## 2. Numerical model## 2.1. Equations and numerical methodwhere ,
, where is the specific heat at
constant volume, is Boltzmann's
constant, is the ionization energy
of hydrogen and is the dissociation
energy of H These equations are solved in a 2D cylindrically symmetric geometry using a temporally and spatially second order accurate MUSCL scheme (van Leer 1977; Falle 1991). The code uses a linear Riemann solver except where the resolved pressure differs from either the left or right state at the cell interface by greater than 10% where it uses a non-linear solver (following Falle 1996, private communication). Non-linear Riemann solvers allow correct treatment of shocks and rarefactions without artificial viscosity or entropy fixes. Applying them only in non-smooth regions of the flow means that, while the benefits are the same, the computational overhead is minimised. This code is an updated version of that described in Downes & Ray (1998). Sometimes negative pressures are predicted by simulations involving radiative cooling. Typically these are overcome by simply resetting the calculated pressure to an arbitrary, but small, positive value. However, this involves injecting internal energy into the system and this is undesirable. A fairly reliable way of overcoming this problem is discussed in Appendix A. ## 2.2. Initial conditionsInitially the ambient density and pressure on the grid are uniform
and defined so that the ambient temperature on the grid is
K. The jet temperature is set to
K. The function
The jet enters the grid at and
and the boundary conditions are set
to force inflow with the jet parameters. with km s Nine simulations were run with varying values of density and velocity perturbation. These are listed in Table 1 which also gives the key we will use to refer to the simulations. In addition simulations of a purely atomic jet, and of a jet with a wide shear layer of almost 25 cells ( cm) were run. The velocity of the jet with the wide shear layer is given by where is given by Eq. 10. Each system was simulated to an age of 300 yrs. Although this is very young compared to the observed age of stellar jets, it was felt that the qualitative behaviour of the system at longer times could reliably be inferred from these results. The densities chosen are rather low to ensure adequate resolution of the system as described above. Unfortunately this precludes the use of the data of McKee et al. (1982) for calculations of the emissions from CO as their calculations are only valid for gases of much higher densities. As a result we present our findings in terms of the mass of molecular gas rather than its luminosity. © European Southern Observatory (ESO) 1999 Online publication: April 28, 1999 |