Three-dimensional Magnetohydrodynamics Research Articles

Parametric Study of ICME Properties Related to Space Weather Disturbances via a Series of Three-Dimensional MHD Simulations

Interplanetary coronal mass ejections (ICMEs) are important drivers of space-weather disturbances observed at the Earth. We use a parameterized ICME model to investigate the relation between the physical properties of an ICME and these disturbances. Compared to those studies focused on deriving a best set of ICME parameter values matched with observed disturbances, this study is aimed at investigating the role of each parameter in producing space-weather disturbances. Toward this end, we performed a series of three-dimensional magnetohydrodynamic (MHD) simulations with different sets of ICME parameter values. These parameters are the location, speed, mass, magnetic field strength, and magnetic field orientation of a spheromak-shaped ICME, which is injected into the solar wind reconstructed from near-Sun data and interplanetary scintillation (IPS) data via an MHD-IPS tomography method. By comparing simulation results to in situ observations near the Earth we discuss how the physical properties of an ICME affect space-weather disturbances at the Earth.

Small Alfvén number limit for incompressible magneto-hydrodynamics in a domain with boundaries

for any fixed Alfven number, the local well-posedness is proved for the equations of three-dimensional ideal incompressible magneto-hydrodynamics in a domain with boundaries. Under appropriate conditions, a smooth solution is shown to exist in a time interval independent of the Alfven number, and the solutions of the original system tend to the solutions of a two-dimensional Euler flow coupled with a linear transport equation as the Alfven number goes to zero.

General-relativistic Resistive Magnetohydrodynamics with Robust Primitive-variable Recovery for Accretion Disk Simulations

Abstract Recent advances in black hole astrophysics, particularly the first visual evidence of a supermassive black hole at the center of the galaxy M87 by the Event Horizon Telescope, and the detection of an orbiting “hot spot” nearby the event horizon of Sgr A* in the Galactic center by the Gravity Collaboration, require the development of novel numerical methods to understand the underlying plasma microphysics. Non-thermal emission related to such hot spots is conjectured to originate from plasmoids that form due to magnetic reconnection in thin current layers in the innermost accretion zone. Resistivity plays a crucial role in current sheet formation, magnetic reconnection, and plasmoid growth in black hole accretion disks and jets. We included resistivity in the three-dimensional general-relativistic magnetohydrodynamics (GRMHD) code BHAC and present the implementation of an implicit–explicit scheme to treat the stiff resistive source terms of the GRMHD equations. The algorithm is tested in combination with adaptive mesh refinement to resolve the resistive scales and a constrained transport method to keep the magnetic field solenoidal. Several novel methods for primitive-variable recovery, a key part in relativistic magnetohydrodynamics codes, are presented and compared for accuracy, robustness, and efficiency. We propose a new inversion strategy that allows for resistive-GRMHD simulations of low gas-to-magnetic pressure ratio and highly magnetized regimes as applicable for black hole accretion disks, jets, and neutron-star magnetospheres. We apply the new scheme to study the effect of resistivity on accreting black holes, accounting for dissipative effects as reconnection.

Application of an artificial neural network to predict the entrance length of three-dimensional magnetohydrodynamics channel flow

In this paper, a feed-forward, back-propagation neural network was employed for modeling the three-dimension magnetohydrodynamics (MHD) developing fluid flow. The aim of the study is to obtain a correlation for calculating the entrance length by applying an artificial neural network (ANN). To collect the data for training ANN, the numerical finite volume method (FVM) was conducted. The data were collected including Reynolds number (Re) ranging from 500 to 1000 and Hartmann number (Ha) ranging from 4 to 14 for a three-dimensional rectangular channel with four different aspect ratios (AR in a three-layer ANN for modeling the flow and computing the entrance length as a function of AR , Re and Ha. The results obtained from the ANN, FVM and the proposed correlations were compared and it was observed that the variation of the entrance length was different for each AR . Thus, two correlations were proposed with the different range of the AR and Ha. The contours and vectors of the velocity along the channel direction and for different cross-sections were illustrated. In addition, the effect of AR and Ha on the entrance length and pressure loss was presented.

A Novel Design of Three-Dimensional MHD Flow of Second-Grade Fluid past a Porous Plate

In this study, a novel theoretical model for three-dimensional (3D) laminar magnetohydrodynamic (MHD) flow of a non-Newtonian second-grade fluid along a plate of semi-infinite length is developed based on slightly sinusoidal transverse suction velocity. The suction velocity involves a steady distribution with a low superimposed perpendicularly varying dispersion. The strength of the uniform magnetic field is incorporated in the normal direction to the wall. The variable suction transforms the fluidic problem into a 3D flow problem because of variable suction velocity in the normal direction to the plane wall. The proposed mathematical modeling and its dynamical analysis are prescribed for the boundary layer flow keeping the magnetic effects without taking into consideration the induced magnetic field. An analytical perturbation technique is employed for the series solutions of the system of ordinary differential equations of velocity profile and pressure. Graphical illustrations are used to analyze the behavior of different proficient parameters of interest. The magnetic parameter is responsible for accelerating the main flow velocity, while controlling the cross flow velocities.

Wavelet-based parallel dynamic mesh adaptation for magnetohydrodynamics in the AMROC framework

Computational magnetohydrodynamics (MHD) for space physics has become an essential area in understanding the multiscale dynamics of geophysical and astrophysical plasma processes, partially motivated by the lack of space data. Full MHD simulations are typically very demanding and may require substantial computational efforts. In particular, computational space-weather forecasting is an essential long-term goal in this area, motivated for instance by the needs of modern satellite communication technology. We present a new feature of a recently developed compressible two- and three-dimensional MHD solver, which has been successfully implemented into the parallel AMROC (Adaptive Mesh Refinement in Object-oriented C++) framework with improvements concerning the mesh adaptation criteria based on wavelet techniques. The developments are related to computational efficiency while controlling the precision using dynamically adapted meshes in space-time in a fully parallel context.

New data-driven method of simulating coronal mass ejections

Context. Coronal mass ejections (CMEs) are large eruptions of plasma and magnetic field from the Sun’s corona. Understanding the evolution of the CME is important to evaluate its impact on space weather. Using numerical simulation, we are able to reproduce the occurrence and evolution process of the CME. Aims. The aim of this paper is to provide a new data-driven method to mimic the coronal mass ejections. By using this method, we can investigate the phsical mechanisms of the flux rope formation and the cause of the CME eruption near the real background. Methods. Starting from a potential magnetic field extrapolation, we have solved a full set of magnetohydrodynamic (MHD) equations by using the conservation element and solution element (CESE) numerical method. The bottom boundary is driven by the vector magnetograms obtained from SDO/HMI and vector velocity maps derived from DAVE4VM method. Results. We present a three-dimensional numerical MHD data-driven model for the simulation of the CME that occurred on 2015 June 22 in the active region NOAA 12371. The numerical results show two elbow-shaped loops formed above the polarity inversion line (PIL), which is similar to the tether-cutting picture previously proposed. The temporal evolutions of magnetic flux show that the sunspots underwent cancellation and flux emergence. The signature of velocity field derived from the tracked magnetograms indicates the persistent shear and converging motions along the PIL. The simulation shows that two elbow-shaped loops were reconnected and formed an inverse S-shaped sigmoid, suggesting the occurrence of the tether-cutting reconnection, which was supported by observations of the Atmospheric Imaging Assembly (AIA) telescope. Analysis of the decline rate of the magnetic field indicates that the flux rope reached a region where the torus instability was triggered. Conclusions. We conclude that the eruption of this CME was caused by multiple factors, such as photosphere motions, reconnection, and torus instability. Moreover, our simulation successfully reproduced the three-component structures of typical CMEs.

Heat transfer enhancement in MHD free surface flow by controlling the electromagnetic force with fin structure

A partly insulated fin (PIF) structure has been proposed to mitigate the temperature stratification of flowing-type liquid metal divertors. This study conducted a three-dimensional magnetohydrodynamics (MHD) flow and heat transfer numerical simulation to investigate the influence of the PIF on the velocity and the temperature field inside the film flow. An analytical model simulated a liquid metal film flow of 25 mm thickness under a transverse magnetic field up to 1.0 T. The simulation was conducted with a PIF, a metal fin, and without a fin. The results showed the generation of a high velocity region near the surface and the velocity was 2.68 times higher than the case without a fin due to the MHD effect. In addition, an upward flow was observed in front of the PIF. The contribution of the flow field generated by the fin to the temperature field was confirmed through numerical analysis, and the highest temperature of the liquid metal surface decreased by 0.96% at its maximum. A deformation of the surface due to the fin was estimated using the pressure distribution obtained from the simulation. The result indicated expected deformation is 21.8 μm at the magnetic field of 1.0 T.

Origin of misalignments: protostellar jet, outflow, circumstellar disc, and magnetic field

Recent observations uncover various phenomena around the protostar such as misalignment between the outflow and magnetic field, precession of the jet, and time variability of the ejected clumps, whose origins are under debate. We perform a three-dimensional resistive magnetohydrodynamics simulation of the protostar formation in a star-forming core whose rotation axis is tilted at an angle $45^\circ$ with respect to the initial magnetic field, in which the protostar is resolved with a spatial resolution of $0.01\,$au. In low-dense outer region, the prestellar core contracts along the magnetic field lines due to the flux freezing. In high-dense inner region, on the other hand, the magnetic dissipation becomes efficient and weakens the magnetic effects when the gas number density exceeds about $10^{11}\,{\rm cm^{-3}}$. Then, the normal direction of the flattened disc is aligned with the angular momentum vector. The outflow, jet, and protostellar ejection are driven from different scales of the circumstellar disc and spout in different directions normal to the warped disc. These axes do not coincide with the global magnetic field direction and vary with time. This study demonstrates that a couple of misalignment natures reported by observations can be simultaneously reproduced only by assuming the star-forming core rotating around a different direction from the magnetic field.

Linear and circular polarization of a 1D relativistic jet model

Context. Polarimetric observations of black holes allow us to probe structures of magnetic fields and plasmas in strong gravity. Aims. We present a study of the polarimetric properties of a synchrotron spectrum emitted from a relativistic jet using a low-dimensional model. Methods. A novel numerical scheme is used to integrate relativistic polarized radiative transfer equations in a slab geometry where the plasma conditions change along the integration path. Results. We find that the simple model of a non-uniform jet can recover basic observational characteristics of some astrophysical sources with a relativistic jet, such as extremely high rotation measures. Our models incorporate a time-dependent component. A small fluctuation in density or temperature of the plasma along the jet produces significant amounts of fluctuations not only in the fractional linear and circular polarizations, but also in the jet internal rotation measures. Conclusions. The low-dimensional models presented here are developed within the same computational framework as the complex three-dimensional general relativistic magnetohydrodynamics simulations of black hole disks and jets, and they offer guidance when interpreting the results from more complex polarization models. The models presented here are scalable to stationary and transient polarized radio emissions produced by relativistic plasma ejected from around compact objects, in both stellar-mass and supermassive black hole systems.

Markov Selections for the Magnetohydrodynamics and the Hall-Magnetohydrodynamics Systems

The magnetohydrodynamics system has found rich applications in applied sciences and has history of intense investigation by researchers including mathematicians. On the other hand, the Hall-magnetohydrodynamics system consists of the former system added by a Hall term which is very singular, and the mathematical development on this system has seen its significant progress only in the last several years. In short, the magnetohydrodynamics system, similarly to the Navier–Stokes equations, is semilinear, while the Hall-magnetohydrodynamics system is quasilinear. In this manuscript, we consider the three-dimensional magnetohydrodynamics, as well as the Hall-magnetohydrodynamics systems, and prove that they have Markov selections. In the case of the magnetohydrodynamics system, we prove furthermore a weak–strong uniqueness result and that any Markov solution has the strong Feller property for regular initial conditions. Consequently, it is deduced that if the magnetohydrodynamics system is well posed starting from one initial data, then it is well posed starting from any initial data, verifying a sharp contrast to the deterministic case in which the well posedness for all time with small initial data is well known. In the case of the Hall-magnetohydrodynamics system, we are also able to prove the weak–strong uniqueness result; however, the proof of strong Feller property seems to break down due to the singularity of the Hall term, about which we elaborate in detail.

On the Gevrey regularity of solutions to the 3D ideal MHD equations

In this paper, similar to the incompressible Euler equation, we prove the propagation of the Gevrey regularity of solutions to the three-dimensional incompressible ideal magnetohydrodynamics (MHD) equations. We also obtain an uniform estimate of Gevery radius for the solution of MHD equation.

Global-in-time solutions to three-dimensional magnetohydrodynamics equations with a class of large initial data

Global-in-time solutions to three-dimensional magnetohydrodynamics equations with a class of large initial data

A multi-GPU finite volume solver for magnetohydrodynamics-based solar wind simulations

Magnetohydrodynamic (MHD) simulations in the domain of spherical shell are a crucial and challenging subject in many fields such as geophysics and solar-terrestrial physics, due to the complication of the MHD equations and the specificity of the domain. Besides, due to the real-time requirement, accelerating the heavy computation is proposed in many practical problems, of which the space weather simulation and forecast from the Sun to Earth is a typical case. Considering these factors, we first develop a new, spatially second-order accurate finite volume (FV) solver for three-dimensional (3D) MHD simulations with the multiple time steps strategy, which is based on the six-component grid for spherical shell domain. Then to speed up the simulation, we implement the solver on multiple GPUs with optimizations of CUDA and establish an effective multi-GPU FV solver on the spherical shell domain. A MHD manufactured solution is used to validate the solvers’ spatial accuracy, and to measure their performances. Results show that both solvers have nice scalability, and speedup ratios of 27.7x to 30.06x are obtained on GPUs. Then we utilize them to study the ambient solar wind for Carrington rotation (CR) 2060. The multi-GPU FV solver can not only obtain speedup ratios of about 29.0x, but capture main features of the solar corona and the mapped in-situ solar wind measurements.

Numerical study of the reconnection process between magnetic cloud and heliospheric current sheet

In this paper, we have used a three-dimensional numerical magnetohydrodynamics model to study the reconnection process between magnetic cloud and heliospheric current sheet. Within a steady-state heliospheric model that gives a reasonable large-scale structure of the solar wind near solar minimum, we injected a spherical plasmoid to mimic a magnetic cloud. When the magnetic cloud moves to the heliospheric current sheet, the dynamic process causes the current sheet to become gradually thinner and the magnetic reconnection begin. The numerical simulation can reproduce the basic characteristics of the magnetic reconnection, such as the correlated/anticorrelated signatures in V and B passing a reconnection exhaust. Depending on the initial magnetic helicity of the cloud, magnetic reconnection occurs at points along the boundary of the two systems where antiparallel field lines are forced together. We find the magnetic filed and velocity in the MC have a effect on the reconnection rate, and the magnitude of velocity can also effect the beginning time of reconnection. These results are helpful in understanding and identifying the dynamic process occurring between the magnetic cloud and the heliospheric current sheet.

How Does the Stellar Wind Influence the Radio Morphology of a Supernova Remnant?

Abstract We simulate the evolution of the stellar wind and the supernova remnant (SNR) originating from a runaway massive star in a uniform Galactic environment based on three-dimensional magnetohydrodynamics models. Taking the stellar wind into consideration, we can explain the radio morphologies of many SNRs. The directions of the kinematic velocity of the progenitor, the magnetic field, and the line of sight are the most important factors influencing the morphologies. If the velocity is perpendicular to the magnetic field, the simulation will give us two different unilateral SNRs and a bilateral symmetric SNR. If the velocity is parallel to the magnetic field, we obtain a bilateral asymmetric SNR and a quasi-circular SNR. Our simulations show the stellar wind plays a key role in the radio evolution of an SNR, which implies that the Galactic global density and magnetic field distribution play a secondary role.

Optimal convergence analysis of Crank–Nicolson extrapolation scheme for the three-dimensional incompressible magnetohydrodynamics

This paper considers a Crank–Nicolson extrapolation scheme based on mixed finite element method to solve the three-dimensional incompressible magnetohydrodynamics (MHD) equations. We prove that the fully discrete scheme is almost unconditionally stable and convergent, i.e., stable and convergent when the time step is less than or equal to a constant. By a new negative norm technique, the optimal error estimates in L2-norm are derived. Meanwhile, the numerical investigations provide a sufficient support for the theoretical analysis.

Correction to: Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics

When we published this article, the biographies of Gregor J Gassner and Stefanie Walch have been mixed up during the type-setting process. Sadly, this mistake remained unnoticed. The correct biographies are: Gregor Gassner is a professor in numerical analysis/scientific computing at the Mathematical Institute at the University of Cologne. Gregor obtained a diploma degree in aerospace engineering (2004) and a diploma degree in mathematics (2005) from the University of Stuttgart. In 2009 he received his doctoral degree at the Institute of Aerodynamics and Gasdynamics, Stuttgart. He got an offer for a Junior professorship at TU Braunschweig in computational fluid dynamics, an offer for scientific computing at the TU Hamburg-Harburg and an offer from University of Cologne, where he joined in 2013. In 2016 he received an ERC starting grant on the topic of adaptive, robust and highly efficient numerical methods for the simulation of non-linear conservation laws. Stefanie Walch is a full professor for theoretical astrophysics at the University of Cologne since 2013. After the diploma in physics in 2004, Stefanie received her doctoral degree in theoretical physics from the Ludwig-Maximilians-Universitat Munchen in 2008. Afterwards she has spent 3 years at Cardiff University in Wales, and approximately 2 years at the Max-Planck-Institute for Astrophysics in Garching as a postdoctoral researcher before being appointed at the University of Cologne. She specialises in the physics of the interstellar medium including star formation and stellar feedback in the form of ionizing radiation, stellar winds, and supernovae. The evolution of gas in galaxies is studied using massively parallel, three-dimensional magneto-hydrodynamics simulations with additional (self-)gravity, radiative transfer, and chemical networks to follow the formation and dissociation of molecules and to bridge the gap to observations in different tracers. Synthetic observations ranging from X-ray emission to CO and dust polarization maps are now used to put modern theories of star formation and feedback to the test. In 2015, she received an ERC Starting Grant on the topic of “The radiative interstellar medium”. The original article has been corrected. The publisher apologises for this mistake.

Ergodicity of a Galerkin approximation of three-dimensional magnetohydrodynamics system forced by a degenerate noise

Magnetohydrodynamics system consists of a coupling of the Navier-Stokes and Maxwell's equations and is most useful in studying the motion of electrically conducting fluids. We prove the existence of a unique invariant, and consequently ergodic, measure for the Galerkin approximation system of the three-dimensional magnetohydrodynamics system. The proof is inspired by those of [E. Weinan and J.C. Mattingly, Ergodicity for the Navier-Stokes equation with degenerate random forcing: Finitedimensional approximation, Comm. Pure Appl. Math. LIV (2001), pp. 1386–1402; M. Romito, Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise, J. Stat. Phys. 114 (2004), pp. 155–177] on the Navier-Stokes equations; however, computations involve significantly more complications due to the coupling of the velocity field equations with those of magnetic field that consists of four non-linear terms.

Production of intense episodic Alfvén pulses: GRMHD simulation of black hole accretion discs

The episodic dynamics of the magnetic eruption of a spinning black hole (BH) accretion disks and its associated intense shapeup of their jets is studied via three-dimensional general-relativistic magnetohydrodynamics (GRMHD). The embedded magnetic fields in the disk get amplified by the magnetorotational instability (MRI) so large as to cause an eruption of magnetic field (recconection) and large chunks of matter episodically accrete toward the roots of the jets upon such an event. We also find that the eruption events produce intensive Alfv\'en pulses, which propagate through the jets. After the eruption, the disk backs to the weakly magnetic states. Such disk activities cause short time variabilities in mass accretion rate at the event horizon as well as electromagnetic luminosity inside the jet. Since the dimensionless strength parameter $a_0=eE/m_e \omega c$ of these Alfv\'en wave pulses is extremely high for a substantial fraction of Eddington accretion rate accretion flow onto a supermassive black hole, the Alfv\'en shocks turn into ultrarelativistic $(a_0\gg 1)$ bow wake acceleration, manifesting into the ultra-high energy cosmic rays and electrons which finally emit gamma-rays. Since our GRMHD model has universality in its spatial and temporal scales, it is applicable to a wide range of astrophysical objects ranging from those of AGN (which is the primary target of this research), to micro-quasars. Properties such as time variabilities of blazar gamma-ray flares and spectrum observed by {\it Fermi} Gamma-ray Observatory are well explained by linear acceleration of electrons by the bow wake.