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\documentclass{article}

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\begin{document}

% The author of the documentation
\author{Tanja Bode \textless tbode@gravity.psu.edu\textgreater\\
        Frank Löffler \textless knarf@cct.lsu.edu\textgreater}

% The title of the document (not necessarily the name of the Thorn)
\title{HydroBase}

% the date your document was last changed, if your document is in CVS, 
% please use:
\date{February 13, 2009}

\maketitle

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\begin{abstract}

HydroBase extends the CactusEinstein framework to include an interface for hydrodynamics to 
work within.  HydroBase's main function is to store the primitive variables, common among 
hydrodynamic simulations, commonly needed parameters, and schedule groups for the main 
functions of a hydrodynamics code.  This has been done with an eye on Whisky, but can be used 
to implement any hydrodynamics formulation.

\end{abstract}

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\section{Introduction}

The idea behind this thorn is to create a slim, common set of variables, parameters and
scheduling groups which can then be used by different hydrodynamics codes. It should contain
the common concepts of different hydrodynamics codes, but at the same time it should be
as slim as possible to remain as general as possible. HydroBase should not contain the
actual source code of typical routines of hydrodynamics codes, it should merely provide
a common setup in which hydrodynamics codes can put their routines.

Because there exist different formulations of the hydrodynamics equations and not all of
them involve concepts like conserved variabled or treat them
differently, which is the reason why these variables are not defined in HydroBase but this
is left to the hydrodynamics codes.

One of the advantages of such a common base is that modules of hydrodynamics codes only
working with entities defined in HydroBase could be used interchangeably. Prime examples
for this are initial data solvers or importers and analysis modules.
Another advantage is that the format of output generated by different hydrodynamics
codes in Cactus would be the same, including variable names and unit conventions, which
would improve the ability to compare results of different codes directly a lot.

\section{Using This Thorn}

HydroBase is to be used as a central part of hydrodynamics fields just as ADMBase is used as a 
central part of spacetime evolution and analysis codes. HydroBase only stores variables which
are common to most if not all hydrodynamics codes solving the Euler
equations, the so called primitive variables. These are also the variables which are needed
to couple to a spacetime solver and which are usually needed by analysis thorns. The usage of
a common set of variables by different hydrodynamics codes creates the possibility to share
parts of the code, e.g.\ initial data solvers or analysis routines. 

Currently the defined primitive variables are (see~\cite{livrevgrfd} for
details):
\begin{itemize}
 \item group \verb|hydrobase_prim_scalar_var|: scalar variables
 \begin{itemize}
  \item \verb|rho|: rest mass density $\varrho$
  \item \verb|press|: pressure $p$
  \item \verb|eps|: internal energy $\epsilon$
 \end{itemize}
 \item group \verb|hydrobase_prim_vector_var|: vector variables
 \begin{itemize}
  \item \verb|velx|, \verb|vely|, \verb|velz|: velocity $v^i$ defined as
      \begin{equation}
	  v^i = \frac{u^i}{\alpha u^0} + \frac{\beta^i}{\alpha}
      \end{equation}
      in terms of the four-velocity $u^\mu$, lapse $\alpha$, and shift vector
      $\beta^i$.
 \end{itemize}
\end{itemize}

HydroBase also sets up scheduling blocks that organize the main functions which modules of a 
hydrodynamics code may need. All of those scheduling blocks are optional, however if used,
they might simplify existing codes and make them more interoperable. HydroBase itself does
not schedule something inside most of the groups which it provides.

Currently the scheduling blocks are:
\begin{itemize}
 \item Initializing the primitive variables
 \item Converting primitive variables to conservative variables
 \item Calculating the right hand side (RHS) in the method of lines (MoL)
 \item Setting and updating an atmosphere mask
 \item Applying boundary conditions
\end{itemize}

In this way the initiation of the primitive variables, methods to recover the conservative
variables, and basic atmosphere handling can be implemented in different thorns while allowing
a central access point for analysis thorns.

\section{Units}

HydroBase uses a specific set of units, so that there are no
misunderstandings between thorns.  These units are derived from the
conventions
\begin{eqnarray}
  M = M_\mathrm{sun} &;& c = G = 1
\end{eqnarray}
which are commonly used in astrophysics and in relativity.

We assume the following definitions and constants of nature:
\begin{eqnarray}
  c             & = & 299792458\, \mathrm{m/s}
  \\
  G             & = & 6.67428\cdot 10^{-11}\, \mathrm{m^3/kg/s^2}
  \\
  \mu_0         & = & 4 \pi 10^{-7}\, \mathrm{N/A^2}
  \\
  \epsilon_0    & = & \frac{1}{\mu_0 c^2}
  \\
  M_\mathrm{sun} & = & 1.98892\cdot10^{30}\, \mathrm{kg}
\end{eqnarray}

This corresponds to the following units for mass, length, time, and
magnetic field:
\begin{eqnarray}
  [M] & = & M_\mathrm{sun}
  \\{}
  [L] & = & [M]\; G/c^2
  \\{}
  [T] & = & [L]\; / c
  \\{}
  [B] & = & 1/[L]\; / \sqrt{\epsilon_0 G / c^2}
\end{eqnarray}

\section{Acknowledgments}

This thorn was produced by Tanja Bode, Roland Haas, Frank Löffler, and Erik Schnetter.

\begin{thebibliography}{9}
\bibitem{livrevgrrfd}
    J.~A. Font.
    \newblock Numerical hydrodynamics in {G}eneral {R}elativity.
    \newblock {\em Living Rev. Relativity}, {\bf 3}, 2000.
    \newblock [Article in on-line journal], cited on 31/07/01,
      http://www.livingreviews.org/ Articles/Volume3/2000-2font/index.html.

\end{thebibliography}

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