Supernova and Hydrodynamic Instabilities
Turbulent Combustion in Type Ia Supernova
, James Glimm
, Yongmin Zhang
SUNY at Stony Brook ,
Brookhaven National Lab
Using the Front Tracking algorithm, we conducted numerical simulations of
Meshkov instabilities in spherical geometry. We demonstrated
scaling invariance with respect to shock Mach number for fluid mixing
statistics such as growth rate and volume fraction.
The images show the cross
sectional Front Plots of the instability when the
spherical interface is pushed outwards by a shock from the heavy fluid. The
images show the interface when hit by a shock of Mach number (top 3: 10,
20, 50; bottom 3: 100, 200, 300). The plots suggest an underlying similarity
which is independent of the shock strength.
Recently, we have proposed a 2D axi
symmetric model of a type Ia
supernova explosion, based on a Front Tracking sharp flame model .The
calculation is free from adjustable turbulent transport parameters, and in this
sense it is the spirit of LES (Large Eddy Simulation) turbulence simulations.
So far, we report successful explosions.
The left picture shows the density plots with tracked flames. The central
density is 2 x 10
g/cc. The mass of the star is 1.4M
. The right picture
shows a preliminary mesh convergence study.
However, a number of physical and modeling issues need to be addressed,
before the estimates of burning are considered to be definitive. So work is
under progress to implement a realistic equation of state, reaction network,
and a turbulence model.
Efficiency of Front Tracking
We studied the effectiveness and efficiency of explicit Front Tracking by
comparing the L
error for spherical shock refraction simulations with and
without tracking. We found that Front Tracking reduces the level of mesh
refinement needed to achieve a specified error tolerance by a significant
factor compared to corresponding methods without tracking, thus
substantially reducing the computational time as well as memory usage for
simulations with contacts or material interfaces.
Top two images show the late time evolution of the density plots for the
tracked and untracked spherical implosion simulations. The bottom two
graphs show the time
dependent contact errors, for various grid sizes, of
implosion and explosion simulations respectively.
 J. Glimm, J. Grove, Y. Zhang. “Interface Tracking for Axisymmetric Flows”,
SIAM J. Sci. Comp. 24:208
 J. Glimm, J. Grove, Y. Zhang, S. Dutta. “Numerical Study of Axisymmetric Richtmyer
Instability and Azimuthal Effect on Spherical Mixing”, J. Stat. Physics, 107:241
 S. Dutta, J. Glimm, J. Grove, D. Sharp, Y. Zhang. “Error Comparison in Tracked and Untracked
Spherical Simulations”, Comp. Math. with Appl, in press, 2003.
 S. Dutta, J. Glimm, J. Grove, D. Sharp, Y. Zhang. “Spherical Richtmyer
Math. Comp. in Simul., in press, 2003.
 Q. Zhang, M. J. Graham. “Scaling Laws for Unstable Interfaces Driven by Strong Shocks in
Cylindrical Geometry”, Phys. Rev. Lett.79:2674
 F. X. Timmes, S. E. Woosley. “The Conductive Propagation of Flames I. Degenerate C+O and
O+Ne+Mg White Dwarfs”, The Astrophysical Journal, 396:649
 A. M. Khokhlov, “Three Dimensional Modeling of the Deflagration Stage of a Type Ia Supernova
Explosion”, The Astrophysical Journal (Submitted), astro
 M. A. Reinicke, W. Hillebrandt, J. C. Niemeyer, “Three Dimensional Simulations of Type Ia
Supernova”, A & A, 391:1167
t = 0.6
t = 0.4
t = 0.4
Scaled growth rate, amplitude and volume fraction are insensitive to the
shock strength for Mach M > 10, 20, 10 respectively