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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The response of lean (ϕ 6 0.4) premixed hydrogen flames to maintained homogeneous isotropic turbulence is investigated using detailed numerical simulation in an idealised three-dimensional configuration over a range of Karlovitz numbers from 10 to 1562. In particular, a focus is placed on turbulence sufficiently intense that the flames can no longer be considered to be in the thin reaction burning regime. This transition to the so-called distributed burning regime is characterised through a number of diagnostics, and the relative roles of molecular and turbulent mixing processes are examined. The phenomenology and statistics of these flames are contrasted with a distributed thermonuclear flame from a related astrophysical study.

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Large-scale simulations are increasingly being used to study complex scientific and engineering phenomena. As a result, advanced visualization and data analysis are also becoming an integral part of the scientific process. Often, a key step in extracting insight from these large simulations involves the definition, extraction, and evaluation of features in the space and time coordinates of the solution. However, in many applications, these features involve a range of parameters and decisions that will affect the quality and direction of the analysis. Examples include particular level sets of a specific scalar field, or local inequalities between derived quantities. A critical step in the analysis is to understand how these arbitrary parameters/decisions impact the statistical properties of the features, since such a characterization will help to evaluate the conclusions of the analysis as a whole. We present a new topological framework that in a single-pass extracts and encodes entire families of possible features definitions as well as their statistical properties. For each time step we construct a hierarchical merge tree a highly compact, yet flexible feature representation. While this data structure is more than two orders of magnitude smaller than the raw simulation data it allows us to extract a set of features for any given parameter selection in a postprocessing step. Furthermore, we augment the trees with additional attributes making it possible to gather a large number of useful global, local, as well as conditional statistic that would otherwise be extremely difficult to compile. We also use this representation to create tracking graphs that describe the temporal evolution of the features over time. Our system provides a linked-view interface to explore the time-evolution of the graph interactively alongside the segmentation, thus making it possible to perform extensive data analysis in a very efficient manner. We demonstrate our framework by extracting and analyzing burning cells from a large-scale turbulent combustion simulation. In particular, we show how the statistical analysis enabled by our techniques provides new insight into the combustion process.

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 KelvinHelmholtz 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 cm À3 , through detailed, fully resolved simulations. A low Mach number, adaptive mesh hydrodynamics code is used to achieve the necessary resolution and long timescales. 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.

The large range of time and length scales involved in Type Ia supernovae (SNe 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, (1Y8) ; 10 7 g cm À3 , 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 SNe Ia, we find a transition density between 1 and 3 ; 10 7 g cm À3 , where the nature of the burning changes qualitatively. By 1 ; 10 7 g cm À3 , 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 $ u 0 l, where u 0 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.