再论磁流体共面黎曼问题

本文证明一般磁流体共面间断D可分解为(这里有图片19980204-119.GIF),符号上的箭头表示各分解产物的传播方向,J为接触间断,W_f包含快激波、快简单波、1→3型中间激波及第一类快合成波,W_s包含慢激波、慢简单波、2→4型中间激波及第一类慢合成波.本文同时对某些特殊间断的分解作了分析.      

磁流体斜激波的碰撞

讨论了磁流体斜激波之间的碰撞及其与接触间断的相互作用规律,主要结论如下:(1)两个快激波碰撞后交换位置,同时出现一接触间断和一慢稀疏波对。(2)两个慢激波碰撞后交换位置且强度减弱,同时出现一接触间断和一块激波对。(3)一前向快激波与一后向慢激波碰撞后交换位置,快激波强度增加,慢激波强度减弱,同时出现一后向快激波、一负接触间断和一前向慢稀疏波。(4)一前向快激波与一正(负)接触间断相互作用后交换位置,快激波减弱,同时出现一后向快稀疏波(快激波)、一后向慢激波和一前向慢激波(慢稀疏波).(5)一前向慢激波与一正(负)接触间断相互作用后交换位置,慢激波减弱,同时出现一后向慢稀疏波(慢激波)和一快稀疏波(快激波)对。      

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.     

磁流体中间激波的相互作用

本文讨论磁流体中间激波的相互作用规律．主要结论：中间激波汇合的产物为后向快简单波、后向慢简单波或慢激波、接触间断、前向慢激波和前向快激波，其中后向波成份和接触间断很弱．当左（右）激波较强时，中国激波碰撞产物为后（前）向快激波、后（前）向慢简单波或慢激波、负（正）切向间断、前（后）向慢简单波和前（后）向快激波．     

磁流体斜激波的汇合

本文讨论磁流体快、慢激波的汇合作用规律,主要结论如下:(1)两个前向快激波汇合之后,形成一更强的前向快激波,尾随一前向慢稀疏波、一正接触间断(后侧密度大于前侧)、一后向慢激波和一后向快稀疏浚。(2)两个前向慢激波汇合之后,形成一更强的前向慢激波,尾随一正接触间断、一后向慢稀疏波和一后向快激波2在前向慢激波前方出现一前向快波,它或为稀疏浚(中、小激波角情况),或为激波(大激波角情况).(3)前向快激波会追上前向慢激波而发生汇合,之后互换位置且强度减弱,尾随一正接触间断和一后向稀疏波对。      

r型网格自适应在间断Galerkin有限元激波捕捉中的应用

间断Galerkin（DG）有限元方法因计算精度高、适用于非结构网格等特点得到广泛研究和应用，其在数值模拟包含强间断流场时存在残差收敛性和计算鲁棒性差问题，均匀分布的网格加剧这一问题并影响激波分辨率。针对该问题，发展了r型网格自适应方法，实现间断Galerkin有限元数值模拟过程中网格自适应加密。基于网格点归一化的压力值作为r型网格自适应中网格点移动驱动力的重要权值，并将网格自适应后的网格点位移变化量与网格点之间的初始位移之比作为驱动力的另一重要权值，实现网格沿激波方向各向异性自适应加密，并且激波附近网格点的相邻网格点同步向激波方向移动。发展了适合间断Galerkin有限元方法的Venkatakrishnan限制器。并列NACA0012翼型超声速算例及三维并列圆柱相互干扰算例结果表明:基于r型网格自适应的间断Galerkin有限元方法能够清晰锐利捕捉激波，提高模拟精度，具有良好的收敛性和鲁棒性。      

一种确定模拟的行星际MHD激波局地参数的新方法

简要阐述了分析模拟的行星际磁流体力学（MHD）激波的局部性质时，采用无厚度局部平面激波这一假设的合理性，说明了在激波未扰动区域（激波上游），物理量在几个小时内的变化很小这一事实，利用平面激波的分析方法，提出了分析模拟的行星际MHD激波的新方法，包括激波位置的确定，上下游状态参数的选择，激波局部参数的计算以及激波的分类，最后应用这种方法对一个二维的MHD模拟结果进行了分析。结果证实了过去文献关于磁流体力学混合激波空间连接和时间演化的链式规则，而且说明位于太阳赤道附近的慢激波和中间激波最终会发展为快激波。     

液压管道脉动流问题的适定性与激波

本文首先讨论脉动流的撞击液压问题解的可微性。在此基础上,对激波的形成及其传播状态进行数学上的分析,并给出激波应满足的间断连结条件和间断稳定性条件。     

耀斑激波的相互作用

采用一维磁流体力学模型和激波装配法，分析两个相继出现的耀斑激波的相互作用.前导激波下游的稀疏波显著改变后随激波的特性，并在它的下游产生强后向快激波.两耀斑激波汇合后将在下游形成密度比约为1.5的接触间断.     

卷积自编码器在非定常可压缩流动降阶模型中的适用性

为有效降低使用计算流体力学(CFD)方法的设计成本和周期，降阶模型(ROM)得到广泛关注。对于复杂的可压缩流动，使用本征正交分解(POD)等线性方法进行流场降维，需要大量模态才能保证流场重建的精度，采用非线性降维方法能够有效减少所需模态数。卷积自编码器(CAE)是一种由编码器和解码器组成的神经网络，能够实现数据降维和重构，可看作是POD方法的非线性拓展。采用CAE进行流场数据的非线性降维，同时使用长短期记忆(LSTM)神经网络进行流场状态的时间演化。对于不可压缩问题，使用自编码器和LSTM结合进行流场重构的方法已有较多研究，选择一维Sod激波管、Shu-Osher问题、二维黎曼问题和开尔文-亥姆霍兹不稳定性算例，测试该ROM对非定常可压缩流动的有效性，同时基于POD方法，在不同模态数下构造Sod激波管和黎曼问题的ROM作为对比。结果表明：对于非定常可压缩流动，CAE-LSTM方法能够在使用较少自由变量数的前提下获得较高的重构和预测精度。     

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.     

Magnetic reconnection coupled with heat conduction

Magnetic reconnection coupled with anisotropic nonlinear heat conduction is studied by using an MHD simulation. Due to the heat conduction effect, the adiabatic slow-mode MHD shocks emanating from the neutral point are dissociated into conduction fronts and isothermal shocks.     

A transient MHD model applicable for the source of solar cosmic ray acceleration

A two-dimensional, time-dependent magnetohydrodynamic (MHD) model is used to describe the possible mechanisms for the source of solar cosmic ray acceleration following a solar flare. The hypothesis is based on the propagation of fast mode MHD shocks following a sudden release of energy. This model has already been used with some success for simulation of some major features of type II shocks and white light coronal transients. In this presentation, we have studied the effects of initial magnetic topology and strength on the formation of MHD shocks. We consider the plasma beta (thermal pressure/magnetic pressure) as a measure of the $\text{initial}$, relative strength of the field. During dynamic mass motion, the Alfvén Mach number is the more appropriate measure of the magnetic field's ability to control the outward motion. We suggest that this model (computed self-consistently) provides the shock wave and the disturbed mass motion behind it as likely sources for solar cosmic ray acceleration.     

Some characteristics of propagation of flare- or CME-associated interplanetary shock waves

Many interplanetary shock waves have a fast mode MHD wave Mach number between one and two and the ambient solar wind plasma and magnetic field are known to fluctuate. Therefore a weak, fast, MHD interplanetary shock wave propagating into a fluctuating solar wind region or into a solar wind stream will be expected to vary its strength.It is possible that an interplanetary shock wave, upon entering such a region will weaken its strength and degenerate into a fast-mode MHD wave. It is even possible that the shock may dissipate and disappear.A model for the propagation of a solar flare - or CME (Coronal Mass Ejections) - associated interplanetary shock wave is given. A physical mechanism is described to calculate the probability that a weak shock which enters a turbulent solar wind region will degenerate into a MHD wave. That is, the shock would disappear as an entropy-generate entity. This model also suggests that most interplanetary shock waves cannot propagate continuously with a smooth shock surface. It is suggested that the surface of an interplanetary shock will be highly distorted and that parts of the shock surface can degenerate into MHD waves or even disappear during its global propagation through interplanetary space. A few observations to support this model will be briefly described.Finally, this model of shock propagation also applies to corotating shocks. As corotating shocks propagate into fluctuating ambient solar wind regions, shocks may degenerate into waves or disappear.     

耀斑激波传播的数值研究

采用一维磁流体力学模型和激波装配法,分析耀斑激波在行星际空间的传播特性和激波下游区的波动结构,并就激波装配法和激波捕捉法的模拟结果的精度和可靠性进行比较.      

Application of ADER Scheme in MHD Simulation

The Arbitrary accuracy Derivatives Riemann problem method(ADER) scheme is a new high order numerical scheme based on the concept of finite volume integration,and it is very easy to be extended up to any order of space and time accuracy by using a Taylor time expansion at the cell interface position.So far the approach has been applied successfully to flow mechanics problems.Our objective here is to carry out the extension of multidimensional ADER schemes to multidimensional MHD systems of conservation laws by calculating several MHD problems in one and two dimensions: (ⅰ) Brio-Wu shock tube problem,(ⅱ) Dai-Woodward shock tube problem,(ⅲ) Orszag-Tang MHD vortex problem.The numerical results prove that the ADER scheme possesses the ability to solve MHD problem,remains high order accuracy both in space and time,keeps precise in capturing the shock.Meanwhile,the compared tests show that the ADER scheme can restrain the oscillation and obtain the high order non-oscillatory result.     

Cone model-based SEP event calculations for applications to multipoint observations

The problem of modeling solar energetic particle (SEP) events is important to both space weather research and forecasting, and yet it has seen relatively little progress. Most important SEP events are associated with coronal mass ejections (CMEs) that drive coronal and interplanetary shocks. These shocks can continuously produce accelerated particles from the ambient medium to well beyond 1 AU. This paper describes an effort to model real SEP events using a Center for Integrated Space weather Modeling (CISM) MHD solar wind simulation including a cone model of CMEs to initiate the related shocks. In addition to providing observation-inspired shock geometry and characteristics, this MHD simulation describes the time-dependent observer field line connections to the shock source. As a first approximation, we assume a shock jump-parameterized source strength and spectrum, and that scatter-free transport occurs outside of the shock source, thus emphasizing the role the shock evolution plays in determining the modeled SEP event profile. Three halo CME events on May 12, 1997, November 4, 1997 and December 13, 2006 are used to test the modeling approach. While challenges arise in the identification and characterization of the shocks in the MHD model results, this approach illustrates the importance to SEP event modeling of globally simulating the underlying heliospheric event. The results also suggest the potential utility of such a model for forcasting and for interpretation of separated multipoint measurements such as those expected from the STEREO mission.     

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.