[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 14)

[knarf at cct.lsu.edu]

User: knarf
Date: 2011/01/24 11:32 AM

Modified:
 /
  ET.tex

Log:
 more on base modules

Directory Changes:

Directory: /
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Property changes on: 
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Directory: /svn:ignore/
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   + *.aux
*.bbl
*.blg
*.log
*.out
*.toc


File Changes:

Directory: /
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File [modified]: ET.tex
Delta lines: +28 -3
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--- ET.tex	2011-01-24 17:20:25 UTC (rev 13)
+++ ET.tex	2011-01-24 17:32:44 UTC (rev 14)
@@ -367,11 +367,36 @@
 detail, because general relativistic codes use different conventions
 in especially those areas.
 
-\paragraph{Vacuum Spacetimes}
+Spacetime evolution methods used within the Cactus framework use
+different formulations, but all are based on the ADM
+construction~\cite{Arnowitt:1962hi}. This makes this formulation the
+natural choice of a common denominator to exchange data between
+modules using different formulations. The following variables are
+declared in the \codename{ADMBase} module:
+the three-metric $\gamma_ij$,
+the extrinsic curvature $K_ij$,
+the lapse function $\alpha$ and shift function $\beta^i$,
+both together with their first time derivatives.
+This base module also defines common parameters to manage interaction
+between different modules, like which type of initial data should
+be setup or which evolution method should be used at run-time.
 
-\paragraph{Relativistic Matter Spacetimes}
+Similar to \codename{ADMBase}, a module called \codename{HydroBase} defines the common
+basis for interactions between modules dealing with relativistic
+hydrodynamics. It is using the conventions of the Valencia
+formulation~\cite{Marti:1991wi,Banyuls:1997zz,Ibanez:2001:godunov}.
+In particular, it defines the rest-mass density $\varrho$, the gas
+pressure $p$, internal energy density $\epsilon$, the
+contravariant gas three velocity defined as
+$v^i = \frac{u^i}{\alpha u^0} + \frac{\beta^i}{\alpha}$, the electron
+fraction $Y_e$, the temperature $T$, the specific entropy per
+particle $s$ and the contravariant magnetic field vector $B^i$, defined
+as $B^i = \frac{1}{\sqrt{4\pi}} n_{\nu} F^{*\nu i}$, in terms of the dual
+$F^{*\mu\nu} = \frac{1}{2}\varepsilon^{\mu\nu\alpha\beta}F_{\alpha\beta}$
+to the Faraday tensor and the unit normal of the foliation of spacetime
+$n^\mu$. \todo{FL: Is this too much information? Should we put some of the
+formulas into a separate eq environment?}
 
-
 \subsection{Initial Data}
 \todo{1/2 page Josh, Bruno}