[Commits] [svn:einsteintoolkit] GRHydro/trunk/doc/ (Rev. 338)

[bcmsma at astro.rit.edu]

User: bmundim
Date: 2012/05/18 12:17 AM

Modified:
 /trunk/doc/
  documentation.tex

Log:
 Correct S_i conserved variable index.

File Changes:

Directory: /trunk/doc/
======================

File [modified]: documentation.tex
Delta lines: +4 -4
===================================================================
--- trunk/doc/documentation.tex	2012-05-17 19:48:27 UTC (rev 337)
+++ trunk/doc/documentation.tex	2012-05-18 05:17:13 UTC (rev 338)
@@ -308,8 +308,8 @@
 where ${\bf q}$ is a set of {\it conserved variables}, ${\bf f}^{(i)}
 ({\bf q})$ the fluxes and ${\bf s} ({\bf q})$ the source
 terms.
-The five conserved variables are labeled $D$, $S^i$, and $\tau$, where
-$D$ is the generalized particle number density, $S^i$ are the generalized
+The five conserved variables are labeled $D$, $S_i$, and $\tau$, where
+$D$ is the generalized particle number density, $S_i$ are the generalized
 momenta in each direction, and $\tau$ is an internal energy term.
 These conserved variables are composed from a set of {\it primitive variables},
 which are $\rho$, the rest-mass density, $p$, the
@@ -334,7 +334,7 @@
 \begin{eqnarray}
   \label{eq:prim2con}
    D &=& \sqrt{\gamma}W\rho \nonumber \\
-   S^i &=& \sqrt{\gamma} \rho h W^2 v^i \nonumber \\
+   S_i &=& \sqrt{\gamma} \rho h W^2 v_i \nonumber \\
    \tau &=& \sqrt{\gamma}\left( \rho h W^2 - p\right) - D, 
 \end{eqnarray}
 where $\gamma$ is the determinant of the spatial 3-metric $\gamma_{ij}$ and 
@@ -1796,7 +1796,7 @@
   attempt is made to convert to primitive variables. If the iterative
   algorithm returns a negative (and hence unphysical) value of $\rho$,
   then $\rho$ is reset to the atmosphere value, the velocities are set
-  to zero, and $P$, $\epsilon$, $S^i$ and $\tau$ are reset to be
+  to zero, and $P$, $\epsilon$, $S_i$ and $\tau$ are reset to be
   consistent with $\rho$ (and $D$). Note that even though the
   polytropic equation of state gives us sufficient information to
   calculate a consistent value of $D$, this is not done.