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.Comment: Accepted to Astrophysical Journal Suppliment (http://iop.org). 56 pages, 15 figures

Low Mach Number Modeling of Type Ia Supernovae. IV. White Dwarf Convection

We present the first three-dimensional, full-star simulations of convection in a white dwarf preceding a Type Ia supernova, specifically the last few hours before ignition. For these long-time calculations we use our low Mach number hydrodynamics code, MAESTRO, which we have further developed to treat spherical stars centered in a three-dimensional Cartesian geometry. The main change required is a procedure to map the one-dimensional radial base state to and from the Cartesian grid. Our models recover the dipole structure of the flow seen in previous calculations, but our long-time integration shows that the orientation of the dipole changes with time. Furthermore, we show the development of gravity waves in the outer, stable portion of the star. Finally, we evolve several calculations to the point of ignition and discuss the range of ignition radii.Comment: 42 pages, some figures degraded to conserve space. Accepted to The Astrophysical Journal (http://journals.iop.org/

Two Dimensional Simulations of Pair-Instability Supernovae

We present preliminary results from two dimensional numerical studies of pair instability supernova (PSN). We study nuclear burning, hydrodynamic instabilities and explosion of very massive stars. Use a new radiation-hydrodynamics code, CASTRO.Comment: Proceedings of "The First Stars and Galaxies: Challenges for the Next Decade", Austin, Texas, March 8-11, 2010. 2 pages, 1 figur

Multidimensional Modeling of Type I X-ray Bursts. I. Two-Dimensional Convection Prior to the Outburst of a Pure Helium 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.Comment: 47 pages including 18 figures; submitted to ApJ; A version with higher resolution figures can be found at http://astro.sunysb.edu/cmalone/research/pure_he4_xrb/ms.pd

Influence of adaptive mesh refinement and the hydro solver on shear-induced mass stripping in a minor-merger scenario

We compare two different codes for simulations of cosmological structure formation to investigate the sensitivity of hydrodynamical instabilities to numerics, in particular, the hydro solver and the application of adaptive mesh refinement (AMR). As a simple test problem, we consider an initially spherical gas cloud in a wind, which is an idealized model for the merger of a subcluster or galaxy with a big cluster. Based on an entropy criterion, we calculate the mass stripping from the subcluster as a function of time. Moreover, the turbulent velocity field is analyzed with a multi-scale filtering technique. We find remarkable differences between the commonly used PPM solver with directional splitting in the Enzo code and an unsplit variant of PPM in the Nyx code, which demonstrates that different codes can converge to systematically different solutions even when using uniform grids. For the test case of an unbound cloud, AMR simulations reproduce uniform-grid results for the mass stripping quite well, although the flow realizations can differ substantially. If the cloud is bound by a static gravitational potential, however, we find strong sensitivity to spurious fluctuations which are induced at the cutoff radius of the potential and amplified by the bow shock. This gives rise to substantial deviations between uniform-grid and AMR runs performed with Enzo, while the mass stripping in Nyx simulations of the subcluster is nearly independent of numerical resolution and AMR. Although many factors related to numerics are involved, our study indicates that unsplit solvers with advanced flux limiters help to reduce grid effects and to keep numerical noise under control, which is important for hydrodynamical instabilities and turbulent flows.Comment: 23 pages, 18 figures, accepted for publication by Astronomy and Computin

Multi-Dimensional Simulations of Pair-Instability Supernovae

We present preliminary results from multidimensional numerical studies of pair instability supernova (PSN), studying the fluid instabilities that occur in multiple spatial dimensions. We use the new radiation-hydrodynamics code, CASTRO, and introduce a new mapping procedure that defines the initial conditions for the multidimensional runs in such a way that conservation of physical quantities is guaranteed at any level of resolution.Comment: Accepted for publication in Computer Physics Communications. 3 pages. 2 fig

3D simulations of Rayleigh-Taylor mixing in core-collapse SNe with CASTRO

We present multidimensional simulations of the post-explosion hydrodynamics in three different 15 solar mass supernova models with zero, 10^{-4} solar metallicity, and solar metallicities. We follow the growth of the Rayleigh-Taylor instability that mixes together the stellar layers in the wake of the explosion. Models are initialized with spherically symmetric explosions and perturbations are seeded by the grid. Calculations are performed in two-dimensional axisymmetric and three-dimensional Cartesian coordinates using the new Eulerian hydrodynamics code, CASTRO. We find as in previous work, that Rayleigh-Taylor perturbations initially grow faster in 3D than in 2D. As the Rayleigh-Taylor fingers interact with one another, mixing proceeds to a greater degree in 3D than in 2D, reducing the local Atwood number and slowing the growth rate of the instability in 3D relative to 2D. By the time mixing has stopped, the width of the mixed region is similar in 2D and 3D simulations provided the Rayleigh-Taylor fingers show significant interaction. Our results imply that 2D simulations of light curves and nucleosynthesis in supernovae (SNe) that die as red giants may capture the features of an initially spherically symmetric explosion in far less computational time than required by a full 3D simulation. However, capturing large departures from spherical symmetry requires a significantly perturbed explosion. Large scale asymmetries cannot develop through an inverse cascade of merging Rayleigh-Taylor structures; they must arise from asymmetries in the initial explosion.Comment: 12 pages, 5 figures, ApJ accepte

A Numerical Study of Methods for Moist Atmospheric Flows: Compressible Equations

We investigate two common numerical techniques for integrating reversible moist processes in atmospheric flows in the context of solving the fully compressible Euler equations. The first is a one-step, coupled technique based on using appropriate invariant variables such that terms resulting from phase change are eliminated in the governing equations. In the second approach, which is a two-step scheme, separate transport equations for liquid water and vapor water are used, and no conversion between water vapor and liquid water is allowed in the first step, while in the second step a saturation adjustment procedure is performed that correctly allocates the water into its two phases based on the Clausius-Clapeyron formula. The numerical techniques we describe are first validated by comparing to a well-established benchmark problem. Particular attention is then paid to the effect of changing the time scale at which the moist variables are adjusted to the saturation requirements in two different variations of the two-step scheme. This study is motivated by the fact that when acoustic modes are integrated separately in time (neglecting phase change related phenomena), or when sound-proof equations are integrated, the time scale for imposing saturation adjustment is typically much larger than the numerical one related to the acoustics