Lax-Friderichs格式在磁流体模拟中的改进和应用

磁流体数值模拟是空间物理研究的重要手段.采用具有TVD（Total Variation Diminishing）特性的Lax-Friderichs差分格式求解了GLM-MHD（Generalized Lagrange Multiplier-Magnetohydrodynamics）方程.为降低格式的数值耗散,引入耗散修正系数对算法的通量计算过程进行改进.二维Rotor算例和磁云-电流片相互作用算例的模拟结果表明,GLM-MHD方法可以有效控制磁场散度误差,相对于泊松校正法可以节省一半以上的计算时间.在不破坏格式稳定性基础上,耗散修正系数有效降低了算法的数值耗散.      

A CLASS OF TWO-STEP TVD MACCORMACK TYPE NUMERICAL SCHEME FOR MHD EQUATIONS

In this paper, a new numerical scheme of Total Variation Diminishing (TVD) Mac-Cormack type for MagnetoHydroDynamic (MHD) equations is proposed by taklng into account of the characteristics such as convergence, stability, resolution. This new scheme is established by solving the MHD equations with a TVD modified MacCormack scheme for the purpose of developing a scheme of quick convergence as well as of TVD property. To show the validation, simplicity and practicability of the scheme for modelling MHD problems, a self-similar Cauchy problem with the discontinuous initial data consisting of constant states, and the collision of two fast MHD shocks, and two-dimensional Orszag and Tang‘s MHD vortex problem are discussed with the numerical results conforming to the existing results obtained by the Roe type TVD, the high-order Godunov scheme, and Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical tests show that this two-step TVD MacCormack numerical scheme for MHD system is of robust operation in the presence of very strong waves, thin shock fronts, thin contact and slip surface discontinuities.     

背景太阳风数值模拟的熵守恒格式

背景太阳风研究是根据行星际扰动传播情况预测空间天气状况的基础,磁流体（MHD）模拟是背景太阳风研究的重要手段.采用一种新的数值计算方式,利用Ideal GLM-MHD将计算过程中产生的磁场散度以c_h的速度向计算区域外传播,从而消去磁场散度;重构部分使用受约束的最小二乘法,将磁场散度作为约束条件添加到重构中,进一步对重构后的磁场梯度进行修正;通量计算采用满足热力学第二定律的熵守恒格式,该格式能够确保在计算过程中熵不增,保证数值稳定.研究结果表明,该方法应用于太阳风数值模拟的求解得到了更加稳定的结果.      

电阻磁流体力学模拟的CESE方法

利用时空守恒元解元方法(CESE)和两种改进方法, 即库朗数不敏感(CNIS)方法与高阶CESE方法求解2.5维电阻磁流体力学(resistive MHD)方程组, 模拟了两个单电流片重联问题. 并考察了上述三种方法所得结果的磁场散度. 分析表明, 三种方法所得到的磁场位形基本没有差别, 但在磁场散度上存在一定差异, 相比另外两种方法, CNIS方法在控制磁场散度方面表现得更好.      

改进的二维三阶半离散中心迎风格式

对二维三阶半离散中心迎风格式中的权函数给出了简化改进. 在保持格式精度的基础上, 改进后的权函数在二维情况下具有更加简单直接的结构而且严格非负. 该改进方法得到的格式仍然具有半离散中心迎风格式的优点, 同时保持了重构函数的非振性. 时间离散采用保持强稳定性的三阶Runge-Kutta方法, 并利用四阶Lax-Wendroff (L-W) 格式计算磁流体算例中的磁场散度. 用该修正格式计算了二维磁流体数值算例, 得到高精度无振荡的结果, 验证了此方法的有效性.      

太阳表面水平运动驱动的磁圈与开放磁场重联的模拟研究

太阳大气的诸多观测事件(如耀斑、喷流等)均被归因于磁重联产生的能量转换. 近年来, 关于太阳风起源, 有研究提出了磁重联使闭合磁圈开放为太阳风供应物质的新模式. 在该模式中, 闭合磁圈被光球超米粒组织对流携带, 向超米粒边界运动, 与位于边界的开放磁场相碰撞进而发生磁重联. 该模式中磁重联的驱动及其效应是本文的研究目标. 磁流体力学(MHD)数值模拟是研究太阳大气磁重联物理过程的重要途径. 本文建立了一个二维MHD数值模型, 结合太阳大气温度和密度的分层分布, 在超米粒组织尺度上模拟了水平流动驱动的闭合磁圈与开放磁场的重联过程. 通过对模拟结果的定量分析, 认为磁重联确实能够将闭合磁圈的物质释放, 进而供应给新的开放磁结构并产生向上流动. 该结果为进一步模拟研究太阳风初始外流奠定了基础.      

一类TVD型组合差分方法及其在磁流体数值计算中的应用

根据太阳风数值模拟的特点，考虑到算法的质量（收敛速度、稳定性、精度等），结合磁流体数值计算的特性，对三维球坐标磁流体动力学（MHD）方程组中的流体部分采用一种修正Lax-Friedrichs差分法而对磁场部分采用MacComack格式，发展了一类快捷的具有TVD特性的组合数值新方法，作为格式的检验，在一维情况下，将其与PPM格式进行了比较，对一维快慢磁流体激波问题得到了与PPM格式精度相同的结果，然后将其诮到定态太阳风的数值模拟上，在不同等离子体β情形下，可得到理想的太阳风定态结构，为今后将此数值模式应用到具有复杂磁场位型或三维直实太阳风暴的数值模拟研究奠定了基础。     

地球弓激波的三维模拟

利用磁流体动力学(MHD)全球模拟结果,根据弓激波的跃变特性确定出弓激波位置,建立了一个新的综合考虑了快磁声马赫数、太阳风动压、行星际磁场强度以及磁层顶曲率半径的弓激波三维位型模型.将新模型与以往模型的模拟结果进行比较发现,新的弓激波全球模型结果可靠,解决了部分现有模型不能描述弓激波三维位型的问题.研究结果表明,在行星际磁场北向时,随着快磁声马赫数的增大,弓激波日下点距离减小,但是在行星际磁场南向时,快磁声马赫数的变化对弓激波日下点距离影响不大;弓激波位型在赤道面与子午面上存在明显的不对称性,而且随着行星际磁场的转向,这种非对称性也会发生相应改变;行星际磁场南向,B_z值较小时,子午面内弓激波位型已经不是简单的抛物线,出现了明显的类似于极尖区磁层顶的凹陷变化区.      

空间等离子体压力各向异性对磁场重联的影响

基于二维时变可压缩磁流体动力学模拟,数值研究了等离子体压力各向异性对磁场重联的影响,发现一个小的压力各向异性(P_⊥=1.02P_//)即可大大加速磁场重联的发展,这可能是由于磁镜不稳定性与撕裂模不稳定性共同起作用.在P_⊥P_//的情况下,撕裂模受到抑制,电流片中不能形成大型磁岛.      

MHD simulations and astrophysical applications

Magnetohydrodynamics is an adequate theoretical framework to study a large variety of astrophysical flows. The generation of magnetic fields by dynamo mechanisms, the development of turbulent flows or the topological change of magnetic fields by reconnection, are just a few examples. First, we describe the basic features of the MHD framework. Second, we make a brief introduction to the physical processes listed above, namely: dynamo action, MHD turbulence, and magnetic reconnection. Finally, we show the results arising from numerical simulations of these processes, for a number of configurations of astrophysical interest.     

磁流体力学激波的特征速度

根据磁流体力学间断面的守恒条件与磁流体力学单波方程的相似性,引入了一个称为磁流体力学激波特征速度的物理量,它是激波在波前后两侧介质中传播速度的几何平均值,当激波很弱时,它趋近于磁流体力学波的速度。本文导出一组以此特征速度为强度参数的激波跃变公式,形式上与单波的公式组非常相像,从而简化了激波跃变量的计算。其中密度跃变公式本身解析地证明:磁流体力学激波与磁流体力学波传播速度之间的关系是由激波是压缩波这一特性直接决定的。      

Magnetic reconnection in solar flares and corresponding radio bursts

The 2D MHD model of the flare magnetic reconnection shows that a reconnection activity, changes of the magnetic field topology and generation of waves are connected. It is found that after the phase of a quasi-stationary reconnection in the extended current sheet above the flare arcade the tearing mode instability produces the plasmoids which then can interact and generate MHD waves. Results of particle-in-cell simulations of the tearing processes, which accelerate electrons, are mentioned. Then all these processes are discussed from the point of view of possible radio emissions. While shocks can contribute to the type II radio burst, the superthermal electrons trapped in plasmoids can generate so called drifting pulsating structures. Furthermore, regions with the MHD turbulence may manifest themselves as the lace or dm-spike bursts.     

Numerical simulation of reconnection in an emerging magnetic flux region

The resistive MHD equations are numerically solved in two dimensions for an initial-boundary-value problem which simulates reconnection between an emerging magnetic flux region and an overlying coronal magnetic field. The solution involves both ideal-MHD and resistive-MHD processes, and the solution shows an evolution which is remarkably suggestive of the preflare, impulsive, and main phases of the flare-cycle.     

Interaction of shocks with a current sheet and reconnection in the solar corona

Interaction of shocks with a current sheet is investigated within a 2D MHD model based on an improved FCT numerical scheme. Basic parameters of the problem are chosen to correspond to situations in the solar corona with low plasma β and moderate shock strength. Slow and fast MHD shocks are introduced with shock normal parallel to magnetic field lines. The interaction with the current sheet causes distortion of the shock front and this distorts the magnetic field lines and generates electric current. Large current densities are generated especially when the fast MHD shock becomes the intermediate MHD shock at the current sheet. Then peak values of the current density are about 3–4 times larger than the initial undisturbed values in the current sheet.     

Global MHD simulations for southward IMF: a pair of wings in the flanks

Global magnetohydrodynamic (MHD) simulations have shown that for southward interplanetary magnetic field nightside reconnection takes place only in a limited spatial scale in the cross-tail direction. Between the end of the nightside reconnection line and the flank magnetopause are regions of closed magnetic field lines which move relatively slowly tailward, compared with the magnetosheath flow on the far side and the jet flow produced by nightside reconnection on the side closer to the midnight. The magetosphere appears to have a pair of extended wings on the nightside. Further refinement of the simulations shows that the wings are not produced by the numerical effects. Similar features have been observed previously and also shown in different simulation models. The existence of the wings in the simulations indicates that the solar wind momentum is transferred to the closed magnetosphere if the simulations are relevant to reality.     

Two-spacecraft observations of reconnection at the magnetopause: Model results and data comparison

We revisit an example of “quasi-steady” magnetic reconnection at the dayside magnetopause on February 11, 1998, observed by Equator-S and Geotail at the dawnside magnetopause. Phan et al. [Phan, T.D. et al., 2000. Extended magnetic reconnection at the Earth’s magnetopause from detection of bi-directional jets. Nature 404, 848–850.] reported oppositely directed jets at these spacecrafts and inferred a length of the reconnection line of about 38R_E. Pinnock et al. [Pinnock, M., Chisham, G., Coleman, I.J., Freeman, M.P., Hairston, M., Villain, J.-P., 2003. The location and rate of dayside reconnection during an interval of southward interplanetary magnetic field. Ann. Geophys. 21, 1467–1482.] used measurements from SuperDARN radars to show that the reconnection electric field was variable. Here we complement this work by obtaining snapshots of the reconnection electric field from the in situ observations. To do this, we apply a reconstruction method based on a model of compressible Petschek-type magnetic reconnection. This independent method uses magnetic field observations as input data to calculate the reconnection electric field. We obtain average values of E_rec in the range of 0.4–2.4 mV/m. Further we infer a distance perpendicular to the reconnection line of 0.4–0.6R_E. The model results are compared with the two studies mentioned above. It thus appears that while the transfer of momentum for this event is indeed large-scale, the actual rate depends on the time it is measured.     

基于简单WENO-间断Galerkin的Euler方程自适应计算

为了得到Euler方程的高精度、高分辨率数值解,介绍了间断Galerkin方法、三角形单元上简单WENO限制器的基本原理以及基于自适应网格加密的激波捕捉方法。将简单WENO限制器-间断Galerkin方法应用到曲边四边形单元上,通过单元边界上高斯积分点的坐标来搜索相邻单元从而得到相邻单元的单元编号,实现了基于“问题单元”的局部网格加密自适应计算。对若干典型问题进行编程计算,结果表明,简单WENO限制器可以应用到曲边四边形单元上,且可适用于局部网格加密时具有“悬挂节点”的非结构网格上的激波捕捉。      

多重激波的数值模拟研究

本文用一维混合粒子模拟Code研究了包括中间激波在内的多重激波.模拟了四种情形,可以分为两类:(1)由快激波和中间激波构成的两重激波,(2)快激波、中间激波和慢激波构成的三重激波.结果表明:多重激波是不稳定的,它趋向于发展成磁流体旋转间断和MHD波,左旋圆偏振波逐渐在上游区内发展起来.文章对导致多重激波不稳定性的可能原因进行了简单的讨论.     

Effect of the Interplanetary Electric Field on the Magnetopause From Global MHD Simulations

The north-south component B_z of the Interplanetary Magnetic Field (IMF) and solar wind dynamic pressure P_d are generally treated as the two main factors in the solar wind that determine the geometry of the magnetosphere. By using the 3D global MHD simulations, we investigate the effect of the Interplanetary Electric Field (IEF) on the size and shape of magnetopause quantitatively. Our numerical experiments confirm that the geometry of the magnetopause are mainly determined by P_dB_z, as expected. However, the dawn-dusk IEFs have great impact on the magnetopause erosion because of the magnetic reconnection, thus affecting the size and shape of the magnetopause. Higher solar wind speed with the same B_z will lead to bigger dawn-dusk IEFs, which means the higher reconnection rate, and then results in more magnetic flux removal from the dayside. Consequently, the dayside magnetopause moves inward and flank magnetopause moves outward.      

简单强磁云的结构特征

本文讨论了1980年12月19日和3月19日两次无大型共转流相联系的行星际简单强磁云事件的磁流体动力学结构特征。此两磁云均以高温、高密度的湍流结构为先导,接着是低温、低密度,磁场很强且倾角单调旋转的磁云本体,后随另一密度稍高的结构。磁云本体内Alfvén波速及磁压对动能密度和热压的比值异常地增高,有利于磁云后的扰动迅速穿越磁云向前传播并向前边界集结。磁云边界上的巨大磁压梯度力及MHD波动在高密度结构内的耗散有可能对磁云前的太阳风进行加速和加热,形成双锯齿流速图象。简单磁云的结构很象典型的日冕质量抛射事件。此外,还简要地分析了磁云引起的地磁暴和宇宙线下降。