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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We describe an approach to parallelization of structured adaptive mesh refinement algorithms. This type of adaptive methodology is based on the use of local grids superimposed on a coarse grid to achieve sufficient resolution in the solution. The key elements of the approach to parallelization are a dynamic load-balancing technique to distribute work to processors and a software methodology for managing data distribution and communications. The methodology is based on a message-passing model that exploits the coarse-grained parallelism inherent in the algorithms. The approach is illustrated for an adaptive algorithm for hyperbolic systems of conservation laws in three space dimensions. A numerical example computing the interaction of a shock with a helium bubble is presented. We give timings to illustrate the performance of the method.

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We present a three-dimensional, time-dependent simulation of a laboratory-scale rod-stabilized premixed turbulent V-flame. The experimental parameters correspond to a turbulent Reynolds number, Re t ‫؍‬ 40, and to a Damkö hler number, Da ‫؍‬ 6. The simulations are performed using an adaptive time-dependent low-Machnumber model with detailed chemical kinetics and a mixture model for differential species diffusion. The algorithm is based on a second-order projection formulation and does not require an explicit subgrid model for turbulence or turbulence͞chemistry interaction. Adaptive mesh refinement is used to dynamically resolve the flame and turbulent structures. Here, we briefly discuss the numerical procedure and present detailed comparisons with experimental measurements showing that the computation is able to accurately capture the basic flame morphology and associated mean velocity field. Finally, we discuss key issues that arise in performing these types of simulations and the implications of these issues for using computation to form a bridge between turbulent flame experiments and basic combustion chemistry. (6)] have made substantial progress in understanding basic flame physics and developing models that can be used for engineering design. However, the inability of theory to deal with the complexity of realistic chemical kinetics in a turbulent flowfield, and the present limitations in experimental diagnostics to resolve 3D flame properties, represent major obstacles to continued progress.Numerical simulation offers the potential to augment theory and experiment and overcome the limitations of standard approaches in analyzing laboratory-scale flames. The excessive computational costs of incorporating detailed transport and chemical kinetics have necessitated compromises in the fidelity or scope of simulations for premixed turbulent combustion. Simulation of laboratory-scale systems typically involves models for subgrid-scale turbulent fluctuations. Approaches based on large eddy simulation or Reynolds-averaged Navier-Stokes fall into this class. In addition to the turbulence model, these approaches require a model for the speed of flame propagation in a turbulent field or some other model for turbulencechemistry interaction.The goal of the present work is to simulate a laboratory-scale flame, Ϸ10-12 cm in length, without a turbulence model, a burning velocity model, or the introduction of some other type of turbulence closure hypothesis. Standard computational tools for this type of simulation are based on high-order (more than four) explicit integration methods for the compressible NavierStokes equations and are typically referred to as direct numerical simulations. The computational requirements of direct numerical simulations have limited most simulations to small-scale 2D models. Recent work by Vervisch et al. (7) presents the simulation of a laboratory-scale ''turbulent'' premixed V-flame in two dimensions and represents the current state-of-the-art in 2D direct numerical simulations. Tanahashi e...

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A heterogeneous continuum model is proposed to describe the dispersion and combustion of an aluminum particle cloud in an explosion. It combines gasdynamic conservation laws for the gas phase with a continuum model for the dispersed phase, as formulated by Nigmatulin. Interphase mass, momentum, and energy exchange are prescribed by the phenomenological model of Khasainov. It incorporates a combustion model based on mass conservation laws for fuel, air, and products. The source/sink terms are treated in the fast-chemistry limit appropriate for such gasdynamic fields, along with a model for mass transfer from the particle phase to the gas. The model takes into account both the afterburning of the detonation products of the booster with air and the combustion of the Al particles with air. The model equations are integrated by high-order Godunov schemes for both the gas and particle phases. Numerical simulations of the explosion fields from 1.5-g shock-dispersed-fuel charges in 3 different chambers are performed. Computed pressure histories are similar to measured waveforms when the ignition temperature model is employed. The predicted product production is 10-14% greater than that measured in the experiments. This fact can be ascribed to unsteady ignition effects not included in the modeling. EXPERIMENTSWe model experiments of shock-dispersed-fuel (SDF) explosions in various chambers. The SDF charge consisted of a 0.5-g spherical PETN booster surrounded by a paper cylinder (Fig. 1); the void volume of 1.6 cm 3 was filled with 1 g of flake aluminum with a bulk density of 0.604 g/cm 3 . The SDF charge was placed at the center of a barometric calorimeter, a circular cylinder of the following dimensions:• L = 21cm, D = 20 cm, L/D = 1.05, and V = 6.6 liters for calorimeter A;• L = 30 cm, D = 30 cm, L/D = 1.0, and V = 21.2 liters for calorimeter B;• L = 37.9 cm, D = 36.9 cm, L/D = 1.03, and V = 40.5 liters for calorimeter C. Fig. 1. Charge construction: (a) 0.5 g PETN booster;(b) Al-SDF charge: 1) paper cylinder; 2) PETN booster charge (0.5 g; 0.5 cm 3 ); 3) loosely packed powdered fuel (1 g; 1.6 cm 3 ).Detonation of the booster charge created a blast wave that dispersed the Al powder and ignited the ensuing Al-air mixture, thereby forming a two-phase combustion cloud embedded in the explosion. Afterburning

We describe the AMReX suite of astrophysics codes and their application to modeling problems in stellar astrophysics. Maestro is tuned to efficiently model subsonic convective flows while Castro models the highly compressible flows associated with stellar explosions. Both are built on the block-structured adaptive mesh refinement library AMReX. Together, these codes enable a thorough investigation of stellar phenomena, including Type Ia supernovae and X-ray bursts. We describe these science applications and the approach we are taking to make these codes performant on current and future many-core and GPU-based architectures.