arXiv subjects

M. Zingale

Publications and source records attributed to M. Zingale.

At least 37 records · Page 2Linked to original sources

arXiv2010

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.

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arXiv2010

MAESTRO, CASTRO, and SEDONA -- Petascale Codes for Astrophysical Applications

Performing high-resolution, high-fidelity, three-dimensional simulations of Type Ia supernovae (SNe Ia) requires not only algorithms that accurately represent the correct physics, but also codes that effectively harness the resources of the most powerful supercomputers. We are developing a suite of codes that provide the capability to perform end-to-end simulations of SNe Ia, from the early convective phase leading up to ignition to the explosion phase in which deflagration/detonation waves explode the star to the computation of the light curves resulting from the explosion. In this paper we discuss these codes with an emphasis on the techniques needed to scale them to petascale architectures. We also demonstrate our ability to map data from a low Mach number formulation to a compressible solver.

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arXiv2010

CASTRO: A New Compressible Astrophysical Solver. I. Hydrodynamics and Self-Gravity

We present a new code, CASTRO, that solves the multicomponent compressible hydrodynamic equations for astrophysical flows including self-gravity, nuclear reactions and radiation. CASTRO uses an Eulerian grid and incorporates adaptive mesh refinement (AMR). Our approach to AMR uses a nested hierarchy of logically-rectangular grids with simultaneous refinement in both space and time. The radiation component of CASTRO will be described in detail in the next paper, Part II, of this series.

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arXiv2010

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.

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arXiv2009

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.

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arXiv2008

Turbulence-Flame Interactions in Type Ia Supernovae

The large range of time and length scales involved in type Ia supernovae (SN Ia) requires the use of flame models. As a prelude to exploring various options for flame models, we consider, in this paper, high-resolution three-dimensional simulations of the small-scale dynamics of nuclear flames in the supernova environment in which the details of the flame structure are fully resolved. The range of densities examined, 1 to $8 \times 10^7$ g cm$^{-3}$, spans the transition from the laminar flamelet regime to the distributed burning regime where small scale turbulence disrupts the flame. The use of a low Mach number algorithm facilitates the accurate resolution of the thermal structure of the flame and the inviscid turbulent kinetic energy cascade, while implicitly incorporating kinetic energy dissipation at the grid-scale cutoff. For an assumed background of isotropic Kolmogorov turbulence with an energy characteristic of SN Ia, we find a transition density between 1 and $3 \times 10^7$ g cm$^{-3}$ where the nature of the burning changes qualitatively. By $1 \times 10^7$ g cm$^{-3}$, energy diffusion by conduction and radiation is exceeded, on the flame scale, by turbulent advection. As a result, the effective Lewis Number approaches unity. That is, the flame resembles a laminar flame, but is turbulently broadened with an effective diffusion coefficient, $D_T \sim u' l$, where $u'$ is the turbulent intensity and $l$ is the integral scale. For the larger integral scales characteristic of a real supernova, the flame structure is predicted to become complex and unsteady. Implications for a possible transition to detonation are discussed.

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arXiv2006

Propagation of the First Flames in Type Ia Supernovae

We consider the competition of the different physical processes that can affect the evolution of a flame bubble in a Type Ia supernovae -- burning, turbulence and buoyancy. Even in the vigorously turbulent conditions of a convecting white dwarf, thermonuclear burning that begins at a point near the center (within 100 km) of the star is dominated by the spherical laminar expansion of the flame, until the burning region reaches kilometers in size. Consequently flames that ignite in the inner ~20 km promptly burn through the center, and flame bubbles anywhere must grow quite large--indeed, resolvable by large-scale simulations of the global system--for significant motion or deformation occur. As a result, any hot-spot that successfully ignites into a flame can burn a significant amount of white dwarf material. This potentially increases the stochastic nature of the explosion compared to a scenario where a simmering progenitor can have small early hot-spots float harmlessly away. Further, the size where the laminar flame speed dominates other relevant velocities sets a characteristic scale for fragmentation of larger flame structures, as nothing--by definition--can easily break the burning region into smaller volumes. This makes possible the development of semi-analytic descriptions of the earliest phase of the propagation of burning in a Type Ia supernovae, which we present here. Our analysis is supported by fully resolved numerical simulations of flame bubbles.

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arXiv2006

New Approaches for Modeling Type Ia Supernovae

Type Ia supernovae (SNe Ia) are the largest thermonuclear explosions in the Universe. Their light output can be seen across great distances and has led to the discovery that the expansion rate of the Universe is accelerating. Despite the significance of SNe Ia, there are still a large number of uncertainties in current theoretical models. Computational modeling offers the promise to help answer the outstanding questions. However, even with today's supercomputers, such calculations are extremely challenging because of the wide range of length and time scales. In this paper, we discuss several new algorithms for simulations of SNe Ia and demonstrate some of their successes.

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arXiv2006

Low Mach Number Modeling of Type Ia Supernovae. II. Energy Evolution

The convective period leading up to a Type Ia supernova (SN Ia) explosion is characterized by very low Mach number flows, requiring hydrodynamical methods well-suited to long-time integration. We continue the development of the low Mach number equation set for stellar scale flows by incorporating the effects of heat release due to external sources. Low Mach number hydrodynamics equations with a time-dependent background state are derived, and a numerical method based on the approximate projection formalism is presented. We demonstrate through validation with a fully compressible hydrodynamics code that this low Mach number model accurately captures the expansion of the stellar atmosphere as well as the local dynamics due to external heat sources. This algorithm provides the basis for an efficient simulation tool for studying the ignition of SNe Ia.

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arXiv2005

Low Mach Number Modeling of Type Ia Supernovae

We introduce a low Mach number equation set for the large-scale numerical simulation of carbon-oxygen white dwarfs experiencing a thermonuclear deflagration. Since most of the interesting physics in a Type Ia supernova transpires at Mach numbers from 0.01 to 0.1, such an approach enables both a considerable increase in accuracy and savings in computer time compared with frequently used compressible codes. Our equation set is derived from the fully compressible equations using low Mach number asymptotics, but without any restriction on the size of perturbations in density or temperature. Comparisons with simulations that use the fully compressible equations validate the low Mach number model in regimes where both are applicable. Comparisons to simulations based on the more traditional anelastic approximation also demonstrate the agreement of these models in the regime for which the anelastic approximation is valid. For low Mach number flows with potentially finite amplitude variations in density and temperature, the low Mach number model overcomes the limitations of each of the more traditional models and can serve as the basis for an accurate and efficient simulation tool.

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arXiv2005

The Physics of Flames in Type Ia Supernovae

We extend a low Mach number hydrodynamics method developed for terrestrial combustion, to the study of thermonuclear flames in Type Ia supernovae. We discuss the differences between 2-D and 3-D Rayleigh-Taylor unstable flame simulations, and give detailed diagnostics on the turbulence, showing that the kinetic energy power spectrum obeys Bolgiano-Obukhov statistics in 2-D, but Kolmogorov statistics in 3-D. Preliminary results from 3-D reacting bubble calculations are shown, and their implications for ignition are discussed.

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arXiv2005

Three-dimensional Numerical Simulations of Rayleigh-Taylor Unstable Flames in Type Ia Supernovae

Flame instabilities play a dominant role in accelerating the burning front to a large fraction of the speed of sound in a Type Ia supernova. We present a three-dimensional numerical simulation of a Rayleigh-Taylor unstable carbon flame, following its evolution through the transition to turbulence. A low Mach number hydrodynamics method is used, freeing us from the harsh timestep restrictions imposed by sound waves. We fully resolve the thermal structure of the flame and its reaction zone, eliminating the need for a flame model. A single density is considered, $1.5\times 10^7 \gcc$, and half carbon\slash half oxygen fuel--conditions under which the flame propagated in the flamelet regime in our related two-dimensional study. We compare to a corresponding two-dimensional simulation, and show that while fire-polishing keeps the small features suppressed in two dimensions, turbulence wrinkles the flame on far smaller scales in the three-dimensional case, suggesting that the transition to the distributed burning regime occurs at higher densities in three dimensions. Detailed turbulence diagnostics are provided. We show that the turbulence follows a Kolmogorov spectrum and is highly anisotropic on the large scales, with a much larger integral scale in the direction of gravity. Furthermore, we demonstrate that it becomes more isotropic as it cascades down to small scales. Based on the turbulent statistics and the flame properties of our simulation, we compute the Gibson scale. We show the progress of the turbulent flame through a classic combustion regime diagram, indicating that the flame just enters the distributed burning regime near the end of our simulation.

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arXiv2004

Direct Numerical Simulations of Type Ia Supernovae Flames I: The Landau-Darrieus Instability

Planar flames are intrinsically unstable in open domains due to the thermal expansion across the burning front--the Landau-Darrieus instability. This instability leads to wrinkling and growth of the flame surface, and corresponding acceleration of the flame, until it is stabilized by cusp formation. We look at the Landau-Darrieus instability for C/O thermonuclear flames at conditions relevant to the late stages of a Type Ia supernova explosion. Two-dimensional direct numerical simulations of both single-mode and multi-mode perturbations using a low Mach number hydrodynamics code are presented. We show the effect of the instability on the flame speed as a function of both the density and domain size, demonstrate the existence of the small scale cutoff to the growth of the instability, and look for the proposed breakdown of the non-linear stabilization at low densities. The effects of curvature on the flame as quantified through measurements of the growth rate and computation of the corresponding Markstein number. While accelerations of a few percent are observed, they are too small to have any direct outcome on the supernova explosion.

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arXiv2004

Direct Numerical Simulations of Type Ia Supernovae Flames II: The Rayleigh-Taylor Instability

A Type Ia supernova explosion likely begins as a nuclear runaway near the center of a carbon-oxygen white dwarf. The outward propagating flame is unstable to the Landau-Darrieus, Rayleigh-Taylor, and Kelvin-Helmholtz instabilities, which serve to accelerate it to a large fraction of the speed of sound. We investigate the Rayleigh-Taylor unstable flame at the transition from the flamelet regime to the distributed-burning regime, around densities of $10^7$ g/cc, through detailed, fully resolved simulations. A low Mach number, adaptive mesh hydrodynamics code is used to achieve the necessary resolution and long time scales. As the density is varied, we see a fundamental change in the character of the burning--at the low end of the density range the Rayleigh-Taylor instability dominates the burning, whereas at the high end the burning suppresses the instability. In all cases, significant acceleration of the flame is observed, limited only by the size of the domain we are able to study. We discuss the implications of these results on the potential for a deflagration to detonation transition.

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arXiv2003

Efficiency Gains from Time Refinement on AMR Meshes and Explicit Timestepping

Block-structured AMR meshes are often used in astrophysical fluid simulations, where the geometry of the domain is simple. We consider potential efficiency gains for time sub-cycling, or time refinement (TR), on Berger-Collela and oct-tree AMR meshes for explicit or local physics (such as explict hydrodynamics), where the work per block is roughly constant with level of refinement. We note that there are generally many more fine zones than there are coarse zones. We then quantify the natural result that any overall efficiency gains from reducing the amount of work on the relatively few coarse zones must necessarily be fairly small. Potential efficiency benefits from TR on these meshes are seen to be quite limited except in the case of refining a small number of points on a large mesh -- in this case, the benefit can be made arbitrarily large, albeit at the expense of spatial refinement efficiency.

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arXiv2003

On Heavy Element Enrichment in Classical Novae

Many classical nova ejecta are enriched in CNO and Ne. Rosner et al. recently suggested that the enrichment might originate in the resonant interaction between large-scale shear flows in the accreted H/He envelope and gravity waves at the interface between the envelope and the underlying C/O white dwarf. The shear flow amplifies the waves, which eventually form cusps and break. This wave breaking injects a spray of C/O into the superincumbent H/He. Using two-dimensional simulations, we formulate a quantitative expression for the amount of C/O per unit area that can be entrained into the H/He at saturation. The fraction of the envelope that is enriched depends on the horizontal distribution of shear velocity and the density contrast between the C/O white dwarf and the H/He layer but is roughly independent of the vertical shape of the shear profile. Using this parameterization for the mixed mass, we then perform several one-dimensional Lagrangian calculations of an accreting white dwarf envelope and consider two scenarios: that the wave breaking and mixing is driven by the convective flows; and that the mixing occurs prior to the onset of convection. In the absence of enrichment prior to ignition, the base of the convective zone, as calculated from mixing-length theory with the Ledoux instability criterion, does not reach the C/O interface. As a result, there is no additional mixing, and the runaway is slow. In contrast, the formation of a mixed layer during the accretion of H/He, prior to ignition, causes a more violent runaway. The envelope can be enriched by <25% of C/O by mass (consistent with that observed in some ejecta) for shear velocities, over the surface, with Mach numbers <0.4.

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arXiv2003

Morphology of Rising Hydrodynamic and Magneto-hydrodynamic Bubbles from Numerical Simulations

Recent Chandra and XMM-Newton observations of galaxy cluster cooling flows have revealed X-ray emission voids of up to 30 kpc in size that have been identified with buoyant, magnetized bubbles. Motivated by these observations, we have investigated the behavior of rising bubbles in stratified atmospheres using the FLASH adaptive-mesh simulation code. We present results from 2-D simulations with and without the effects of magnetic fields, and with varying bubble sizes and background stratifications. We find purely hydrodynamic bubbles to be unstable; a dynamically important magnetic field is required to maintain a bubble's integrity. This suggests that, even absent thermal conduction, for bubbles to be persistent enough to be regularly observed, they must be supported in large part by magnetic fields. Thermal conduction unmitigated by magnetic fields can dissipate the bubbles even faster. We also observe that the bubbles leave a tail as they rise; the structure of these tails can indicate the history of the dynamics of the rising bubble.

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arXiv2003

The Response of Model and Astrophysical Thermonuclear Flames to Curvature and Stretch

Critically understanding the `standard candle'-like behavior of Type Ia supernovae requires understanding their explosion mechanism. One family of models for Type Ia Supernovae begins with a deflagration in a Carbon-Oxygen white dwarf which greatly accelerates through wrinkling and flame instabilities. While the planar speed and behavior of astrophysically-relevant flames is increasingly well understood, more complex behavior, such as the flame's response to stretch and curvature, has not been extensively explored in the astrophysical literature; this behavior can greatly enhance or suppress instabilities and local flame-wrinkling, which in turn can increase or decrease the bulk burning rate. In this paper, we explore the effects of curvature on both nuclear flames and simpler model flames to understand the effect of curvature on the flame structure and speed.

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