Dongwook Lee

COMPARING NUMERICAL METHODS FOR ISOTHERMAL MAGNETIZED SUPERSONIC TURBULENCE

Many astrophysical applications involve magnetized turbulent flows with shock waves. Ab initio star formation simulations require a robust representation of supersonic turbulence in molecular clouds on a wide range of scales imposing stringent demands on the quality of numerical algorithms. We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine popular astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. These applications employ a variety of numerical approaches, including both split and unsplit, finite difference and finite volume, divergence preserving and divergence cleaning, a variety of Riemann solvers, and a range of spatial reconstruction and time integration techniques. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss the convergence of various characteristics for the turbulence decay test and the impact of various components of numerical schemes on the accuracy of solutions. The nine codes gave qualitatively the same results, implying that they are all performing reasonably well and are useful for scientific applications. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method and using little to no explicit artificial viscosity. Codes that fall short in one or more of these areas are still useful, but they must compensate for higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices about choosing optimal applications for their specific astrophysical problems.

A solution accurate, efficient and stable unsplit staggered mesh scheme for three dimensional magnetohydrodynamics

Abstract In this paper, we extend the unsplit staggered mesh scheme (USM) for 2D magnetohydrodynamics (MHD) [D. Lee, A.E. Deane, An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics, J. Comput. Phys. 228 (2009) 952–975] to a full 3D MHD scheme. The scheme is a finite-volume Godunov method consisting of a constrained transport (CT) method and an efficient and accurate single-step, directionally unsplit multidimensional data reconstruction-evolution algorithm, which extends Colella’s original 2D corner transport upwind (CTU) method [P. Colella, Multidimensional upwind methods for hyperbolic conservation laws, J. Comput. Phys. 87 (1990) 446–466]. We present two types of data reconstruction-evolution algorithms for 3D: (1) a reduced CTU scheme and (2) a full CTU scheme. The reduced 3D CTU scheme is a variant of a simple 3D extension of Collela’s 2D CTU method and is considered as a direct extension from the 2D USM scheme. The full 3D CTU scheme is our primary 3D solver which includes all multidimensional cross-derivative terms for stability. The latter method is logically analogous to the 3D unsplit CTU method by Saltzman [J. Saltzman, An unsplit 3D upwind method for hyperbolic conservation laws, J. Comput. Phys. 115 (1994) 153–168]. The major novelties in our algorithms are twofold. First, we extend the reduced CTU scheme to the full CTU scheme which is able to run with CFL numbers close to unity. Both methods utilize the transverse update technique developed in the 2D USM algorithm to account for transverse fluxes without solving intermediate Riemann problems, which in turn gives cost-effective 3D methods by reducing the total number of Riemann solves. The proposed algorithms are simple and efficient especially when including multidimensional MHD terms that maintain in-plane magnetic field dynamics. Second, we introduce a new CT scheme that makes use of proper upwind information in taking averages of electric fields. Our 3D USM schemes can be easily combined with various reconstruction methods (e.g., first-order Godunov, second-order MUSCL-Hancock, third-order PPM and fifth-order WENO), and a wide choice of 1D based Riemann solvers (e.g., local Lax–Friedrichs, HLLE, HLLC, HLLD, and Roe). The 3D USM-MHD solver is available in the University of Chicago Flash Center’s official FLASH release.

THE FERMI BUBBLES: SUPERSONIC ACTIVE GALACTIC NUCLEUS JETS WITH ANISOTROPIC COSMIC-RAY DIFFUSION

TheFermiGamma-RaySpaceTelescope reveals two large bubbles in the Galaxy, which extend nearly symmetrically ∼50 ◦ above and below the Galactic center. Using three-dimensional (3D) magnetohydrodynamic simulations that self-consistently include the dynamical interaction between cosmic rays (CRs) and thermal gas and anisotropic CR diffusion along the magnetic field lines, we show that the key characteristics of the observed gamma-ray bubbles and the spatially correlated X-ray features in the ROSAT 1.5 keV map can be successfully reproduced by recent jet activity from the central active galactic nucleus. We find that after taking into account the projection of the 3D bubbles onto the sky the physical heights of the bubbles can be much smaller than previously thought, greatly reducing the formation time of the bubbles to about a Myr. This relatively small bubble age is needed to reconcile the simulations with the upper limit of bubble ages estimated from the cooling time of high-energy electrons. No additional physical mechanisms are required to suppress large-scale hydrodynamic instabilities because the evolution time is too short for them to develop. The simulated CR bubbles are edge-brightened, which is consistent with the observed projected flat surface brightness distribution. Furthermore, we demonstrate that the sharp edges of the observed bubbles can be due to anisotropic CR diffusion along magnetic field lines that drape around the bubbles during their supersonic expansion, with suppressed perpendicular diffusion across the bubble surface. Possible causes of the slight bends of the Fermi bubbles to the west are also discussed.

THE POST-MERGER MAGNETIZED EVOLUTION OF WHITE DWARF BINARIES: THE DOUBLE-DEGENERATE CHANNEL OF SUB-CHANDRASEKHAR TYPE Ia SUPERNOVAE AND THE FORMATION OF MAGNETIZED WHITE DWARFS

Type Ia supernovae (SNe Ia) play a crucial role as standardizable cosmological candles, though the nature of their progenitors is a subject of active investigation. Recent observational and theoretical work has pointed to merging white dwarf binaries, referred to as the double-degenerate channel, as the possible progenitor systems for some SNe Ia. Additionally, recent theoretical work suggests that mergers which fail to detonate may produce magnetized, rapidly rotating white dwarfs. In this paper, we present the first multidimensional simulations of the post-merger evolution of white dwarf binaries to include the effect of the magnetic field. In these systems, the two white dwarfs complete a final merger on a dynamical timescale, and are tidally disrupted, producing a rapidly rotating white dwarf merger surrounded by a hot corona and a thick, differentially rotating disk. The disk is strongly susceptible to the magnetorotational instability (MRI), and we demonstrate that this leads to the rapid growth of an initially dynamically weak magnetic field in the disk, the spin-down of the white dwarf merger, and to the subsequent central ignition of the white dwarf merger. Additionally, these magnetized models exhibit new features not present in prior hydrodynamic studies of white dwarf mergers, including the development of MRI turbulence in the hot disk, magnetized outflows carrying a significant fraction of the disk mass, and the magnetization of the white dwarf merger to field strengths ~2 × 108 G. We discuss the impact of our findings on the origins, circumstellar media, and observed properties of SNe Ia and magnetized white dwarfs.

COSMOLOGICAL MAGNETOHYDRODYNAMIC SIMULATIONS OF CLUSTER FORMATION WITH ANISOTROPIC THERMAL CONDUCTION

The intracluster medium (ICM) has been suggested to be buoyantly unstable in the presence of magnetic field and anisotropic thermal conduction. We perform first cosmological simulations of galaxy cluster formation that simultaneously include magnetic fields, radiative cooling, and anisotropic thermal conduction. In isolated and idealized cluster models, the magnetothermal instability (MTI) tends to reorient the magnetic fields radially whenever the temperature gradient points in the direction opposite to gravitational acceleration. Using cosmological simulationsofclusterformationwedetectradialbiasinthevelocityandmagneticfields.Suchradialbiasisconsistent with either the inhomogeneous radial gas flows due to substructures or residual MTI-driven field rearrangements that are expected even in the presence of turbulence. Although disentangling the two scenarios is challenging, we do not detect excess bias in the runs that include anisotropic thermal conduction. The anisotropy effect is potentially detectable via radio polarization measurements with LOFAR and the Square Kilometer Array and future X-ray spectroscopic studies with the International X-ray Observatory. We demonstrate that radiative cooling boosts the amplification of the magnetic field by about two orders of magnitude beyond what is expected in the non-radiative cases. This effect is caused by the compression of the gas and frozen-in magnetic field as it accumulates in the cluster center. At z = 0 the field is amplified by a factor of about 10 6 compared to the uniform magnetic field that evolved due to the universal expansion alone. Interestingly, the runs that include both radiative cooling and thermal conduction exhibit stronger magnetic field amplification than purely radiative runs. In these cases, buoyant restoring forces depend on the temperature gradients rather than the steeper entropy gradients. Thus, the ICM is more easily mixed and the winding up of the frozen-in magnetic field is more efficient, resulting in stronger magneticfield amplification. We also demonstrate that thermal conduction partially reduces the gas accretion driven by overcooling despite the fact that the effective conductivity is suppressed below the Spitzer‐Braginskii value.

Developed turbulence and nonlinear amplification of magnetic fields in laboratory and astrophysical plasmas

Significance Magnetic fields exist throughout the universe. Their energy density is comparable to the energy density of the fluid motions of the plasma in which they are embedded, making magnetic fields essential players in the dynamics of the luminous matter in the universe. The origin and the amplification of these magnetic fields to their observed strengths are far from being understood. The standard model for the origin of these galactic and intergalactic magnetic fields is through the amplification of seed fields via turbulent processes to the level consistent with current observations. For this process to be effective, the amplification needs to reach a strongly nonlinear phase. Experimental evidence of the initial nonlinear amplification of magnetic fields is presented in this paper. The visible matter in the universe is turbulent and magnetized. Turbulence in galaxy clusters is produced by mergers and by jets of the central galaxies and believed responsible for the amplification of magnetic fields. We report on experiments looking at the collision of two laser-produced plasma clouds, mimicking, in the laboratory, a cluster merger event. By measuring the spectrum of the density fluctuations, we infer developed, Kolmogorov-like turbulence. From spectral line broadening, we estimate a level of turbulence consistent with turbulent heating balancing radiative cooling, as it likely does in galaxy clusters. We show that the magnetic field is amplified by turbulent motions, reaching a nonlinear regime that is a precursor to turbulent dynamo. Thus, our experiment provides a promising platform for understanding the structure of turbulence and the amplification of magnetic fields in the universe.

Numerical simulations of the attenuation of the fundamental slow magnetoacoustic standing mode in a gravitationally stratified solar coronal arcade

Aims. We aim to explore the influence of thermal conduction on the attenuation of the fundamental standing slow magnetoacoustic mode in a two-dimensional (2D) potential arcade that is embedded in a gravitationally stratified solar corona. Methods. We numerically solve the time-dependent magnetohydrodynamic equations to find the spatial and temporal signatures of the mode. Results. We find that this mode is strongly attenuated on a time-scale of about 6 waveperiods. Conclusions. The effect of non-ideal plasma such as thermal conduction is to enhance the attenuation of slow standing waves. The numerical results are similar to previous observational data and theoretical findings for the one-dimensional plasma.

Evolution of FLASH, a multi-physics scientific simulation code for high-performance computing

The FLASH code has evolved into a modular and extensible scientific simulation software system over the decade of its existence. During this time it has been cumulatively used by over a thousand researchers to investigate problems in astrophysics, cosmology, and in some areas of basic physics, such as turbulence. Recently, many new capabilities have been added to the code to enable it to simulate problems in high-energy density physics. Enhancements to these capabilities continue, along with enhancements enabling simulations of problems in fluid-structure interactions. The code started its life as an amalgamation of already existing software packages and sections of codes developed independently by various participating members of the team for other purposes. The code has evolved through a mixture of incremental and deep infrastructural changes. In the process, it has undergone four major revisions, three of which involved a significant architectural advancement. Along the way, a software process evolved that addresses the issues of code verification, maintainability, and support for the expanding user base. The software process also resolves the conflicts arising out of being in development and production simultaneously with multiple research projects, and between performance and portability. This paper describes the process of code evolution with emphasis on the design decisions and software management policies that have been instrumental in the success of the code. The paper also makes the case for a symbiotic relationship between scientific research and good software engineering of the simulation software.

The excitation of 5-min oscillations in the solar corona

Aims. We aim to study excitation of the observed ∼5-min oscillations in the solar corona by localized pulses that are launched in the photosphere. Methods. We solve the full set of nonlinear one-dimensional Euler equations numerically for the velocity pulse propagating in the solar atmosphere that is determined by the realistic temperature profile. Results. Numerical simulations show that an initial velocity pulse quickly steepens into a leading shock, while the nonlinear wake in the chromosphere leads to the formation of consecutive pulses. The time interval between the arrivals of two neighboring pulses to a detection point in the corona is approximately 5 min. Therefore, the consecutive pulses may result in the ∼5-min oscillations that are observed in the solar corona. Conclusions. The ∼5-min oscillations observed in the solar corona can be explained in terms of consecutive shocks that result from impulsive triggers launched within the solar photosphere by granulation and/or reconnection.

Ongoing verification of a multiphysics community code: FLASH

When developing a complex, multi‐authored code, daily testing on multiple platforms and under a variety of conditions is essential. It is therefore necessary to have a regression test suite that is easily administered and configured, as well as a way to easily view and interpret the test suite results. We describe the methodology for verification of FLASH, a highly capable multiphysics scientific application code with a wide user base. The methodology uses a combination of unit and regression tests and an in‐house testing software that is optimized for operation under limited resources. Although our practical implementations do not always comply with theoretical regression‐testing research, our methodology provides a comprehensive verification of a large scientific code under resource constraints.Copyright