THE GLOBAL WELL-POSEDNESS OF SOLUTIONS TO COMPRESSIBLE ISENTROPIC TWO-FLUID MAGNETOHYDRODYNAMICS IN A STRIP DOMAIN

In this paper,we consider a model of compressible isentropic two-fluid magneto-hydrodynamics without resistivity in a strip domain in three dimensional space.By exploiting the two-tier energy method developed in[Anal PDE,2013,6:1429–1533],we prove the global well-posedness of the governing model around a uniform magnetic field which is non-parallel to the horizontal boundary.Moreover,we show that the solution converges to the steady state at an almost exponential rate as time goes to infinity.Compared to the work of Tan and Wang[SIAM J Math Anal,2018,50:1432–1470],we need to overcome the difficulties caused by particles.

Electron Magnetohydrodynamics Magnetic Reconnection Experiment on Keda Linear Magnetized Plasma Device

We conduct an electron magnetohydrodynamics magnetic reconnection experiment with guide-field in our Keda linear magnetized plasma device, in which two pulsed currents with the same direction are conducted in parallel with the axial direction of the main chamber of the device using two long aluminum sticks. After approximately 5μs, an X-type magnetic field line topology is formed at the center of the chamber. With the formation of the X-type topology of magnetic field lines, we can also find the rapid increase of the current and ratio of the common flux to the private flux in this area. Additionally, a reduction in the plasma density and the plasma density concentration along one pair of separatrices can also be found.

The Richtmyer-Meshkov instability of a double-layer interface in convergent geometry with magnetohydrodynamics

The interaction between a converging cylindrical shock and double density interfaces in the presence of a saddle magnetic field is numerically investigated within the framework of ideal magnetohydrodynamics.Three fluids of differing densities are initially separated by the two perturbed cylindrical interfaces.The initial incident converging shock is generated from a Riemann problem upstream of the first interface.The effect of the magnetic field on the instabilities is studied through varying the field strength.It shows that the Richtmyer-Meshkov and Rayleigh-Taylor instabilities are mitigated by the field,however,the extent of the suppression varies on the interface which leads to non-axisymmetric growth of the perturbations.The degree of asymmetry of the interfacial growth rate is increased when the seed field strength is increased.

KINETIC FUNCTIONS IN MAGNETOHYDRODYNAMICS WITH RESISTIVITY AND HALL EFFECT

We consider a nonlinear hyperbolic system of two conservation laws which arises in ideal magnetohydrodynamics and includes second-order terms accounting for magnetic resistivity and Hall effect. We show that the initial value problem for this model may lead to solutions exhibiting complex wave structures, including undercompressive nonclassical shock waves. We investigate numerically the subtle competition that takes place between the hyperbolic, diffusive, and dispersive parts of the system. Following Abeyratne, Knowles, LeFloch, and Truskinovsky, who studied similar questions arising in fluid and solid flows, we determine the associated kinetic function which characterizes the dynamics of undereompressive shocks driven by resistivity and Hall effect. To this end, we design a new class of ＂schemes with eontroled dissipation＂, following recent work by LeFloch and Mohammadian. It is now recognized that the equivalent equation associated with a scheme provides a guideline to design schemes that capture physically relevant, nonclassical shocks. We propose a new class of schemes based on high-order entropy conservative, finite differences for the hyperbolic flux, and high-order central differences for the resistivity and Hall terms. These schemes are tested for several regimes of （co-planar or not） initial data and parameter values, and allow us to analyze the properties of nonclassical shocks and establish the existence of monotone kinetic functions in magnetohydrodynamics.

A STUDY ON THE BOUNDARY LAYER FOR THE PLANAR MAGNETOHYDRODYNAMICS SYSTEM

The paper aims to estimate the thickness of the boundary layer for the planar MHD system with vanishing shear viscosity μ. Under some conditions on the initial and boundary data, we show that the thickness is of the order √μ｜lnμ｜. Note that this estimate holds also for the Navier-Stokes system so that it extends the previous works even without the magnetic effect.

Parallel finite element computation of incompressible magnetohydrodynamics based on three iterations

Based on local algorithms,some parallel finite element(FE)iterative methods for stationary incompressible magnetohydrodynamics(MHD)are presented.These approaches are on account of two-grid skill include two major phases:find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution,and then locally solve linearized residual subproblems by one of three iterations(Stokes-type,Newton,and Oseen-type)on subdomains with fine grid in parallel to approximate the high frequency component.Optimal error estimates with regard to two mesh sizes and iterative steps of the proposed algorithms are given.Some numerical examples are implemented to verify the algorithm.

Traveling Wave Solutions of the Incompressible Ideal Hall Magnetohydrodynamics

The solutions of incompressible ideal Hall magnetohydrodynamics are obtained by using the traveling wave method. It is shown that the velocity and magnetic field parallel to the wave vector can be arbitrary constants. The velocity and magnetic field perpendicular to the wave vector are both helical waves. Moreover, the amplitude of the velocity perpendicular to the wave vector is related to the wave number and the circular frequency. In addition, further studies indicate that, no matter whether the uniform ambient magnetic field exists or not, the forms of the travelling wave solutions do not change.

Galerkin-Petrov least squares mixed element method for stationary incompressible magnetohydrodynamics

The Galerkin-Petrov least squares method is combined with the mixed finite element method to deal with the stationary, incompressible magnetohydrodynamics system of equations with viscosity. A Galerkin-Petrov least squares mixed finite element format for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of its solution are derived. Through this method, the combination among the mixed finite element spaces does not demand the discrete Babuska-Brezzi stability conditions so that the mixed finite element spaces could be chosen arbitrartily and the error estimates with optimal order could be obtained.

LOCAL EXISTENCE AND BLOW-UP CRITERION OF 3D IDEAL MAGNETOHYDRODYNAMICS EQUATIONS

We investigate the local existence of smooth solutions of a 3D ideal magneto-hydrodynamics （MHD） equations in a bounded domain and give a blow-up criteria to thisequations with respect to vorticists.

NONLINEAR GALERKIN MIXED ELEMENT METHODS FOR STATIONARY INCOMPRESSIBLE MAGNETOHYDRODYNAMICS

A nonlinear Galerkin mixed element （NGME） method for the stationary incompressible magnetohydrodynamics equations is presented. And the existence and error estimates of the NGME solution are derived.

Lattice Bhatnagar-Gross-Krook Simulations in 2-D Incompressible Magnetohydrodynamics

Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results.

Helical Mode Absolute Statistical Equilibrium of Ideal Three-Dimensional Hall Magnetohydrodynamics

Using the Fourier helical decomposition, we obtain the absolute statistical equilibrium spectra of left- and right-handed helical modes in the incompressible ideal Hall magnetohydrodynamics (MHD). It is shown that the left-handed helical modes play a major role on the spectral transfer properties of turbulence when the generalized helicity and magnetic helicity are both positive. In contrast, the right-handed helical modes will play a major role when both are negative. Furthermore, we also find that if the generalized helicity and magnetic helicity have opposite signs, the tendency of equilibrium spectra to condense at the large or small wave numbers will be presented in different helical sectors. This indicates that the generalized helicity dominates the forward cascade and the magnetic helicity dominates the inverse cascade properties of the Hall MHD turbulence.

Gas-Kinetic BGK Scheme for Three Dimensional Magnetohydrodynamics

The gas-kinetic theory based flux splitting method has been successfully proposed for solving one-and two-dimensional ideal magnetohydrodynamics by Xu et al. [J.Comput.Phys.,1999;2000],respectively.This paper extends the kinetic method to solve three-dimensional ideal magnetohydrodynamics equations,where an adaptive parameter 17 is used to control the numerical dissipation in the flux splitting method. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy and resolve strong discontinuous waves in three dimensional ideal MHD problems.

Magnetohydrodynamics convective flow in a vertical slot through a porous medium

An analysis is presented with magnetohydrodynamics natural convective flow of a viscous Newtonian fluid saturated porous medium in a vertical slot. The flow in the porous media has been modeled using the Brinkman model. The fully-developed two-dimensional flow from capped to open ends is considered for which a continuum of solutions is obtained. The influence of pertinent parame-ters on the flow is delineated and appropriate conclusions are drawn. The asymptotic behaviour and the volume flux are analyzed and incorporated graphically for the three-parameter family of solution.

Comparison between Two Vertical Enclosures Filled With Porous Media under the Effect of Radiation and Magnetohydrodynamics

A numerical study has been carried out to investigate the temperature distribution and the natural convection heat transfer in axisymmetric two-dimensional vertical saturated porous cylinder with steady state laminar flow. A comparison between two situations is done under the effect of MHD （magnetohydrodynamics） and radiation. In the two situations, the vertical walls of the cylinder are cooled with constant wall temperature and a constant heat generation subjected along the centerline of the cylinder. The first case for cylinder with insulated upper surface and cooled bottom surface while the second case for cylinder with cooled upper surface and insulated bottom surface. The governing equations used are continuity, momentum and energy equations which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 programming. The parameters affected the system are Rayleigh number ranging within （102≤ Ra ≤104）, radiation parameter （0≤ Rd ≤ 2） and magnetohydrodynamics MHD （Mn） （0 ≤ Mn≤ 2）.The results show that the temperature of Case 1 is more than that in Case 2 at constant Ra, Mn and Rd while the value of the stream in Case 2 is greater than that in Case 1. Nu increase with the increase of Rd and increasing Mn caused the temperature to increase and the streamline dropped while Nu decreased. A correlation has been set up to give the average Nusselt number variation with Ra, Rd and Mn for which the results are found to be in good agreement with previously published researches.

Magnetohydrodynamics bio-convection flow at Casson fluid stagnation point in porous medium:Cross-diffusion effect and heat production

This study examines the effect of heat production and radiation absorption on the magnetohydrodynamic Cassonfluidflow at the stagnation point in a porous medium.We convert the group offluidflow equations,which are non-linear partial differential equations with suitable boundary constraints,into a set of non-linear ordinary differential equations using similarity transformations.The homotopy analysis method(HAM)solves the converted system of ordinary differential equations.We draw graphs for numerous values of non-dimensional pa-rameters and tables of surface drag force,rates of heat transfer,and mass transfer to analyze the relationship between velocityfield,temperaturefield,concentrationfield,and other essential parameters involved in the study.We have proven that the Dufour number,radiation parameter,and heat generation parameter elevate thefluid temperature,whereas the magnetic parameter lowers it.The Cassonfluid parameter,buoyancy force parameter,and mixed convection param-eter all promotefluid movement throughout theflowfield.The presented tabular data allows us to see the trend of heat and mass transfer rates,as well as drag force rates,against important parameters,enhancing our understanding of these rates.

Hyperbolic Divergence Cleaning in Lattice Boltzmann Magnetohydrodynamics

Magnetohydrodynamics couples the Navier-Stokes and Maxwell’s equations to describe the flow of electrically conducting fluids in magnetic fields.Maxwell’s equations require the divergence of the magnetic field to vanish,but this condition is typically not preserved exactly by numerical algorithms.Solutions can develop artifacts because structural properties of the magnetohydrodynamic equations then fail to hold.Magnetohydrodynamics with hyperbolic divergence cleaning permits a nonzero divergence that evolves under a telegraph equation,designed to both damp the divergence,and propagate it away from any sources,such as poorly resolved regions with large spatial gradients,without significantly increasing the computational cost.We show that existing lattice Boltzmann algorithms for magnetohydrodynamics already incorporate hyperbolic divergence cleaning,though they typically use parameter values for which it reduces to parabolic divergence cleaning under a slowly-varying approximation.We recover hyperbolic divergence cleaning by adjusting the relaxation rate for the trace of the tensor that represents the electric field,and absorb the contribution from the symmetric-traceless part of this tensor using a change of variables.Numerical experiments confirm that the qualitative behaviour changes from parabolic to hyperbolic when the relaxation time for the trace of the electric field tensor is increased.

A Finite Element Variational Multiscale Method for Stationary Incompressible Magnetohydrodynamics Equations

In this paper,we propose a variational multiscale method(VMM)for the stationary incompressible magnetohydrodynamics equations.This method is defined by large-scale spaces for the velocity field and the magnetic field,which aims to solve flows at high Reynolds numbers.We provide a new VMM formulation and prove its stability and convergence.Finally,some numerical experiments are presented to indicate the optimal convergence of our method.

Observation of Standing Slow Magneto-acoustic Waves in a Flaring Active Region Corona Loop

Intensity fluctuations are frequently observed in different regions and structures of the solar corona.These fluctuations may be caused by magneto-hydrodynamic(MHD)waves in coronal plasma.MHD waves are prime candidates for the dynamics,energy transfer,and anomalous temperature of the solar corona.In this paper,analysis is conducted on intensity and temperature fluctuations along the active region coronal loop(NOAA AR 13599)near solar flares.The intensity and temperature as functions of time and distance along the loop are extracted using images captured by the Atmospheric Imaging Assembly(AIA)instrument onboard the Solar Dynamics Observatory(SDO)space telescope.To observe and comprehend the causes of intensity and temperature fluctuations,after conducting initial processing,and applying spatial and temporal frequency filters to data,enhanced distance-time maps of these variables are drawn.The space-time maps of intensities show standing oscillations at wavelengths of 171,193,and 211A with greater precision and clarity than earlier findings.The amplitude of these standing oscillations(waves)decreases and increases over time.The average values of the oscillation period,damping time,damping quality,projected wavelength,and projected phase speed of standing intensity oscillations are in the range of 15-18 minutes,24-31 minutes,1.46″-2″,132″-134″,and 81-100 km s^(-1),respectively.Also,the differential emission measure peak temperature values along the loop are found in the range of 0.51-3.98 MK,using six AIA passbands,including 94,131,171,193,211,and 335?.Based on the values of oscillation periods,phase speeds,damping time,and damping quality,it is inferred that the fluctuations in intensity are related to standing slow magneto-acoustic waves with weak damping.

FlowBreakdown of Hybrid Nanofluid on a Rigid Surface with Power Law Fluid as Lubricated Layers

Thiswork investigates an oblique stagnation point flowof hybrid nanofluid over a rigid surface with power lawfluidas lubricated layers. Copper (Cu) and Silver (Ag) solid particles are used as hybrid particles acting in water H2O asa base fluid. The mathematical formulation of flow configuration is presented in terms of differential systemthat isnonlinear in nature. The thermal aspects of the flow field are also investigated by assuming the surface is a heatedsurface with a constant temperature T. Numerical solutions to the governing mathematical model are calculatedby the RK45 algorithm. The results based on the numerical solution against various flow and thermal controllingparameters are presented in terms of line graphs. The specific results depict that the heat flux increases over thelubricated-indexed parameter.