C. M. Malone

MAESTRO: AN ADAPTIVE LOW MACH NUMBER HYDRODYNAMICS ALGORITHM FOR STELLAR FLOWS

Many astrophysical phenomena are highly subsonic, requiring specialized numerical methods suitable for long-time integration. In a series of earlier papers we described the development of MAESTRO, a low Mach number stellar hydrodynamics code that can be used to simulate long-time, low-speed flows that would be prohibitively expensive to model using traditional compressible codes. MAESTRO is based on an equation set derived using low Mach number asymptotics; this equation set does not explicitly track acoustic waves and thus allows a significant increase in the time step. MAESTRO is suitable for two- and three-dimensional local atmospheric flows as well as three-dimensional full-star flows. Here, we continue the development of MAESTRO by incorporating adaptive mesh refinement (AMR). The primary difference between MAESTRO and other structured grid AMR approaches for incompressible and low Mach number flows is the presence of the time-dependent base state, whose evolution is coupled to the evolution of the full solution. We also describe how to incorporate the expansion of the base state for full-star flows, which involves a novel mapping technique between the one-dimensional base state and the Cartesian grid, as well as a number of overall improvements to the algorithm. We examine the efficiency and accuracy of our adaptive code, and demonstrate that it is suitable for further study of our initial scientific application, the convective phase of Type Ia supernovae.

MULTIDIMENSIONAL MODELING OF TYPE I X-RAY BURSTS. I. TWO-DIMENSIONAL CONVECTION PRIOR TO THE OUTBURST OF A PURE 4He ACCRETOR

We present multidimensional simulations of the early convective phase preceding ignition in a Type I X-ray burst using the low Mach number hydrodynamics code, MAESTRO. A low Mach number approach is necessary in order to perform long-time integration required to study such phenomena. Using MAESTRO, we are able to capture the expansion of the atmosphere due to large-scale heating while capturing local compressibility effects such as those due to reactions and thermal diffusion. We also discuss the preparation of one-dimensional initial models and the subsequent mapping into our multidimensional framework. Our method of initial model generation differs from that used in previous multidimensional studies, which evolved a system through multiple bursts in one dimension before mapping onto a multidimensional grid. In our multidimensional simulations, we find that the resolution necessary to properly resolve the burning layer is an order of magnitude greater than that used in the earlier studies mentioned above. We characterize the convective patterns that form and discuss their resulting influence on the state of the convective region, which is important in modeling the outburst itself.

THE CONVECTIVE PHASE PRECEDING TYPE Ia SUPERNOVAE

The convective flow in the moments preceding the explosion of a Type Ia supernova determines where the initial flames that subsequently burn through the star first ignite. We continue our exploration of the final hours of this convection using the low Mach number hydrodynamics code, MAESTRO. We present calculations exploring the effects of slow rotation and show diagnostics that examine the distribution of likely ignition points. In the current calculations, we see a well-defined convection region persist up to the point of ignition, and we see that even a little rotation is enough to break the coherence of the convective flow seen in the radial velocity field. Our results suggest that off-center ignition may be favored, with ignition ranging out to a radius of 100 km and a maximum likelihood of ignition at a radius around 50 km.

Multidimensional modeling of type I X-ray bursts. II. Two-dimensional convection in a mixed H/He accretor

Type I X-ray bursts are thermonuclear explosions of accreted material on the surface of neutron stars in low-mass X-ray binaries. Prior to the ignition of a subsonic burning front, runaway burning at the base of the accreted layer drives convection that mixes fuel and heavy-element ashes. In this paper, the second in a series, we explore the behavior of this low Mach number convection in mixed hydrogen/helium layers on the surface of a neutron star using two-dimensional simulations with the Maestro code. Maestro takes advantage of the highly subsonic flow field by filtering dynamically unimportant sound waves while retaining local compressibility effects, such as those due to stratification and energy release from nuclear reactions. In these preliminary calculations, we find that the rp-process approximate network creates a convective region that is split into two layers. While this splitting appears artificial due to the approximations of the network regarding nuclear flow out of the breakout reaction {sup 18}Ne(α, p){sup 21}Na, these calculations hint at further simplifications and improvements of the burning treatment for use in subsequent calculations in three dimensions for a future paper.

Astrophysical applications of the MAESTRO code

Convective velocities in a white dwarf leading up to a Type la supernova or in the accreted layers on a neutron star preceding an X-ray burst are very subsonic. Under these conditions, sound waves can be neglected, but capturing compressibility effects due to nuclear reactions and background stratification is critical to accurately model the flow. We have developed a new algorithm, MAESTRO, based on a low Mach number formulation that exploits the separation of scales between the fluid velocity and the speed of sound. Here, we provide a brief overview of MAESTRO and present the initial astrophysical applications of the algorithm.

Meeting the Challenges of Modeling Astrophysical Thermonuclear Explosions: Castro, Maestro, and the AMReX Astrophysics Suite

Author(s): Zingale, M; Almgren, AS; Barrios Sazo, MG; Beckner, VE; Bell, JB; Friesen, B; Jacobs, AM; Katz, MP; Malone, CM; Nonaka, AJ; Willcox, DE; Zhang, W | Abstract: