Supernova and Hydrodynamic Instabilities

1. Supernova and Hydrodynamic Instabilities Srabasti Dutta1, James Glimm1,2, Yongmin Zhang1 1SUNY at Stony Brook , 2Brookhaven National Lab Spherical Richtmyer-Meshkov Instability Turbulent Combustion in Type Ia Supernova t = 0.6 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 109 g/cc. The mass of the star is 1.4MSun. 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. Using the Front Tracking algorithm, we conducted numerical simulations of Richtmyer-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. Efficiency of Front Tracking Untracked t = 0.4 Tracked t = 0.4 Scaled growth rate, amplitude and volume fraction are insensitive to the shock strength for Mach M > 10, 20, 10 respectively. References [1] J. Glimm, J. Grove, Y. Zhang. “Interface Tracking for Axisymmetric Flows”, SIAM J. Sci. Comp. 24:208-236, 2002. [2] J. Glimm, J. Grove, Y. Zhang, S. Dutta. “Numerical Study of Axisymmetric Richtmyer-Meshkov Instability and Azimuthal Effect on Spherical Mixing”, J. Stat. Physics, 107:241-260, 2002. [3] 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. [4] S. Dutta, J. Glimm, J. Grove, D. Sharp, Y. Zhang. “Spherical Richtmyer-Meshkov Instability”, Math. Comp. in Simul., in press, 2003. [5] Q. Zhang, M. J. Graham. “Scaling Laws for Unstable Interfaces Driven by Strong Shocks in Cylindrical Geometry”, Phys. Rev. Lett.79:2674-2677, 1997. [6] F. X. Timmes, S. E. Woosley. “The Conductive Propagation of Flames I. Degenerate C+O and O+Ne+Mg White Dwarfs”, The Astrophysical Journal, 396:649-667, 1992. [7] A. M. Khokhlov, “Three Dimensional Modeling of the Deflagration Stage of a Type Ia Supernova Explosion”, The Astrophysical Journal (Submitted), astro-ph/0008463. [8] M. A. Reinicke, W. Hillebrandt, J. C. Niemeyer, “Three Dimensional Simulations of Type Ia Supernova”, A & A, 391:1167-1172, 2002. We studied the effectiveness and efficiency of explicit Front Tracking by comparing the L1-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.