The Cellular Nuclear Burning problem is used primarily to test the function of the Burn simulation unit. The problem exhibits regular steady-state behavior and is based on one-dimensional models described by Chappman (1899) and Jouguet (1905) and Zel'dovich (Ostriker 1992), von Neumann (1942), and Doring (1943). This problem is solved in two dimensions. A complete description of the problem can be found in a recent paper by Timmes, Zingale et al(2000).
A 13 isotope -chain plus heavy-ion reaction network is used
in the calculations. A definition of what we mean by an
-chain reaction network is prudent. A strict
-chain
reaction network is only composed of (
,
) and
(
,
) links among the 13 isotopes
He,
C,
O,
Ne,
Mg,
Si,
S,
Ar,
Ca,
Ti,
Cr,
Fe, and
Ni. It is
essential, however, to include (
,p)(p,
) and
(
,p)(p,
) links in order to obtain reasonably accurate
energy generation rates and abundance levels when the temperature
exceeds
2.5
10
K. At these elevated temperatures
the flows through the (
,p)(p,
) sequences are faster
than the flows through the (
,
) channels. An
(
,p)(p,
) sequence is, effectively, an
(
,
) reaction through an intermediate isotope. In our
-chain reaction network, we include 8 (
,p)(p,
)
sequences plus the corresponding inverse sequences through the
intermediate isotopes
Al,
P,
Cl,
K,
Sc,
V,
Mn, and
Co by assuming steady state
proton flows. The two-dimensional calculations are performed in a planar geometry of size 256.0 cm by 25.0 cm.
The
initial conditions consist of a constant density of 10
g
cm
, temperature of 2
10
K, composition of pure
carbon X(
C)=1, and material velocity of
= 0 cm
s
. Near the x=0 boundary the initial conditions are perturbed to the
values given by the appropriate Chapman-Jouguet solution: a density of
4.236
10
g cm
, temperature of 4.423
10
K,
and material velocity of
= 2.876
10
cm s
.
Choosing different values
or different extents of the perturbation simply change how long it
takes for the initial conditions to achieve a near ZND state, as well as
the block structure of the mesh. Each block contains 8 grid points in the
x-direction, and 8 grid points in the y-direction. The default parameters for
cellular burning are given in Table 35.16.
The initial conditions and perturbation given above ignite the nuclear
fuel, accelerate the material, and produce an over-driven detonation
that propagates along the x-axis. The initially over-driven
detonation is damped to a near ZND state on short time-scale. After
some time, which depends on the spatial resolution and boundary
conditions, longitudinal instabilities in the density cause the planar
detonation to evolve into a complex, time-dependent structure. Figure 35.70 shows the pressure field of the detonation after
1.2610
s. The interacting transverse wave
structures are particularly vivid, and extend about 25 cm behind the
shock front. Figure 35.71 shows a close up of this traverse
wave region. Periodic boundary conditions are used at the walls parallel to
the y-axis while reflecting boundary conditions were used for the walls
parallel to the x-axis.
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