NND格式在多维理想磁流体方程组中的应用

采用修正的四步Runge-Kutta方法求解三维一般曲线坐标系下的理想磁流体方程组,为克服数值振荡,加特征型NND格式进行后处理.特征型NND格式推广到求解三维磁流体(MHD)问题需要知道雅可比通量的左右特征矩阵,在具体计算时需要克服矩阵的奇性.本文用三维程序采用推广的特征NND格式计算了一维MHD激波管和二维(MHD)喷管流动,计算结果表明,特征NND格式保持了TVD格式高精度的优点,又具有计算简单的特点,在包括强弱间断等复杂波系的定常和非定常MHD流场数值模拟中是成功的.     

Modelling of Solar Wind, CME Initiation and CME Propagation

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 background solar wind and of the CME initiation parameters, such as the initial magnetic polarity, on the evolution and on the geo-effectiveness of CMEs. First, three different solar wind models are reconstructed using the same numerical grid and the same numerical scheme. Then, different CME initiation models are considered: Magnetic foot point shearing and magnetic flux emergence. For the fast CME evolution studies, a very simple CME model is considered: 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 thus, the geo-effectiveness).     

Numerical Magnetohydrodynamic (MHD) Modeling of Coronal Mass Ejections (CMEs)

The Coronal Mass Ejection (CME) is arguably the most important discovery of solar eruptive phenomena in the 20th century. It is now also recognized that CMEs have great impact on the Earth's environment by inducing geomagnetic storms. Thus, development of simulation models to understand the physical mechanisms of CME initiation and propagation has become a challenge in the solar MHD community. In this paper we shall summarize chronologically the development of the theoretical analyses, and the successes and failures of the numerical magnetohydrodynamic (MHD) simulations of coronal mass ejections (CMEs) during the past two decades. The chronological development of numerical simulation models and the evolution of the numerical methods to treat this class of problems are presented. The most appropriate way to model CMEs is to have (i) a realistic pre-event coronal atmosphere, and (ii) realistic driving mechanisms. Details of the progress and assessment of the theoretical and modeling efforts for the understanding of the physics of the CME initiation and propagation will be presented, and the numerical methods to construct these simulation models will be discussed.     

Numerical Simulation of 2D Supersonic Magnetohydrodynamic Channel and Study on Hall Effect

In this research effort,numerical simulation of two-dimensional magnetohydrodynamic(MHD) channel is performed and Hall effect is studied.The computational model consists of the Navier-Stokes(N-S) equations coupled with electrical-magnetic source terms,Maxwell equations and the generalized Ohm’s law.Boundary conditions for the electrical potential equation considering Hall effect are derived.To start with,the MHD channel with single-pair electrodes is studied and flow of the electric current is in accordance with physical principle.Then the MHD channel with five-pair electrodes is numerically simulated.The results show that the electrical current concentrates on the downstream of the anode and the upstream of the cathode due to Hall effect,and the flow field becomes asymmetrical.At the current value of the magnetic interaction parameter,the electrical-magnetic force affects the flow remarkably,decreasing the outlet Mach number and increasing the outlet pressure;what’s more,the flow structure in the channel becomes extremely complex.Performances of MHD channels with continual electrodes and segmented electrodes are compared.The results show that performance of the MHD channel with segmented electrodes is better than that with continual electrodes with the increase of Hall parameter.     

基于电子束电离的磁流体力学进气道流动控制数值模拟

采用基于电子束电离的磁流体力学(MHD)控制系统,对高超声速流场附面层,以及非设计状态下的高超声速进气道流场的磁流体控制进行了深入研究.控制方程为低磁雷诺数Navier-Stokes方程,采用等离子体动力学模型与电子束模型模拟空气电离过程.研究结果表明:①电子束电离能有效提高流场的电导率,增强磁场对流场的控制效率;②基于电子束诱导电离的MHD控制系统能有效地控制高超声速流场的附面层,但其控制效率跟电子束能量大小相关;③基于电子束诱导电离的MHD控制系统能有效地改变非设计状态下高超声速飞行器的斜激波结构,使进气道重新满足Shock-on-lip(SOL)条件,但进气道的总压恢复系数以及流量将会降低.      

太阳风磁帆推进性能数值研究

利用考虑行星际磁场作用的磁流体动力学模型，建立了磁帆三维数值模拟方法，对计算方法的可靠性进行了验证，发现了线圈尾部的磁重联现象，研究了太阳风来流速度、等离子体离子数密度以及攻角对磁帆推进性能的影响。得出以下结论：不同速度、不同离子数密度的太阳风主要通过改变z方向电流的大小改变洛伦兹力，进而影响磁帆的推进性能：太阳风离子数密度恒定时，随着来流速度由30 km/s逐渐增大至75 km/s,z方向电流最大值由4 205 A/m²增至14 709 A/m²，磁帆所受推力由3.39 N增至13.40 N；太阳风来流速度恒定时，随着离子数密度由1.8×10¹⁹ m^-3增大至4.5×10¹⁹ m^-3,z方向电流最大值由6 039 A/m²增至10 585 A/m²，磁帆所受推力由6.62 N增至12.27 N。磁帆攻角变化，主要通过磁场构型的变化影响磁帆推进性能：攻角为0°和90°时的磁层半径分别为0.14 m和0.18 m，...     

Numerical 3-D time-dependent MHD model of the solar wind

A fully three-dimensional, time-dependent MHD model of the solar corona and the solar wind is developed. The proposed model is an upgrading of the steady-state model (Usmanov, 1993a,b). A numerical self-consistent solution for 3-D MHD equations is constructed for the region between the solar photosphere and 1.5 AU. The unique features of the proposed model are: (i) uniform coverage and self-consistent treatment of the regions of subsonic/sub-Alfvénic and supersonic/super-Alfvénic flows, (ii) as a background for transients, a steady-state solution for the ambient solar wind is used. The parameters of the initial pulses are prescribed in terms of the near-Sun shock velocities (as inferred from the metric Type II radio burst observations) relative to the preshock steady-state flow parameters.     

非结构网格高超声速化学非平衡MHD流场数值模拟

 在非结构网格上对考虑化学非平衡效应的二维高超声速磁流体绕钝头体流动进行了数值模拟。控制方程由二维理想磁流体动力学（MHD）方程和组元连续方程两部分组成,化学动力学模型为5组元17反应模型。MHD方程空间离散采用AUSM格式,时间推进采用显式5步龙格-库塔格式,并通过弱耦合的方式与化学反应控制方程结合在一起。计算模型为二维钝头体,外加磁场为偶极子场,磁场源位于钝头体内部。在高超声速来流条件下,对有、无磁场干扰,是否考虑化学反应下的4种工况进行了数值计算,得到了满意的结果,并与有限的参考文献进行了对比。结果表明本文发展的方法能准确地模拟考虑化学非平衡效应的高超声速MHD流场。     

三维磁流体动力学管道流动加减速控制数值研究

阐述了磁流体动力学(MHD)控制流场作用机理.在小磁雷诺数条件下,运用数值模拟方法,对不同外加电磁场条件下三维MHD管道流动的流场情况进行研究,得出不同磁场、电场等MHD参数作用下MHD加速器的性能.对MHD加速器的应用前景进行了展望.计算结果显示,电场取6000V/m,磁场为0.92T 情况下,流场的加速性能可达13.46%,并且可以通过减小磁场或增大电场进一步提高加速性能;在仅添加0.92T磁场条件下,速度减速可达16.35%.     

Numerical simulation of magnetohydrodynamic shock propagation in the corona

Recent developments in the field of numerical simulation models for the study of shock wave propagation in the corona are presented. These models are based on gasdynamic (GD) and ideal (that is, dissipationless, except at shocks) magnetohydrodynamic (MHD) theories. The characteristics and physical interpretations of the results derived from these models are discussed in some detail.The most significant physical results obtained to date are provided by the two-dimensional non-planar, time-dependent, MHD numerical simulation model. In this model, the non-linear interaction among the three essential MHD waves, i.e., fast-, slow-, and Alfvén waves are demonstrated. Finally, the physical relevance of these numerical simulation models in relation to observed solar activity is presented.An invited paper presented at STIP Workshop on Shock Waves in the Solar Corona and Interplanetary Space, 15–19 June, 1980, Smolenice, Czechoslovakia.     

A Parallel Adaptive 3D MHD Scheme for Modeling Coronal and Solar Wind Plasma Flows

A parallel adaptive mesh refinement (AMR) scheme is described for solving the governing equations of ideal magnetohydrodynamics (MHD) in three space dimensions. This solution algorithm makes use of modern finite-volume numerical methodology to provide a combination of high solution accuracy and computational robustness. Efficient and scalable implementations of the method have been developed for massively parallel computer architectures and high performance achieved. Numerical results are discussed for a simplified model of the initiation and evolution of coronal mass ejections (CMEs) in the inner heliosphere. The results demonstrate the potential of this numerical tool for enhancing our understanding of coronal and solar wind plasma processes. This revised version was published online in June 2006 with corrections to the Cover Date.     

二维折角管道内超声速流动的多重网格计算

本文应用Euler模型和隐式TVD格式计算了二维折角管道内的超声速流动问题,为了有效地模拟激波和膨胀波系的相互干扰及壁面的反射,本文试将多重网格法和TVD格式结合起来进行数值求解。考虑到目前绝大部分文章采用V-循环多重网格法,我们对多重网格法中的几种多层次循环形式(V-循环、W-循环)进行了比较性的数值计算,旨在从中发现合适的多层次循环求解的形式,以期充分发挥多重网格法在Euler方程求解过程中的效益。同时,本文也是对多重网格法和TVD格式结合求解的一次初步尝试。     

基于HLLC格式的理想MHD方程数值模拟

针对理想MHD(magnetohydrodynamics)方程数值求解困难的问题,基于原始的HLLC (Harten-Lax-Van Leer Contact wave)近似黎曼解方法,发展出一种新的适用于理想MHD问题的通量计算格式。控制方程采用有限体积法离散,时间推进采用隐式的LU-SGS（lower-upper symmetric Gauss-Seidel）格式,并且采用双曲型散度清除技术来抑制磁场散度的累积。通过一维激波管问题的数值模拟表明,HLLC-MHD格式能准确的分辨并捕捉复杂的磁流体力学波系结构,保证数值计算的精度,最大的数值计算误差不超过10%;通过二维的Rotor问题的数值模拟研究表明,HLLC-MHD格式能够应用于多维理想MHD问题的数值模拟,并且能够准确捕捉多维情况下磁流场中的阿尔文波;通过对比有、无散度清除的Rotor问题计算结果表明,双曲型散度清除技术可以将磁场散度峰值从50降低到2,有效抑制高磁场散度区域的散度累积,同时也会将误差传播到低散度区域,并且引起边界处散度的累积,影响计算的稳定性。      

横截面形状对超声速磁流体发生器性能的影响

通过三维数值模拟研究了不同横截面形状的磁流体(MHD)发生器的热、电磁流动特性,发生器入口采用超声速来流条件,旨在应用于磁流体旁路超燃冲压发动机推进系统。数值模拟采用低磁雷诺数下磁流体五方程模型,通过熵条件格式和超松弛迭代(SOR)法联合算法分别求解Navier-Stokes方程组和电势方程。研究表明在电极壁面上电场、电流以及洛伦兹力等电磁场参数呈周期性变化,由于电极端点效应,电磁场参数在电极端点出现周期性的极值,而在管道中心电极端点效应对电流影响并不大,沿着流向电流保持连续变化。对不同管道横截面形状的发生器的数值模拟表明:由于涡电流和二次流效应的影响,形状参数较小的发生器焦耳热较为严重,二次流较弱;而形状参数较大的发生器焦耳热较小,二次流增强。因此,当形状参数α=0.8时可获得较好的焓提取率和电效率。     

烧蚀外形三维粘性流场数值模拟

本文通过求解层流Navier-Stokes方程,数值模拟了三维奶头型烧蚀外形粘性流场。差分格式为Yee和Harten的迎风隐式TVD格式,在空间方向具有二阶精度。计算得到了高质量的激波和合理的流场结构。物面压力分布与实验结果进行比较,符合较好。     

End-to-End Modeling of the Solar Terrestrial System

Traditionally modeling for space science has concentrated on developing simulations for individual components of the solar terrestrial system. In reality these regions are coupled together. This coupling can be as simple as the driving of the magnetosphere – ionosphere – thermosphere system by the solar wind or as a complicated as the feedback of the ionospheric conductivity and currents on the magnetosphere. As part of the CISM project we are beginning a concentrated effort to compressively model the entire system. This approach includes chains of models. In the first chain physics based numerical models are utilized while in the second chain empirical models are coupled together. The first half of this paper discusses the numerical modeling approach by highlighting the coupling of pairs of regions within the system. In the second section we present results from empirical models which are combined to make long term forecasts of conditions in the geospace environment. It is expected that a validated and reliable forecast model for space weather can be obtained by combining the strongest elements of each chain.     

飞机亚跨超绕流的数值模拟研究

本文以Euler方程为数学模型,采用一种高精度的TVD(Total Variation Dimishing)离散格式及一种含近似因式分解的推进迭代方法,求解亚跨超绕流’流场。通过若干算例的试算,证明方法是可行的,可以用来模拟飞机的复杂流场。     

Numerical Simulations of Stellar Winds

We discuss steady-state transonic outflows obtained by direct numerical solution of the hydrodynamic and magnetohydrodynamic equations. We make use of the Versatile Advection Code, a software package for solving systems of (hyperbolic) partial differential equations. We model thermally and magneto-centrifugally driven stellar outflows as generalizations of the well-known Parker and Weber-Davis wind solutions. To obtain steady-state solutions efficiently, we exploit fully implicit time stepping. Wind solutions containing both a 'wind' and a 'dead' zone are presented. We emphasize the boundary conditions imposed at the stellar surface. For axisymmetric wind solutions, we use the knowledge of the flux functions to verify the numerical solutions. This revised version was published online in June 2006 with corrections to the Cover Date.     

基于磁流体控制的高超声速进气道黏性效应

建立引入电磁源项的二维低磁雷诺数磁流体动力学(MHD)方程组,对高超声速二维前体/进气道黏性流场进行了数值模拟.在给出了进气道高于设计马赫数的非设计工况下黏性流场的基本特征基础上,进一步分析了施加MHD控制对进气道黏性效应的影响.结果表明:施加MHD控制可以有效抑制非设计工况下内进气道表面的附面层分离,改善上壁面的热状况,平衡上、下壁面之间的热负担;黏性作用下,进气道流场及性能参数随磁感强度的变化规律与无黏模型计算结果存在较大差别,对磁流体控制的高超声速进气道研究不可忽略黏性的影响.      

一种求解透平叶栅三维流场的高精度TVD格式

本文提出了一种应用三阶精度Chakravarthy-OsherTVD格式求解环形透平叶栅三维定常流场的隐式近似因子分解方法。控制方程为柱座标速度分量表示的任意曲线座标系下的三维欧拉方程。采用Beam-Warming近似分解, 对隐式项进行迎风差分, 得到了时间精度为一阶、空间精度为5点三阶的隐式格式。算例对5点三阶和5点二阶精度的格式进行了比较。表明空间三阶精度隐格式对计算结果没有明显改进, 但收敛残差有较大降低。