No abstract

In this paper we describe a community toolkit which is designed to provide parallel support with adaptive mesh capability for a large and important class of computational models, those using structured, logically cartesian meshes.The package of Fortran 90 subroutines, called PARAMESH, is designed to provide an application developer with an easy route to extend an existing serial code which uses a logically cartesian structured mesh into a parallel code with adaptive mesh refinement.Alternatively, in its simplest use, and with minimal effort, it can operate as a domain decomposition tool for users who want to parallelize their serial codes, but who do not wish to use adaptivity.The package can provide them with an incremental evolutionary path for their code, converting it first to uniformly refined parallel code, and then later if they so desire, adding adaptivity.

The turbulent Rayleigh-Taylor instability is investigated in the limit of strong mode-coupling using a variety of high-resolution, multimode, three dimensional numerical simulations ͑NS͒. The perturbations are initialized with only short wavelength modes so that the self-similar evolution ͑i.e., bubble diameter D b ϰamplitude h b) occurs solely by the nonlinear coupling ͑merger͒ of saturated modes. After an initial transient, it is found that h b ϳ␣ b Agt 2 , where AϭAtwood number, gϭacceleration, and tϭtime. The NS yield D b ϳh b /3 in agreement with experiment but the simulation value ␣ b ϳ0.025Ϯ0.003 is smaller than the experimental value ␣ b ϳ0.057Ϯ0.008. By analyzing the dominant bubbles, it is found that the small value of ␣ b can be attributed to a density dilution due to fine-scale mixing in our NS without interface reconstruction ͑IR͒ or an equivalent entrainment in our NS with IR. This may be characteristic of the mode coupling limit studied here and the associated ␣ b may represent a lower bound that is insensitive to the initial amplitude. Larger values of ␣ b can be obtained in the presence of additional long wavelength perturbations and this may be more characteristic of experiments. Here, the simulation data are also analyzed in terms of bubble dynamics, energy balance and the density fluctuation spectra.

We present a case study of validating an astrophysical simulation code. Our study focuses on validating FLASH, a parallel, adaptive-mesh hydrodynamics code for studying the compressible, reactive flows found in many astrophysical environments. We describe the astrophysics problems of interest and the challenges associated with simulating these problems. We describe methodology and discuss solutions to difficulties encountered in verification and validation. We describe verification tests regularly administered to the code, present the results of new verification tests, and outline a method for testing general equations of state. We present the results of two validation tests in which we compared simulations to experimental data. The first is of a laser-driven shock propagating through a multi-layer target, a configuration subject to both Rayleigh-Taylor and Richtmyer-Meshkov instabilities. The second test is a classic Rayleigh-Taylor instability, where a heavy fluid is supported against the force of gravity by a light fluid. Our simulations of the multi-layer target experiments showed good agreement with the experimental results, but our simulations of the Rayleigh-Taylor instability did not agree well with the experimental results. We discuss our findings and present results of additional simulations undertaken to further investigate the Rayleigh-Taylor instability.Comment: 76 pages, 26 figures (3 color), Accepted for publication in the ApJ

A leading theory for the initiation of coronal mass ejections (CMEs) is the breakout model, in which magnetic reconnection above a filament channel is responsible for disrupting the coronal magnetic field. We present the first simulations of the complete breakout process including the initiation, the plasmoid formation and ejection, and the eventual relaxation of the coronal field to a more potential state. These simulations were performed using a new numerical code that solves the numerical cavitation problems that prevented previous simulations from calculating a complete ejection. Furthermore, the position of the outer boundary in the new simulations is increased out to 30 R , which enables determination of the full structure and dynamics of the ejected plasmoid. Our results show that the ejection occurs at a speed on the order of the coronal Alfvén speed and hence that the breakout model can produce fast CMEs. Another key result is that the ejection speed is not sensitive to the refinement level of the grid used in the calculations, which implies that, at least for the numerical resistivity of these simulations, the speed is not sensitive to the Lundquist number. We also calculate, in detail, the helicity of the system and show that the helicity is well conserved during the breakout process. Most of the helicity is ejected from the Sun with the escaping plasmoid, but a significant fraction (of order 10%) remains in the corona. The implications of these results for observation and prediction of CMEs and eruptive flares is discussed.

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.

We look in detail at the process of mapping an astrophysical initial model from a stellar evolution code onto the computational grid of an explicit, Godunov type code while maintaining hydrostatic equilibrium. This mapping process is common in astrophysical simulations, when it is necessary to follow short-timescale dynamics after a period of long timescale buildup. We look at the effects of spatial resolution, boundary conditions, the treatment of the gravitational source terms in the hydrodynamics solver, and the initialization process itself. We conclude with a summary detailing the mapping process that yields the lowest ambient velocities in the mapped model.Comment: 59 pages, 21 figures, accepted to ApJS. Some figures are degraded for size constraint

We present an algorithm for treating mesh refinement interfaces in numerical relativity. We detail the behavior of the solution near such interfaces located in the strong field regions of dynamical black hole spacetimes, with particular attention to the convergence properties of the simulations. In our applications of this technique to the evolution of puncture initial data with vanishing shift, we demonstrate that it is possible to simultaneously maintain second order convergence near the puncture and extend the outer boundary beyond 100M, thereby approaching the asymptotically flat region in which boundary condition problems are less difficult and wave extraction is meaningful.Comment: 18 pages, 12 figures. Minor changes, final PRD versio