangement. + +\subsection{Only atmosphere} +\label{sec:only-atmo} + +For testing purposes, this routine sets all the points to the values of the atmosphere. + + +\subsection{Simple wave} +\label{sec:simple-wave} + +This routine stes initial data for a simple wave with sinusoidal initial function for the velocity, +as described in Anile, Miller, Motta, {\it Formation and damping of relativistic strong + shocks},Phys. Fluids {\bf 26}, 1450 (1983). + + + +\begin{thebibliography}{1} + +\bibitem{livrevsrrfd} +J.~M. Mart{\'{\i}} and E.~M{\"u}ller. +\newblock Numerical hydrodynamics in {S}pecial {R}elativity. +\newblock {\em Living Rev. Relativity}, {\bf 3}, 1999. +\newblock [Article in online journal], cited on 31/7/01, + http://www.livingreviews.org/Articles/Volume2/1999-3marti/index.html. + +\bibitem{hydro1} +J.~A. Font, M. Miller, W. Suen and M. Tobias. +\newblock Three Dimensional Numerical General Relativistic +Hydrodynamics I: Formulations, Methods, and Code Tests +\newblock {\em Phys. Rev.}, {\bf D61}, 044011, 2000. + +\end{thebibliography} + + +\include{interface} +\include{param} +\include{schedule} + +\end{document} + + -- cgit v1.2.3