Table of contents

The Center for Space Plasma and Aeronomic Research (CSPAR) at the University of Alabama in Huntsville (UAH) and Maison de la Simulation at the French Alternative Energies and Atomic Energy Commission (Commissariat a l'energie atomique et aux energies alternatives, CEA) organized the 10th annual International Conference on Numerical Modeling of Space Plasma Flows (ASTRONUM- 2015) on June 8-12, 2015 in Avignon, France.

The Program Committee consisted of Tahar Amari (CNRS Ecole Polytechnique, France), Edouard Audit (CEA/CNRS Maison de la Simulation, Gif-sur-Yvette, France, co-chair), Phillip Colella (Lawrence Berkeley National Laboratory, USA), José María Ibáñez, University of Valencia, Spain), Ewald Müller (Max-Planck-Institute for Astrophysics, Garching, Germany), Nikolai Pogorelov (University of Alabama in Huntsville/CSPAR, USA, chair), Kazunari Shibata (Kyoto University, Japan), James Stone (Princeton University, USA), Brian Van Straalen (Lawrence Berkeley National Laboratory, USA), and Gary P. Zank (University of Alabama in Huntsville/CSPAR).

The conference attracted 67 scientists representing different branches of the plasma simulation community. The distinctive feature of this conference is a combination of diverse research topics, all of which are essential for performing high-resolution, continuum mechanics and particle simulations of physical phenomena in space physics and astrophysics. Among such topics were software packages for modeling and analyzing plasma flows; advanced numerical methods for space, astrophysical and geophysical flows; large-scale fluid-based, kinetic, and hybrid simulations; turbulence and cosmic ray transport; and magnetohydrodynamics. The applications discussed included cosmology and galaxy formation, supernova explosions, physics of the Sun-heliosphere- magnetosphere environments, the interstellar medium and star formation, stellar physics, experimental plasma physics, astrophysical accretion, numerical methods for ideal and non-ideal, relativistic and nonrelativistic MHD, etc. The proceedings volume is structured so that it covers all of these topics.

A distinctive feature of the ASTRONUM conference series is based on the idea that modelers working in seemingly distant fields should have an opportunity to share their scientific achievements with the broad community of computational scientists performing numerical experiments. As in previous ASTRONUM meetings, we were interested in physical systems that are coupled across a multiplicity of spatial and temporal scales via collision-like integral terms that incorporate diverse physical processes.

The contributors to this volume are both young researchers and renowned experts in space physics and astrophysics, applied mathematics, and computer science, particularly data handling and visualization. This book describes the application of numerical methods and the algorithms themselves, allowing us to discuss the challenges that theory imposes on numerical schemes for solving partial differential equations describing collisional and collisionless processes in space and astrophysical plasmas.

We would like to thank the participants who submitted their papers to Proceedings of ASTRONUM- 2015 and especially to those who reviewed manuscripts thus ensuring the high quality of this publication. We also are grateful to Valerie Belle and Adeline Holton for the excellent management of the conference.

The book will be useful to graduate and postgraduate students majoring in space physics, astrophysics, numerical, engineering, and applied mathematics. It is also aimed at specialists in applied mathematics, and various fields of physics that involve flows of partially ionized plasmas at both the collisional and collisionless levels.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

Electron magnetohydrodynamics (EMHD) provides a simple fluid-like description of physics below the proton gyro-scale in collisionless plasmas, such as the solar wind. In this paper, we discuss forward and inverse cascades in EMHD turbulence in the presence of a strong mean magnetic field. Similar to Alfvén waves, EMHD waves, or EMHD perturbations, propagate along magnetic field lines. Therefore, two types of EMHD waves can exist: waves moving parallel to and waves moving anti-parallel to the the magnetic field lines. For energy cascade in EMHD turbulence, the relative amplitudes of opposite-traveling waves are important. When the amplitudes are balanced, we will see fully-developed forward cascade with a k^-7/3 energy spectrum and a scale-dependent anisotropy. On the other hand, when the amplitudes are imbalanced, we will see inverse cascade, as well as (presumably not fully developed) forward cascade. The underlying physics for the inverse cascade is magnetic helicity conservation.

Star formation is inefficient. Only a few percent of the available gas in molecular clouds forms stars, leading to the observed low star formation rate (SFR). The same holds when averaged over many molecular clouds, such that the SFR of whole galaxies is again surprisingly low. Indeed, considering the low temperatures, molecular clouds should be highly gravitationally unstable and collapse on their global mean freefall timescale. And yet, they are observed to live about 10-100 times longer, i.e., the SFR per freefall time (SFR_ff) is only a few percent. Thus, other physical mechanisms must provide support against quick global collapse. Magnetic fields, turbulence and stellar feedback have been proposed as stabilising agents controlling star formation, but it is still unclear which of these processes is the most important and what their relative contributions are. Here I present high-resolution, adaptive- mesh-refinement simulations of star cluster formation that include turbulence, magnetic fields, and protostellar jet/outflow feedback. These simulations produce nearly realistic star formation rates consistent with observations, but only if turbulence, magnetic fields and feedback are included simultaneously.

Supersonic turbulence is believed to be at the heart of star formation. We have performed smoothed particle magnetohydrodynamics (SPMHD) simulations of the small- scale dynamo amplification of magnetic fields in supersonic turbulence. The calculations use isothermal gas driven at rms velocity of Mach 10 so that conditions are representative of starforming molecular clouds in the Milky Way. The growth of magnetic energy is followed for 10 orders in magnitude until it reaches saturation, a few percent of the kinetic energy. The results of our dynamo calculations are compared with results from grid-based methods, finding excellent agreement on their statistics and their qualitative behaviour. The simulations utilise the latest algorithmic developments we have developed, in particular, a new divergence cleaning approach to maintain the solenoidal constraint on the magnetic field and a method to reduce the numerical dissipation of the magnetic shock capturing scheme. We demonstrate that our divergence cleaning method may be used to achieve  ∇ • B = 0 to machine precision, albeit at significant computational expense.

The phenomenology of the emission of pulsars and magnetars depends dramatically on the structure and properties of their magnetic field. In particular it is believed that the outbursting and flaring activity observed in AXPs and SRGs is strongly related to their internal magnetic field. Recent observations have moreover shown that charges are present in their magnetospheres supporting the idea that their magnetic field is tightly twisted in the vicinity of the star. In principle these objects offer a unique opportunity to investigate physics in a regime beyond what can be obtained in the laboratory. We will discuss the properties of equilibrium models of magnetized neutron stars, and we will show how internal and external currents can be related. These magnetic field configurations will be discussed considering also their stability, relevant for their origin and possibly connected to events like SNe and GRBs. We will also show what kind of deformations they induce in the star, that could lead to emission of gravitational waves. In the case of a twisted magnetosphere we will show how the amount of twist regulates their general topology. A general formalism based on the simultaneous numerical solution of the general relativistic Grad-Shafranov equation and Einstein equations will be presented.

Protoplanetary disks are circumstellar disks of gas and dust, from which planets may eventually form or be in the process of forming. Recent direct imaging of them has enabled us to derive the density and temperature distributions. Interestingly they often show quite different features depending on the wavelength observed. The near-infrared emission is dominated by scattering of stellar light while the mm- and submm- wave emissions are dominated by thermal dust emission. Thus, the near-infrared emission traces a low density surface layer where stellar light is scattered toward us. The mm- and submm- wave emission trace the high density part of the disk near the mid plane. In order to explain the wavelength- dependent images, we have constructed a passive disk model for HL Tau and HD142527. The former shows concentric rings in the ALMA image while the latter shows a highly asymmetric arc. Our models are based on the multi-color radiation transfer calculation. It takes account of radiation ranging from 100 nm to 3.16 mm. We used the M1 model to solve the radiative equilibrium. Our model gives some constraints on the optical properties of the dust.

This paper presents a new hydrodynamic model of interacting galaxies based on the joint solution of multicomponent hydrodynamic equations, first moments of the collisionless Boltzmann equation and the Poisson equation for gravity. Using this model, it is possible to formulate a unified numerical method for solving hyperbolic equations. This numerical method has been implemented for hybrid supercomputers with Intel Xeon Phi accelerators. The collision of spiral and disk galaxies considering the star formation process, supernova feedback and molecular hydrogen formation is shown as a simulation result.

We use extensive global hydrodynamic disk gas+dust simulations with embedded planets to model the dust ring and gap structures in the HL Tau protoplanetary disk observed with the Atacama Large Millimeter/Submillimeter Array (ALMA). Since the HL Tau is a relatively massive disk, we find the disk self-gravity (DSG) plays an important role in the gap formation induced by the planets. Our simulation results demonstrate that DSG is necessary in explaining of the dust ring and gap in HL Tau disk. The comparison of simulation results shows that the dust rings and gap structures are more evident when the fully 2D DSG (non-axisymmetric components are included) is used than if 1D axisymmetric DSG (only the axisymetric component is included) is used, or the disk self-gravity is not considered. We also find that the couple dust+gas+planet simulations are required because the gap and ring structure is different between dust and gas surface density.

In this work we focus on the technical details of the numerical simulations of the non-thermal transient Swift J1644+57, whose emission is probably produced by a two- component jet powered by a tidal disruption event. In this context we provide details of the coupling between the relativistic hydrodynamic simulations and the radiative transfer code. First, we consider the technical demands of one-dimensional simulations of a fast relativistic jet, and show to what extent (for the same physical parameters of the model) do the computed light curves depend on the numerical parameters of the different codes employed. In the second part we explain the difficulties of computing light curves from axisymmetric two dimensonal simulations and discuss a procedure that yields an acceptable tradeoff between the computational cost and the quality of the results.

We study the influence of numerical methods and grid resolution on the termination of the magnetorotational instability (MRI) by means of parasitic instabilities in threedimensional shearing-disc simulations reproducing typical conditions found in core-collapse supernovae. Whether or not the MRI is able to amplify weak magnetic fields in this context strongly depends, among other factors, on the amplitude at which its growth terminates. The qualitative results of our study do not depend on the numerical scheme. In all our models, MRI termination is caused by Kelvin-Helmholtz instabilities, consistent with theoretical predictions. Quantitatively, however, there are differences, but numerical convergence can be achieved even at relatively low grid resolutions if high-order reconstruction methods are used.

We propose a 3D gasdynamic numerical model for the study of the interaction between the extended envelopes of hot Jupiters, overfilling their Roche lobes, and non-stationary stellar wind. In the model we use a Roe-Osher numerical scheme with Eindfeldt entropy fix. To test the model we have simulated a flow structure, forming due to the interaction between the extended quasi-stationary envelope of the hot Jupiter planet HD 209458b and the bow shock formed ahead of a propagating coronal mass ejection (CME). We have adopted the solar CME parameters in our computations and taken into account the fact that the planet is located close to its host star. The simulation results show that the bow shock of the CME partially destroys the stream, starting from the Li point of the quasi-closed planet's envelope. A bow shock, existing ahead of the planet in its orbital motion when the stellar wind is undisturbed, almost disappears when the CME shock passes through the system.

A great possible achievement for the MMS mission would be crossing electron diffusion regions (EDR). EDR are regions in proximity of reconnection sites where electrons decouple from field lines, breaking the frozen in condition. Decades of research on reconnection have produced a widely shared map of where EDRs are. We expect reconnection to take place around a so called x-point formed by the intersection of the separatrices dividing inflowing from outflowing plasma. The EDR forms around this x-point as a small electron scale box nested inside a larger ion diffusion region. But this point of view is based on a 2D mentality. We have recently proposed that once the problem is considered in full 3D, secondary reconnection events can form [Lapenta et al., Nature Physics, 11, 690, 2015] in the outflow regions even far downstream from the primary reconnection site. We revisit here this new idea confirming that even using additional indicators of reconnection and even considering longer periods and wider distances the conclusion remains true: secondary reconnection sites form downstream of a reconnection outflow causing a sort of chain reaction of cascading reconnection sites. If we are right, MMS will have an interesting journey even when not crossing necessarily the primary site. The chances are greatly increased that even if missing a primary site during an orbit, MMS could stumble instead on one of these secondary sites.

We describe the development and application of a time-dependent model of the solar wind. The model is empirically driven, starting from magnetic maps created with the Air Force Data Assimilative Photospheric flux Transport (ADAPT) model at a daily cadence. Potential field solutions are used to model the coronal magnetic field, and an empirical specification is used to develop boundary conditions for an MHD model of the solar wind. The time-dependent MHD simulation shows classic features of stream structure in the interplanetary medium that are seen in steady-state models; it also shows time evolutionary features that do not appear in a steady-state approach. The model results compare reasonably well with 1 AU OMNI observations. Data gaps when SOLIS magnetograms were unavailable hinder the model performance. The reasonable comparisons with observations suggest that this modeling approach is suitable for driving long term models of the outer heliosphere. Improvements to the ingestion of magnetograms in flux transport models will be necessary to apply this approach in a time-dependent space weather model.

Physical processes are discussed related to the heliotail which is formed when the solar wind interacts with the local interstellar medium. Although astrotails are commonly observed, the heliotail observations are only indirect. As a consequence, the direct comparison of the observed astrophysical objects and the Sun is impossible. This requires proper theoretical understanding of the heliotail formation and evolution, and numerical simulations in sufficiently large computational boxes. In this paper, we review some previous results related to the heliotail flow and show new simulations which demonstrate that the solar wind collimation inside the Parker spiral field lines diverted by the heliopause toward the heliotail is unrealistic. On the contrary, solar cycle effects ensure that the solar wind density reaches its largest values near the solar equatorial plane. We also argue that a realistic heliotail should be very long to account for the observed anisotropy of 1-10 TeV cosmic rays.

Suprathermal energetic particles, such as solar energetic particles (SEPs) in the inner heliosphere and pickup ions (PUIs) in the outer heliosphere and the very local interstellar medium, often form a thermodynamically dominant component in their various environments. In the supersonic solar wind beyond > 10 AU, in the inner heliosheath (IHS), and in the very local interstellar medium (VLISM), PUIs do not equilibrate collisionally with the background plasma. Similarly, SEPs do not equilibrate collisionally with the background solar wind in the inner heliosphere. In the absence of equilibration between plasma components, a separate coupled plasma description for the energetic particles is necessary. Using a collisionless Chapman-Enskog expansion, we derive a closed system of multi-component equations for a plasma comprised of thermal protons and electrons, and suprathermal particles (SEPs, PUIs). The energetic particles contribute an isotropic scalar pressure to leading order, a collisionless heat flux at the next order, and a collisionless stress tensor at the second-order. The collisionless heat conduction and viscosity in the multi-fluid description results from a nonisotropic energetic particle distribution. A simpler single-fluid MHD-like system of equations with distinct equations of state for both the background plasma and the suprathermal particles is derived. We note briefly potential pitfalls that can emerge in the numerical modeling of collisionless plasma flows that contain a dynamically important energetic particle component.

The Relativistic Resistive Magnetohydrodynamic (RRMHD) equations are a hyperbolic system of partial differential equations used to describe the dynamics of relativistic magnetized fluids with a finite conductivity. Close to the ideal magnetohydrodynamic regime, the source term proportional to the conductivity becomes potentially stiff and cannot be handled with standard explicit time integration methods. We propose a new class of methods to deal with the stiffness fo the system, which we name Minimally Implicit Runge-Kutta methods. These methods avoid the development of numerical instabilities without increasing the computational costs in comparison with explicit methods, need no iterative extra loop in order to recover the primitive (physical) variables, the analytical inversion of the implicit operator is trivial and the several stages can actually be viewed as stages of explicit Runge-Kutta methods with an effective time-step. We test these methods with two different one-dimensional test beds in varied conductivity regimes, and show that our second-order schemes satisfy the theoretical expectations.

Classical MHD reconnection theories, both the stationary Sweet-Parker model and the tearing instability, are known to provide rates which are too slow to explain the observations. However, a recent analysis has shown that there exists a critical threshold on current sheet's thickness, namely a/L ∼ S^-1/3, beyond which the tearing modes evolve on fast macroscopic Alfvénic timescales, provided the Lunquist number S is high enough, as invariably found in solar and astrophysical plasmas. Therefore, the classical Sweet-Parker scenario, for which the diffusive region scales as a/L ∼ S^-1/2 and thus can be up to ∼ 100 times thinner than the critical value, is likely to be never realized in nature, as the current sheet itself disrupts in the elongation process. We present here two-dimensional, compressible, resistive MHD simulations, with S ranging from 10⁵ to 10⁷, that fully confirm the linear analysis. Moreover, we show that a secondary plasmoid instability always occurs when the same critical scaling is reached on the local, smaller scale, leading to a cascading explosive process, reminiscent of the flaring activity.

The current study shows the characteristics of the kink-type electromagnetic mode excited in the thin current layer formed around the x-line during the quasi-steady phase of magnetic reconnection. The linear wave analyses are carried out for the realistic current sheet profile which differs significantly from the Harris current sheet. It is found that the peak growth rate is very sensitive to the current sheet width even though the relative drift velocity at the center of the current sheet is fixed. This indicates that the mode is excited by the velocity shear rather than the relative drift velocity. Thus, the mode is termed here a current sheet shear mode. It is also shown that the wavenumber k_y has a clear mass ratio dependency as k_yλ_i ∝ (m_i/m_e)^1/4, implying the coupling of the ion and electron dynamics, where λ_iis the ion inertia length.

The Biermann Battery effect is frequently invoked in cosmic magnetogenesis and studied in High-Energy Density laboratory physics experiments. Unfortunately, direct implementation of the Biermann effect in MHD codes is known to produce unphysical magnetic fields at shocks whose value does not converge with resolution. We show that this convergence breakdown is due to naive discretization, which fails to account for the fact that discretized irrotational vector fields have spurious solenoidal components that grow without bound near a discontinuity. We show that careful consideration of the kinetics of ion viscous shocks leads to a formulation of the Biermann effect that gives rise to a convergent algorithm. We note a novel physical effect a resistive magnetic precursor in which Biermann-generated field in the shock "leaks" resistively upstream. The effect appears to be potentially observable in experiments at laser facilities.

The Multi-Level Multi-Domain (MLMD) method is a semi-implicit adaptive method for Particle-In-Cell plasma simulations. It has been demonstrated in the past in simulations of Maxwellian plasmas, electrostatic and electromagnetic instabilities, plasma expansion in vacuum, magnetic reconnection [1, 2, 3]. In multiple occasions, it has been commented on the coupling between the coarse and the refined grid solutions. The coupling mechanism itself, however, has never been explored in depth. Here, we investigate the theoretical bases of grid coupling in the MLMD system. We obtain an evolution law for the electric field solution in the overlap area of the MLMD system which highlights a dependance on the densities and currents from both the coarse and the refined grid, rather than from the coarse grid alone: grid coupling is obtained via densities and currents.

We describe an initial implementation of an electrostatic Particle-in-Cell (ES-PIC) module with adaptive Cartesian mesh in our Unified Flow Solver framework. Challenges of PIC method with cell-based adaptive mesh refinement (AMR) are related to a decrease of the particle-per-cell number in the refined cells with a corresponding increase of the numerical noise. The developed ES-PIC solver is validated for capacitively coupled plasma, its AMR capabilities are demonstrated for simulations of streamer development during high-pressure gas breakdown. It is shown that cell-based AMR provides a convenient particle management algorithm for exponential multiplications of electrons and ions in the ionization events.

We examine the two-fluid cosmic-ray magnetohydrodynamic (CR MHD) equations to take account of the dynamical effects of cosmic rays (CRs) in the simplest form. For simplicity we assume that the pressure of the CRs is proportional to the energy density, P_cr = (γ_cr − 1)E_cr, where γ_cr denotes the adiabatic index of CRs. We find the fully conservative form of the CR MHD equations and derive the Rankine-Hugoniot relation for a shock. One component of the CR MHD equations describes conservation of total number of CRs where the number density is defined as ρ_cr = P_cr^1/γcr. We also find the Riemann solution, which provides us approximate Riemann fluxes fluxes for numerical solutions. We have also identified origin of spurious oscillation originating from the pressure balance mode across which the CR pressure has a jump while the total pressure is continuous. We propose the two step method to solve the CR MHD equations. We use 1D shock tube problems to compare our method with others.

We present the design and implementation of a spectral code, called SpectralPlasmaSolver (SPS), for the solution of the multi-dimensional Vlasov-Maxwell equations. The method is based on a Hermite-Fourier decomposition of the particle distribution function. The code is written in Fortran and uses the PETSc library for solving the non-linear equations and preconditioning and the FFTW library for the convolutions. SPS is parallelized for shared- memory machines using OpenMP. As a verification example, we discuss simulations of the two-dimensional Orszag-Tang vortex problem and successfully compare them against a fully kinetic Particle-In-Cell simulation. An assessment of the performance of the code is presented, showing a significant improvement in the code running-time achieved by preconditioning, while strong scaling tests show a factor of 10 speed-up using 16 threads.

We present an implementation of a fully parallel hybrid framework for the evolution of Lagrangian particles coupled to a MHD fluid for the PLUTO code. For the applications of interest, particles represent ensembles of electrons whose spectral energy distribution is governed by a kinetic transport equation that takes into account different physical processes such as diffusive shock acceleration, synchrotron emission and adiabatic expansion. An application to model non-thermal emission from extragalactic jets shows the effectiveness and strength of the approach in describing not only the dynamics but also the radiation properties of jets and, in general, of high-energy astrophysical plasma environments.

We describe a new method for the solution of the ideal MHD equations in special relativity which adopts the following strategy: (i) the main scheme is based on Discontinuous Galerkin (DG) methods, allowing for an arbitrary accuracy of order N+1, where N is the degree of the basis polynomials; (ii) in order to cope with oscillations at discontinuities, an "a-posteriori" sub-cell limiter is activated, which scatters the DG polynomials of the previous time-step onto a set of 2N+1 sub-cells, over which the solution is recomputed by means of a robust finite volume scheme; (iii) a local spacetime Discontinuous-Galerkin predictor is applied both on the main grid of the DG scheme and on the sub-grid of the finite volume scheme; (iv) adaptive mesh refinement (AMR) with local time-stepping is used. We validate the new scheme and comment on its potential applications in high energy astrophysics.