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author | bmundim <bmundim@c83d129a-5a75-4d5a-9c4d-ed3a5855bf45> | 2012-05-18 05:17:13 +0000 |
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committer | bmundim <bmundim@c83d129a-5a75-4d5a-9c4d-ed3a5855bf45> | 2012-05-18 05:17:13 +0000 |
commit | 38c73944d2e4cd7a22261278313274791b076848 (patch) | |
tree | 3f5ee2faa57e3b5f7a9f775d2ba389f46e90d665 /doc | |
parent | 9eaaeff77102591f18987eacc3fdc0ac5583d1cf (diff) |
Correct S_i conserved variable index.
git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinEvolve/GRHydro/trunk@338 c83d129a-5a75-4d5a-9c4d-ed3a5855bf45
Diffstat (limited to 'doc')
-rw-r--r-- | doc/documentation.tex | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/doc/documentation.tex b/doc/documentation.tex index 9387fbf..b6f3ff9 100644 --- a/doc/documentation.tex +++ b/doc/documentation.tex @@ -308,8 +308,8 @@ the flux conservative form 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 @@ energy, and $W$, the Lorentz factor, via the following relations \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 @@ used in three separate places. These are 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. |