Magnetogravitational Instability of Anisotropic Plasma with Finite Ion Larmor and Generalized Polytrope Law

The effect of finite ion Larmor radius corrections on the propagation of small perturbations through self gravitating, anisotropic system with generalized polytrope law is investigated. The polytrope laws are considered for the pressure components in parallel and perpendicular directions to the magnetic field. The polytrope model proposed by Abraham-Shranuer can be reduced to CGL equations with double adiabatic equations of state and MHD set of equations with isothermal equation of state. The effects of FLR and polytrope indices are discussed on the gravitational, firehose and mirror instability. The critical Jeans wave numbers are found to depend on polytropic indices and derived for CGL and MHD cases. The FLR corrections are found effective in shorter wave length region and produce stabilizing influence. The condition of mirror instability is uninfluenced by FLR but dependent on polytropic indices.     

A positive MUSCL-Hancock scheme for ideal magnetohydrodynamics

We present a highly robust second order accurate scheme for the Euler equations and the ideal MHD equations. The scheme is of predictor–corrector type, with a MUSCL scheme following as a special case. The crucial ingredients are an entropy stable approximate Riemann solver and a new spatial reconstruction that ensures positivity of mass density and pressure. For multidimensional MHD, a new discrete form of the Powell source terms is vital to ensure the stability properties. The numerical examples show that the scheme has superior stability compared to standard schemes, while maintaining accuracy. In particular, the method can handle very low values of pressure (i.e. low plasma β$\beta$ or high Mach numbers) and low mass densities.     

大气压下自由燃烧弧的温度场和速度场的数值模拟

采用标准SIMPLE算法，并作了一些修正，给出了具体的计算步骤和流程图，将其应用于磁流体动力学(MHD)方程进行数值求解．得到了轴对称情况下，自由燃烧弧的温度场和速度场的分布，并和实验结果进行了比较。分析了不同辐射模型对温度场的影响，发现辐射导致电弧温度降低，但不同的辐射模型对于电弧的温度影响不大。     

Energy decay laws in strongly anisotropic magnetohydrodynamic turbulence

We investigate the influence of a uniform magnetic field B(0)=B(0)e( parallel) on energy decay laws in incompressible magnetohydrodynamic (MHD) turbulence. The nonlinear transfer reduction along B(0) is included in a model that distinguishes parallel and perpendicular directions, following a phenomenology of Kraichnan. We predict a slowing down of the energy decay due to anisotropy in the limit of strong B(0), with distinct power laws for energy decay of shear- and pseudo-Alfvén waves. Numerical results from the kinetic equations of Alfvén wave turbulence recover these predictions, and MHD numerical results clearly tend to follow them in the lowest perpendicular planes.     

Generation of short-lived large-amplitude magnetohydrodynamic pulses by dispersive focusing

Large-amplitude MHD waves are routinely observed in space plasmas. We suggest that dispersive focusing, previously proposed for the excitation of freak waves in the ocean, can be also responsible for the excitation of short-lived large-amplitude MHD waves in space plasmas. The DNLS equation describes MHD waves propagating in plasmas at moderate angles with respect to the equilibrium magnetic field. We obtained an analytical solution of the linearised DNLS equation governing the generation of large-amplitude MHD waves from small-amplitude wave trains due to the dispersive focusing. Our numerical solutions of the full DNLS equation confirm this result.     

Splitting based finite volume schemes for ideal MHD equations

We design finite volume schemes for the equations of ideal magnetohydrodynamics (MHD) and based on splitting these equations into a fluid part and a magnetic induction part. The fluid part leads to an extended Euler system with magnetic forces as source terms. This set of equations are approximated by suitable two- and three-wave HLL solvers. The magnetic part is modeled by the magnetic induction equations which are approximated using stable upwind schemes devised in a recent paper [F. Fuchs, K.H. Karlsen, S. Mishra, N.H. Risebro, Stable upwind schemes for the Magnetic Induction equation. Math. Model. Num. Anal., Available on conservation laws preprint server, submitted for publication, URL: <http://www.math.ntnu.no/conservation/2007/029.html>]. These two sets of schemes can be combined either component by component, or by using an operator splitting procedure to obtain a finite volume scheme for the MHD equations. The resulting schemes are simple to design and implement. These schemes are compared with existing HLL type and Roe type schemes for MHD equations in a series of numerical experiments. These tests reveal that the proposed schemes are robust and have a greater numerical resolution than HLL type solvers, particularly in several space dimensions. In fact, the numerical resolution is comparable to that of the Roe scheme on most test problems with the computational cost being at the level of a HLL type solver. Furthermore, the schemes are remarkably stable even at very fine mesh resolutions and handle the divergence constraint efficiently with low divergence errors.     

Maxwell's equations in divergence form for general media with applications to MHD

Maxwell's equations in media with general constitutive relations are reformulated in covariant form as a system of divergence equations without constraints. Our reformulation enables us to express general electro-magneto-fluid problems as hyperbolic systems in divergence form. We illustrate this method on the MHD problem. In the absence of constraints, a general representation is derived for the characteristics form for first-order systems of quasi-linear partial differential equations in vector fields and scalars. Using this covariant formulation of characteristics, we find that the principle of covariance imposes a very rigid structure on the infinitesimally small amplitude waves in MHD. To demonstrate the power of the reformulation, we study numerically ultra-relativistic wave breaking using the divergence formulation of MHD.This material is based upon work supported by NSF grant AST 84-51725. Some of the work has been performed at the Department of Applied Mathematics, Caltech     

Characterization of the three-dimensional supersonic flow for the MHD generator

A numerical procedure based on a five-wave MHD model associated with non-ideal, low magnetic Reynolds number MHD flows was developed in the present study for analyzing the flow fields in the MHD generator of a MHD bypass scramjet. The numerical procedure is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations, in conjunction with an SOR method for solving the elliptic equation governing the electrical potential. It was found that a separation would take place near the downstream edge of the second electrode, where the local adverse pressure gradient is large, and the core of the flow field is characterized as a 2-D flow due to the Hartmann effects along the direction of the magnetic field. The electric current lines would be increasingly distorted as the magnetic interactive parameter increases, and even induce an eddy current. Induced eddy current was also found in the different cross-sections along the axial direction, all of these would definitely deteriorate the performance of the MHD generator. The cross-sectional M-shape velocity profile found along the axial direction between the insulating walls is responsible for the formation of the vortex flow at the corner of the insulator cross-section, which, in turn, induces the corner eddy current at the corner. A numerical parametric study was also performed, and the computed performance parameters for the MHD generator suggest that, in order to enhance the performance of MHD generator, the magnetic interaction parameter should be elevated.     

FOI-PERFECT程序对电磁驱动高能量密度系统的三维弛豫磁流体力学模拟

提出一个完整的弛豫磁流体力学模型用于电磁驱动高能量密度系统的数值模拟, 它由弛豫电磁波动、弛豫热输运、P1/3近似辐射输运以及流体力学构成。电磁部分在真空区退化为电磁传播, 在等离子体物质区退化为磁扩散近似, 并且相速和群速是有上界的。这意味着弛豫磁流体力学能退化到传统的电阻性磁流体力学, 并且能用显式方法数值求解, 便于大规模高效并行化。基于此弛豫磁流体力学模型开发了三维辐射磁流体力学程序FOI-PERFECT, 指出了所采用的关键数值技术, 并给出了一些应用例子。     

Pressure based finite volume method for calculation of compressible viscous gas flows

A pressure based, iterative finite volume method is developed for calculation of compressible, viscous, heat conductive gas flows at all speeds. The method does not need the use of under-relaxation coefficient in order to ensure a convergence of the iterative process. The method is derived from a general form of system of equations describing the motion of compressible, viscous gas. An emphasis is done on the calculation of gaseous microfluidic problems. A fast transient process of gas wave propagation in a two-dimensional microchannel is used as a benchmark problem. The results obtained by using the new method are compared with the numerical solution obtained by using SIMPLE (iterative) and PISO (non-iterative) methods. It is shown that the new iterative method is faster than SIMPLE. For the considered problem the new method is slightly faster than PISO as well. Calculated are also some typical microfluidic subsonic and supersonic flows, and the Rayleigh–Bénard convection of a rarefied gas in continuum limit. The numerical results are compared with other analytical and numerical solutions.     

Nonlinear theory of magnetohydrodynamic flows of a compressible fluid in the shallow water approximation

Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describes static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the height of the free boundary on the density of the fluid. Self-similar continuous and discontinuous solutions are obtained for a system on a slope, and a solution is found to the initial discontinuity decay problem in this case.     

An unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations

Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with nonlinear numerical instabilities. One approach for controlling the discrete divergence is through a so-called constrained transport method, which is based on first predicting a magnetic field through a standard finite volume solver, and then correcting this field through the appropriate use of a magnetic vector potential. In this work we develop a constrained transport method for the 3D ideal MHD equations that is based on a high-resolution wave propagation scheme. Our proposed scheme is the 3D extension of the 2D scheme developed by Rossmanith [J.A. Rossmanith, An unstaggered, high-resolution constrained transport method for magnetohydrodynamic flows, SIAM J. Sci. Comput. 28 (2006) 1766], and is based on the high-resolution wave propagation method of Langseth and LeVeque [J.O. Langseth, R.J. LeVeque, A wave propagation method for threedimensional hyperbolic conservation laws, J. Comput. Phys. 165 (2000) 126]. In particular, in our extension we take great care to maintain the three most important properties of the 2D scheme: (1) all quantities, including all components of the magnetic field and magnetic potential, are treated as cell-centered; (2) we develop a high-resolution wave propagation scheme for evolving the magnetic potential; and (3) we develop a wave limiting approach that is applied during the vector potential evolution, which controls unphysical oscillations in the magnetic field. One of the key numerical difficulties that is novel to 3D is that the transport equation that must be solved for the magnetic vector potential is only weakly hyperbolic. In presenting our numerical algorithm we describe how to numerically handle this problem of weak hyperbolicity, as well as how to choose an appropriate gauge condition. The resulting scheme is applied to several numerical test cases.     

Computational Model of Thermal‐Fluid Flow in a Radio‐Frequency Plasma Torch

The paper aims to clarify the modelling results concerning the heat transfer and fluid flow in a radio‐frequency plasma torch with argon at atmospheric pressure. Fluid numerical simulation requires the coupling of magnetohydrodynamics (MHD) and thermal phenomena. This model combines Navier–Stokes equations with the Maxwell's equations for compressible fluid and electromagnetic phenomena successively. A numerical formulation based on the finite element method is used. In this study, fluid flow and temperature equations are simultaneously solved (direct method, instead of using the indirect method) using a finite elements method (FEM) for optically thin argon plasmas under the assumptions of local thermodynamic equilibrium (LTE) and laminar flow. Appropriate boundary conditions are given, and nonlinear parameters such as the thermal and electrical conductivity of the gas and input power used in the simulation are detailed. We have found that the source of power is located on the torch wall in this type of inductive discharge. The center can be heated by conduction and convection via electromagnetic phenomena (power loss and Lorentz force). (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

采用非交错网格压力修正法计算不可压及可压亚、跨、超音速流动

采用非交错网格压力修正法计算不可压及可压亚、跨、超音速流动朱斌，蔡睿贤，蒋洪德（中国科学院工程热物理研究所北京１０００８０）关键词：压力修正法，亚、跨、超音速流动一、前言源于计算不可压流动的压力修正方法，由于具有计算时间短及不受马赫数限制的优点，近年...     

Higgs interchange and bound states of superheavy fermions

Hypothetical superheavy fourth-generation fermions with a very small coupling with the rest of the Standard Model can give rise to long enough lived bound states. The production and the detection of these bound states would be experimentally feasible at the LHC. Extending, in the present study, the analysis of other authors, a semirelativistic wave equation is solved using an accurate numerical method to determine the binding energies of these possible superheavy fermion-bound states. The interaction given by the Yukawa potential of the Higgs boson exchange is considered; the corresponding relativistic corrections are calculated by means of a model based on the covariance properties of the Hamiltonian. We study the effects given by the Coulomb force. Moreover, we calculate the contributions given by the Coulombic and confining terms of the strong interaction in the case of superheavy quark bound states. The results of the model are critically analysed.     

Treatment of Confinement in the Faddeev Approach to Three-Quark Problems

We present a method to solve the Faddeev integral equations of the semirelativistic constituent quark model. In such a model the quark–quark interaction is modeled by an infinitely rising confining potential and the kinetic energy is taken in a relativistic form. We solve the integral equations in Coulomb–Sturmian basis. This basis facilitates an exact treatment of the confining potentials.     

SSS程序在电磁内爆中的数值模拟

 对SSS程序的边界条件进行修改,将修改后的SSS程序用于固体套筒内爆实验的数值模拟,并与现有的一维磁流体力学程序的计算结果进行比较,对比结果表明,对SSS程序的改造是成功的,也可以预见将SSS程序改造成一维磁流体力学计算程序是可行的。     

Evaluation of the vibrational modes of the human skull as it relates to bone-conducted sound

Analytic and numerical models are used to study bone-conducted sound and how it relates to the vibrational modes of the human skull. The analytic model is based on the solution to the acoustic and elastic wave equations and the constraining boundary conditions for a fluid-filled elastic sphere. Both models predict that most of the acoustic energy of bone-conducted sound exists in the form of surface wave vibrations at the interface between two acoustic media rather than in the bone or cranial chamber. These surface waves have phase speeds much slower than the bulk sound speed for bone. The analytic model, based on spherical elastic shells, predicts a phase speed of 775 m/s and the first resonance frequency at 1500 Hz while the numerical solution yields approximate phase speeds of 450 m/s and provides a visual display of the surface waves and diffraction effects.     

Reaction-diffusion fronts in periodically layered media

We compute the effective wavefront speeds of reaction-diffusion equations in periodically layered media with coefficients that have small-amplitude oscillations around a uniform mean state. We compare them with the corresponding wavefront speeds in the uniform state. We analyze a one-dimensional model where wave propagation is along the layering direction of the medium and a two-dimensional shear flow model where wave propagation is othogonal to the layering direction. We find that the effective wave speed is smaller in the one-dimensional model and is larger in the two-dimensional model for both bistable cubic and quadratic nonlinearities of the Kolmogorov-Petrovskii-Piskunov form. We derive approximate expressions for the wave speeds in the bistable case.Dedicated to Jerry Percus on the occasion of his 65th birthday.     

Wave Instabilities of a Collisionless Plasma in Fluid Approximation

Wave properties and instabilities in a magnetized, anisotropic, collisionless, rarefied hot plasma in fluid approx‐imation are studied, using the 16‐moments set of the transport equations obtained from the Vlasov equations. These equations differ from the CGL‐MHD fluid model (single fluid equations by Chew, Goldberger, and Low [5,9]) by including two anisotropic heat flux evolution equations, where the fluxes invalidate the double polytropic CGL laws. We derived the general dispersion relation for linear compressible wave modes. Besides the classic incompressible fire hose modes there appear four types of compressible wave modes: two fast and slow mirror modes – strongly modified compared to the CGL model – and two thermal modes. In the presence of initial heat fluxes along the magnetic field the wave properties become different for the waves running forward and backward with respect to the magnetic field. The well known discrepancies between the results of the CGL‐MHD fluid model and the kinetic theory are now removed: i) The mirror slow mode instability criterion is now the same as that in the kinetic theory. ii) Similarly, in kinetic studies there appear two kinds of fire hose instabilities ‐ incompressible and compressible ones. These two instabilities can arise for the same plasma parameters, and the instability of the new compressible oblique fire hose modes can become dominant. The compressible fire hose instability is the result of the resonance coupling of three retrograde modes ‐ two thermal modes and a fast mirror mode. The results can be applied to the theory of solar and stellar coronal and wind models (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)