B. van der Holst

Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics

Relativistic hydro and magnetohydrodynamics provide continuum fluid descriptions for gas and plasma dynamics throughout the visible universe. We present an overview of state-of-the-art modeling in special relativistic regimes, targeting strong shock-dominated flows with speeds approaching the speed of light. Significant progress in its numerical modeling emerged in the last two decades, and we highlight specifically the need for grid-adaptive, shock-capturing treatments found in several contemporary codes in active use and development. Our discussion highlights one such code, MPI-AMRVAC (Message-Passing Interface-Adaptive Mesh Refinement Versatile Advection Code), but includes generic strategies for allowing massively parallel, block-tree adaptive simulations in any dimensionality. We provide implementation details reflecting the underlying data structures as used in MPI-AMRVAC. Parallelization strategies and scaling efficiencies are discussed for representative applications, along with guidelines for data formats suitable for parallel I/O. Refinement strategies available in MPI-AMRVAC are presented, which cover error estimators in use in many modern AMR frameworks. A test suite for relativistic hydro and magnetohydrodynamics is provided, chosen to cover all aspects encountered in high-resolution, shock-governed astrophysical applications. This test suite provides ample examples highlighting the advantages of AMR in relativistic flow problems.

Alfvén wave solar model (AWSoM): Coronal heating

We present a new version of the Alfven wave solar model, a global model from the upper chromosphere to the corona and the heliosphere. The coronal heating and solar wind acceleration are addressed with low-frequency Alfven wave turbulence. The injection of Alfven wave energy at the inner boundary is such that the Poynting flux is proportional to the magnetic field strength. The three-dimensional magnetic field topology is simulated using data from photospheric magnetic field measurements. This model does not impose open-closed magnetic field boundaries; those develop self-consistently. The physics include the following. (1) The model employs three different temperatures, namely the isotropic electron temperature and the parallel and perpendicular ion temperatures. The firehose, mirror, and ion-cyclotron instabilities due to the developing ion temperature anisotropy are accounted for. (2) The Alfven waves are partially reflected by the Alfven speed gradient and the vorticity along the field lines. The resulting counter-propagating waves are responsible for the nonlinear turbulent cascade. The balanced turbulence due to uncorrelated waves near the apex of the closed field lines and the resulting elevated temperatures are addressed. (3) To apportion the wave dissipation to the three temperatures, we employ the results of the theories of linear wave damping and nonlinear stochastic heating. (4) We have incorporated the collisional and collisionless electron heat conduction. We compare the simulated multi-wavelength extreme ultraviolet images of CR2107 with the observations from STEREO/EUVI and the Solar Dynamics Observatory/AIA instruments. We demonstrate that the reflection due to strong magnetic fields in the proximity of active regions sufficiently intensifies the dissipation and observable emission.

A DATA-DRIVEN, TWO-TEMPERATURE SOLAR WIND MODEL WITH ALFVEN WAVES

We have developed a new three-dimensional magnetohydrodynamic (MHD) solar wind model coupled to the Space Weather Modeling Framework (SWMF) that solves for the different electron and proton temperatures. The collisions between the electrons and protons are taken into account as well as the anisotropic thermal heat conduction of the electrons. The solar wind is assumed to be accelerated by the Alfven waves. In this paper, we do not consider the heating of closed magnetic loops and helmet streamers but do address the heating of the protons by the Kolmogorov dissipation of the Alfven waves in open field-line regions. The inner boundary conditions for this solar wind model are obtained from observations and an empirical model. The Wang-Sheeley-Arge model is used to determine the Alfven wave energy density at the inner boundary. The electron density and temperature at the inner boundary are obtained from the differential emission measure tomography applied to the extreme-ultraviolet images of the STEREO A and B spacecraft. This new solar wind model is validated for solar minimum Carrington rotation 2077 (2008 November 20 through December 17). Due to the very low activity during this rotation, this time period is suitable for comparing the simulated corotating interaction regions (CIRs) with in situ ACE/WIND data. Although we do not capture all MHD variables perfectly, we do find that the time of occurrence and the density of CIRs are better predicted than by our previous semi-empirical wind model in the SWMF that was based on a spatially reduced adiabatic index to account for the plasma heating.

CRASH: A BLOCK-ADAPTIVE-MESH CODE FOR RADIATIVE SHOCK HYDRODYNAMICS-IMPLEMENTATION AND VERIFICATION

We describe the Center for Radiative Shock Hydrodynamics (CRASH) code, a block-adaptive-mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with a gray or multi-group method and uses a flux-limited diffusion approximation to recover the free-streaming limit. Electrons and ions are allowed to have different temperatures and we include flux-limited electron heat conduction. The radiation hydrodynamic equations are solved in the Eulerian frame by means of a conservative finite-volume discretization in either one-, two-, or three-dimensional slab geometry or in two-dimensional cylindrical symmetry. An operator-split method is used to solve these equations in three substeps: (1) an explicit step of a shock-capturing hydrodynamic solver; (2) a linear advection of the radiation in frequency-logarithm space; and (3) an implicit solution of the stiff radiation diffusion, heat conduction, and energy exchange. We present a suite of verification test problems to demonstrate the accuracy and performance of the algorithms. The applications are for astrophysics and laboratory astrophysics. The CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with a new radiation transfer and heat conduction library and equation-of-state and multi-group opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework.

Hybrid block-AMR in cartesian and curvilinear coordinates: MHD applications

Abstract We present a novel, hybrid block-adaptive scheme for use in solving sets of near-conservation laws in general orthogonal coordinate systems. The adaptive mesh refinement (AMR) scheme is block-based, i.e. individual grids have a pre-fixed number of grid cells, and is implemented for any-dimensionality D . Its ‘hybrid’ character relaxes the common approach where a block that needs refinement triggers 2 D subblocks when grids are refined by a factor of 2. This introduces ‘incomplete families’ in the grid hierarchy, but approaches the optimal fit to developing flow features inherent in the original patch-based AMR strategy. Our hybrid block-AMR approach is compared with a patch-based AMR one, both exploiting OpenMP parallelism. The implementation is able to handle general curvilinear coordinates, for which restriction and prolongation formulae are presented along with boundary treatments at ‘singular’ boundaries. Demonstrative examples cover hydro- and magnetohydrodynamic (MHD) applications, including tests on a 2D polar grid, a 2.5D spherical and a 3D cylindrical configuration. The applications cover classical up to relativistic MHD simulations, of particular relevance for astrophysical magnetized jet and stellar wind studies.

A Global Two-temperature Corona and Inner Heliosphere Model: A Comprehensive Validation Study

The recent solar minimum with very low activity provides us a unique opportunity for validating solar wind models. During CR2077 (2008 November 20 through December 17), the number of sunspots was near the absolute minimum of solar cycle 23. For this solar rotation, we perform a multi-spacecraft validation study for the recently developed three-dimensional, two-temperature, Alfven-wave-driven global solar wind model (a component within the Space Weather Modeling Framework). By using in situ observations from the Solar Terrestrial Relations Observatory (STEREO) A and B, Advanced Composition Explorer (ACE), and Venus Express, we compare the observed proton state (density, temperature, and velocity) and magnetic field of the heliosphere with that predicted by the model. Near the Sun, we validate the numerical model with the electron density obtained from the solar rotational tomography of Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph C2 data in the range of 2.4 to 6 solar radii. Electron temperature and density are determined from differential emission measure tomography (DEMT) of STEREO A and B Extreme Ultraviolet Imager data in the range of 1.035 to 1.225 solar radii. The electron density and temperature derived from the Hinode/Extreme Ultraviolet Imaging Spectrometer data are also used to compare with the DEMT as well as the model output. Moreover, for the first time, we compare ionic charge states of carbon, oxygen, silicon, and iron observed in situ with the ACE/Solar Wind Ion Composition Spectrometer with those predicted by our model. The validation results suggest that most of the model outputs for CR2077 can fit the observations very well. Based on this encouraging result, we therefore expect great improvement for the future modeling of coronal mass ejections (CMEs) and CME-driven shocks.

A GLOBAL WAVE-DRIVEN MAGNETOHYDRODYNAMIC SOLAR MODEL WITH A UNIFIED TREATMENT OF OPEN AND CLOSED MAGNETIC FIELD TOPOLOGIES

We describe, analyze, and validate the recently developed Alfv´ en Wave Solar Model, a three-dimensional global model starting from the top of the chromosphere and extending into interplanetary space (out to 1–2 AU). This model solves the extended, two-temperature magnetohydrodynamics equations coupled to a wave kinetic equation for low-frequency Alfv´ en waves. In this picture, heating and acceleration of the plasma are due to wave dissipation and to wave pressure gradients, respectively. The dissipation process is described by a fully developed turbulent cascade of counterpropagating waves. We adopt a unified approach for calculating the wave dissipation in both open and closed magnetic field lines, allowing for a self-consistent treatment in any magnetic topology. Wave dissipation is the only heating mechanism assumed in the model; no geometric heating functions are invoked. Electron heat conduction and radiative cooling are also included. We demonstrate that the large-scale, steady state (in the corotating frame) properties of the solar environment are reproduced, using three adjustable parameters: the Poynting flux of chromospheric Alfv´ en waves, the perpendicular correlation length of the turbulence, and a pseudoreflection coefficient. We compare model results for Carrington rotation 2063 (2007 November–December) with remote observations in the extreme-ultraviolet and X-ray ranges from the Solar Terrestrial Relations Observatory, Solar and Heliospheric Observatory, and Hinode spacecraft and with in situ measurements by Ulysses. The results are in good agreement with observations. This is the first global simulation that is simultaneously consistent with observations of both the thermal structure of the lower corona and the wind structure beyond Earth’s orbit.

On the effect of the initial magnetic polarity and of the background wind on the evolution of CME shocks

The shocks and magnetic clouds caused by Coronal Mass Ejections (CMEs) in the solar corona and interplanetary (IP) space play an important role in the study of space weather. In the present paper, numerical simulations of some simple CME models were performed by means of a finite volume, explicit solver to advance the equations of ideal magnetohydrodynamics. The aim is to quantify here both the effect of the background wind model and of the initial polarity on the evolution of the IP CMEs and the corresponding shocks.
To simulate the CMEs, a high density-pressure plasma blob is superposed on different steady state solar wind models. The evolution of an initially non-magnetized plasma blob is compared with that of two magnetized ones (with both normal and inverse polarity) and the differences are analysed and quantified. Depending on the launch angle of the CME and the polarity of the initial flux rope, the velocity of the shock front and magnetic cloud is decreased or increased. Also the spread angle of the CME and the evolution path of the CME in the background solar wind is substantially different for the different CME models and the different wind models. A quantitative comparison of these simulations shows that these effects can be quite substantial and can clearly affect the geo-effectiveness and the arrival time of the events.

Inverse and normal coronal mass ejections : evolution up to 1 AU

Simulations of Coronal Mass Ejections (CMEs) evolving in the interplanetary (IP) space from the Sun up to 1 AU are performed in the framework of ideal magnetohydrodynamics (MHD) by the means of a finite volume, explicit solver. The aim is to quantify the effect of the initiation parameters, such as the initial magnetic polarity, on the evolution and on the geo-effectiveness of CMEs. The CMEs are simulated by means of a very simple model: a high density and high pressure magnetized plasma blob is superposed on a background steady state solar wind model with an initial velocity and launch direction. The simulations show that the initial magnetic polarity substantially affects the IP evolution of the CMEs influencing the propagation velocity, the shape, the trajectory and even the geo-effectiveness. We also tried to reproduce the physical values (density, velocity, and magnetic field) observed by the ACE spacecraft after the halo CME event that occurred on April 4, 2000.

Simulation of a Breakout Coronal Mass Ejection in the Solar Wind

The initiation and evolution of coronal mass ejections (CMEs) is studied by means of the breakout model embedded in a 2.5D axisymmetric solar wind in the framework of numerical magnetohydrodynamics (MHD). The initial, steady equilibrium contains a pre-eruptive region consisting of three arcades with alternating magnetic flux polarity and with correspondingly three neutral lines on the photosphere. The magnetic tension of the overlying closed magnetic field of the helmet streamer keeps this structure in place. The most crucial part of the initial breakout topology is the existence of an X-point on the leading edge of the central arcade. By shearing part of this arcade, the reconnection with the overlying streamer field is turned on. The initial phase of the erupting arcade then closely follows the original breakout scenario. The breakout reconnection opens the overlying field in an energetically efficient way leading to an ever faster eruption. However, from a certain moment two new reconnections set in on the sides of the erupting central arcade and the breakout reconnection stops. The consequence of this change in reconnection location is twofold: (1) the lack of breakout reconnection so that the breakout plasmoid fails to become a fast CME; and (2) an eventual disconnection of the large helmet top resulting in a slow CME.