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

Modified: / ET.tex

Log: more on base modules

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File [modified]: ET.tex Delta lines: +28 -3 =================================================================== --- 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}