From f01c8cb3856f99c62b3f13aa052aa6aa47d2f359 Mon Sep 17 00:00:00 2001 From: bmundim Date: Tue, 13 Mar 2012 17:06:08 +0000 Subject: epsilon: specific internal energy (ie energy/mass) git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinEvolve/GRHydro/trunk@315 c83d129a-5a75-4d5a-9c4d-ed3a5855bf45 --- doc/documentation.tex | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) (limited to 'doc') diff --git a/doc/documentation.tex b/doc/documentation.tex index fdca0c8..9387fbf 100644 --- a/doc/documentation.tex +++ b/doc/documentation.tex @@ -204,11 +204,11 @@ still there for reference. For the equations of state, two ``types'' are recognized, controlled by the parameter {\tt GRHydro\_eos\_type}. These are {\tt "Polytype"} -where the pressure is a function of the density, $P=P(\rho)$, and the +where the pressure is a function of the rest-mass density, $P=P(\rho)$, and the more generic {\tt "General"} type where the pressure is a function -of the density and the internal energy, $P=P(\rho, \epsilon)$. For the +of the rest-mass density and the specific internal energy, $P=P(\rho, \epsilon)$. For the {\tt Polytype} equations of state one fewer equation is evolved and -the specific internal energy is set directly from the density. The +the specific internal energy is set directly from the rest-mass density. The actual equation of state used is controlled by the parameter {\tt GRHydro\_eos\_table}. Polytype equations of state include {\tt "2D\_Polytrope"} and general equations of state include {\tt @@ -312,8 +312,8 @@ 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 density, $p$, the -pressure, $v^i$, the fluid 3-velocities, $\epsilon$, the internal +which are $\rho$, the rest-mass density, $p$, the +pressure, $v^i$, the fluid 3-velocities, $\epsilon$, the specific internal energy, and $W$, the Lorentz factor, via the following relations % from GRHydro/src/Prim2con.F90 % w = 1.d0 / sqrt(1.d0 - (gxx*dvelx*dvelx + gyy*dvely*dvely + gzz & @@ -342,7 +342,7 @@ $h \equiv 1 + \epsilon + p/\rho$. Only five of the primitive variables are independent. Usually the Lorentz factor is defined in terms of the velocities and the metric as $W = (1-\gamma_{ij}v^i v^j)^{-1/2}$. -Also one of the pressure, density or internal energy terms is given in +Also one of the pressure, rest-mass density or specific internal energy terms is given in terms of the other two by an {\it equation of state}. The fluxes are usually defined in terms of both the conserved -- cgit v1.2.3