in collaboration with Mike Zingale
We have developed a new algorithm for low speed flows in white dwarfs, which includes the compressiblity effects due to the background stratification. This is a generalization of the pseudo-incompressible model of Durran (1989), accounting for the thermodynamics of the stellar equation of state.
Some comparisons with compressible and anelastic solvers are documented in the ApJ paper. In all cases, a 500 km portion of a one-dimensional white dwarf initial model was mapped into the domain and given a small perturbation near the base.
The gravitational acceleration, g, is taken as -1.9e10 -- this is the value one would get from the midpoint of the radius range we are considering.
The domain size is:
xmin = 0.e0 xmax = 5.e7 ymin = 5.e7 ymax = 1.e8
The initial temperature perturbation is done in pressure equilibrium. The temperature is specified as:
pert_ellipse = ((xcc - xctr)/r_pert)**2 + &
((ycc - yctr)/r_pert)**2
tempZone = temp_ambient + &
(temp_perturb - temp_ambient)* &
(0.5d0 + 0.5d0*tanh((2.0 - sqrt(pert_ellipse))/0.9d0))
tempZone = max(min(temp_perturb,tempZone), temp_ambient)
with
xctr = 2.5e7 yctr = 6.25e7 r_pert = 1.25e6 temp_pert = 6.e9
Here, temp_ambient is the temperature in the zone before any perturbation -- this just ensures that the perturbation does not decrease the temperature anywhere. The pressure in the perturbation is unchanged, so a new density is found with the new temperature through the EOS.