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.