Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence

Abstract

We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine 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. 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 convergence of various characteristics for the turbulence decay test and impacts of various components of numerical schemes on the accuracy of solutions. 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 which fall short in one or more of these areas are still useful, but they must compensate 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 in picking optimal applications for their specific astrophysical problems.

17 pages, 5 color figures, revised version to appear in ApJ, 735, July 2011

References in corpus (60)

• Theory of Star Formation
• E pur si muove: Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh
• Cosmological Hydrodynamics with Adaptive Mesh Refinement: a new high resolution code called RAMSES
• Control of star formation by supersonic turbulence
• A General Theory of Turbulence-Regulated Star Formation, From Spirals to ULIRGs
• The Stellar IMF from Turbulent Fragmentation
• Comparing the statistics of interstellar turbulence in simulations and observations: Solenoidal versus compressive turbulence forcing
• Slow Star Formation in Dense Gas: Evidence and Implications
• The Statistics of Supersonic Isothermal Turbulence
• Analytical theory for the initial mass function: CO clumps and prestellar cores
• Structural Analysis of Molecular Clouds: Dendrograms
• Dissipation in Compressible MHD Turbulence
• An Unsplit Godunov Method for Ideal MHD via Constrained Transport
• The Universality of the Stellar IMF
• The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing
• Kinetic Energy Decay Rates of Supersonic and Super-Alfvenic Turbulence in Star-Forming Clouds
• The Universality of Turbulence in Galactic Molecular Clouds
• The Star Formation Rate of Supersonic MHD Turbulence
• A High Order Godunov Scheme with Constrained Transport and Adaptive Mesh Refinement for Astrophysical MHD
• A Super-Alfvenic Model of Dark Clouds
• Stable magnetic fields in stellar interiors
• Simulating Radiating and Magnetized Flows in Multi-Dimensions with ZEUS-MP
• Second Order Accurate Schemes for Magnetohydrodynamics With Divergence-Free Reconstruction
• An Ab Initio Approach to the Solar Coronal Heating Problem
• A new Jeans resolution criterion for (M)HD simulations of self-gravitating gas: Application to magnetic field amplification by gravity-driven turbulence
• On the Divergence-Free Condition in Godunov-Type Schemes for Ideal Magnetohydrodynamics: the Upwind Constrained Transport Method
• Two regimes of Turbulent Fragmentation and the stellar IMF from Primordial to Present Day Star Formation
• Analytical theory for the initial mass function: II. Properties of the flow
• High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
• Magnetohydrodynamic Simulations of Disk Galaxy Formation: the Magnetization of The Cold and Warm Medium
• Bottleneck effect in three-dimensional turbulence simulations
• Kinematic Dynamos using Constrained Transport with High Order Godunov Schemes and Adaptive Mesh Refinement
• A Second-Order Unsplit Godunov Scheme for Cell-Centered MHD: the CTU-GLM scheme
• Mach number dependence of the onset of dynamo action
• Cosmological AMR MHD with Enzo
• Algorithmic comparisons of decaying, isothermal, supersonic turbulence
• Intermittency and Universality in Fully-Developed Inviscid and Weakly-Compressible Turbulent Flows
• Inertial range scaling in numerical turbulence with hyperviscosity
• Structure Function Scaling in Compressible Super-Alfvenic MHD Turbulence
• Dissipation and Heating in Supersonic Hydrodynamic and MHD Turbulence
• Astrophysical turbulence modeling
• Solar Flux Emergence Simulations
• Relativistic Hydrodynamic Flows Using Spatial and Temporal Adaptive Structured Mesh Refinement
• Synthetic Molecular Clouds from Supersonic MHD and Non-LTE Radiative Transfer Calculations
• A Simple and Accurate Riemann Solver for Isothermal MHD
• A Parallel Mesh-Adaptive Framework for Hyperbolic Conservation Laws
• Adaptive Mesh Refinement for Supersonic Molecular Cloud Turbulence
• Mass and Magnetic distributions in Self Gravitating Super Alfvenic Turbulence with AMR
• CosmoMHD: A Cosmological Magnetohydrodynamics Code
• Ambipolar Drift Heating in Turbulent Molecular Clouds
• Evolution and Distribution of Magnetic Fields from AGNs in Galaxy Clusters. I. The Effect of Injection Energy and Redshift
• Dissipative Structures in Supersonic Turbulence
• The Super-Alfvénic Model of Molecular Clouds: Predictions for Mass-to-Flux and Turbulent-to-Magnetic Energy Ratios
• Numerical Star-Formation Studies -- A Status Report
• Piecewise Parabolic Method on a Local Stencil for Magnetized Supersonic Turbulence Simulation
• The Super-Alfvénic Model of Molecular Clouds: Predictions for Zeeman Splitting Measurements
• Simulating Supersonic Turbulence in Magnetized Molecular Clouds
• Interstellar Turbulence and Star Formation
• Simulations of the IMF in Clusters
• Cluster Turbulence: Simulation Insights

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• Enzo: An Adaptive Mesh Refinement Code for Astrophysics
• The Star Formation Rate of Turbulent Magnetized Clouds: Comparing Theory, Simulations, and Observations
• On the Star Formation Efficiency of Turbulent Magnetized Clouds
• The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project
• Simulations of magnetic fields in isolated disk galaxies
• The Big Problems in Star Formation: the Star Formation Rate, Stellar Clustering, and the Initial Mass Function
• Magnetohydrodynamics on an unstructured moving grid
• The Stagger-grid: A Grid of 3D Stellar Atmosphere Models - I. Methods and General Properties
• Subsonic turbulence in smoothed particle hydrodynamics and moving-mesh simulations
• A General Theory of Turbulent Fragmentation
• Resolved magnetic dynamo action in the simulated intracluster medium
• Magnetic Field Amplification in Galaxy Clusters and its Simulation
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• Supermassive Black Hole Formation at High Redshifts via Direct Collapse: Physical Processes in the Early Stage
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• Dynamical evolution of magnetic fields in the intracluster medium
• The structure and statistics of interstellar turbulence
• Structure distribution and turbulence in self-consistently supernova-driven ISM of multiphase magnetized galactic discs
• Energy transfer in compressible magnetohydrodynamic turbulence
• Scaling Laws of Passive-Scalar Diffusion in the Interstellar Medium
• Turbulent Disks are Never Stable: Fragmentation and Turbulence-Promoted Planet Formation
• Abundance of 26Al and 60Fe in evolving Giant Molecular Clouds
• Pebble dynamics and accretion onto rocky planets. I. Adiabatic and convective models
• Morphology of radio relics I: What causes the substructure of synchrotron emission?
• Dust-polarization maps for local interstellar turbulence
• Supernova Driving. II. Compressive Ratio in Molecular-Cloud Turbulence
• Magnetized interstellar molecular clouds: II. The Large-Scale Structure and Dynamics of Filamentary Molecular Clouds
• Tracking the distribution of ${}^{26}$Al and ${}^{60}$Fe during the early phases of star and disk evolution
• The nucleation fraction of Local Volume galaxies
• A survey of the thermal and non-thermal properties of cosmic filaments
• Are Cosmological Gas Accretion Streams Multiphase and Turbulent?
• Magnetohydrodynamic Simulation Code CANS+: Assessments and Applications
• High-order Magnetohydrodynamics for Astrophysics with an Adaptive Mesh Refinement Discontinuous Galerkin Scheme
• The Probability Distribution of Density Fluctuations in Supersonic Turbulence
• Evolution of primordial magnetic fields during large-scale structure formation
• 3D Solar Null Point Reconnection MHD Simulations
• DISPATCH: A Numerical Simulation Framework for the Exa-scale Era. I. Fundamentals
• Residual Energy in Magnetohydrodynamic Turbulence
• Flux Correlations in Supersonic Isothermal Turbulence
• Calibration of the mixing-length parameter $\alpha$ for the MLT and FST models by matching with CO${}^5$BOLD models
• The early phases of the type Iax supernova SN 2011ay
• Figuring Out Gas & Galaxies In Enzo (FOGGIE) VI: The Circumgalactic Medium of $L^{\ast }$ Galaxies is Supported in an Emergent, Non-Hydrostatic Equilibrium
• Supernova Driving. III. Synthetic Molecular Cloud Observations
• Bird's eye view of molecular clouds in the Milky Way: I. Column density and star formation from sub-pc to kpc scales
• Probing the cold magnetized Universe with SPICA-POL (B-BOP)
• A comparison between grid and particle methods on the small-scale dynamo in magnetised supersonic turbulence
• Studies of Turbulence Dissipation in Taurus Molecular Cloud with Core Velocity Dispersion (CVD)
• Testing Hydrodynamics Schemes in Galaxy Disc Simulations
• Thermodynamic fluctuations in solar photospheric three-dimensional convection simulations and observations
• The density distribution and physical origins of intermittency in supersonic, highly magnetised turbulence with diverse modes of driving
• Anchoring Magnetic Fields in Turbulent Molecular Clouds II - from 0.1 to 0.01 parsec
• A high-order weighted finite difference scheme with a multi-state approximate Riemann solver for divergence-free magnetohydrodynamic simulations
• Dependence of the saturation level of magnetorotational instability on gas pressure and magnetic Prandtl number
• Testing the concept of integral approach to derivatives within the smoothed particle hydrodynamics technique in astrophysical scenarios
• Compression of turbulent magnetized gas in Giant Molecular Clouds
• A Multistate Low-dissipation Advection Upstream Splitting Method for Ideal Magnetohydrodynamics
• The driving mode of shock-driven turbulence
• WISDOM Project XII. Clump properties and turbulence regulated by clump-clump collisions in the dwarf galaxy NGC404
• The impact of magnetic fields on the chemical evolution of the supernova-driven ISM
• An eclipsing M-dwarf close to the hydrogen burning limit from NGTS
• Numerical viscosity and resistivity in MHD turbulence simulations
• Improved calibration of the radii of cool stars based on 3D simulations of convection: implications for the solar model
• Supersonic turbulence in 3D isothermal flow collision
• Turbulence decay and cloud core relaxation in molecular clouds
• AZEuS: An Adaptive Zone Eulerian Scheme for Computational MHD
• Star-forming regions of the Aquila rift cloud complex. II. Turbulence in molecular cores probed by NH3 emission
• Lagrangian statistics of a shock-driven turbulent dynamo in decaying turbulence
• Are the Formation and Abundances of Metal-Poor Stars the Result of Dust Dynamics?
• Simulating SZ intensity maps of giant AGN cocoons
• cuHARM : a new GPU accelerated GR-MHD code and its application to ADAF disks
• Unravelling cosmic velocity flows: a Helmholtz-Hodge decomposition algorithm for cosmological simulations
• Inflationary and phase-transitional primordial magnetic fields in galaxy clusters
• Entropy-Conserving Scheme for Modeling Nonthermal Energies in Fluid Dynamics Simulations
• On the role of magnetic fields in star formation
• Vortex-p: a Helmholtz-Hodge and Reynolds decomposition algorithm for particle-based simulations
• On the origin of compressive turbulence in protoclumps in high redshift disks
• Inaccuracy of Spatial Derivatives in Simulations of Supersonic Turbulence
• Large Scale Dynamo in a Primordial Accretion Flow -- An Interpretation from Hydrodynamic Simulation
• The impact of magnetic fields on the IMF in star-forming clouds near a supermassive black hole
• Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows
• On the interpretation of XRISM X-ray measurements of turbulence in the intracluster medium: a comparison with cosmological simulations
• Capturing Turbulence with Numerical Dissipation: a Simple Dynamical Model for Unresolved Turbulence in Hydrodynamic Simulations
• A simple and efficient solver for self-gravity in the DISPATCH astrophysical simulation framework
• A new framework of multidimensional pulsating stellar envelopes I.: Properties of turbulent convection in static RR Lyrae envelope models with SPHERLS
• Hydrodynamic and Magnetohydrodynamic Simulations of Wire Turbulence
• Magnetic Fields in Molecular Clouds -- Observation and Interpretation
• Effects of spatial resolution on inferences of atmospheric quantities from simulations
• Towards convergence of turbulent dynamo amplification in cosmological simulations of galaxies
• Higher-order magnetohydrodynamic numerics
• From 2D to 3D: Recovering Turbulent Density Dispersions from Noisy Data