日冕物质抛射的数值研究
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摘要
采用理想磁流体力学方程组(MHD)作为太阳大气动力学过程的控制方程组，定性数值模拟日冕物质抛射(CME)现象。
首先，根据不同形式MHD方程组的特点，发展与之相适应的数值算法。首次推广了无振荡、无自由参数格式（NND），把它应用于守恒形式的MHD方程组。主要做了两个方面的工作，第一，为了降低由磁场散度数值上不为零造成的Lorentz力误差，把磁场分解成两部分，一部分为势场，不随时间变化，另一部分为非势场，随时间变化，得到改进的守恒形式MHD方程组。第二，针对MHD方程组的特点 提出了一种适用于守恒型MHD方程组的通量分裂方法，这种方法能够把NND格式有效地应用于MHD方程组。对非守恒形式的MHD方程组，把二阶精度的MacCormackII格式推广应用到三维MHD方程组，首次把无反射投影特征线边界条件应用于三维情况下的内边界，有效地稳定了数值计算。采用这种数值模式进行计算，得到了1998年5月1935卡林顿周稳定和自洽的背景太阳风，这为模拟CME事件打下了基础。
其次，为消除一般两维MHD模式在太阳子午面内极区的几何奇异性，引入两维MHD方程组的新模式，采用这种模式成功地模拟了98年5月2日观测到的子午面内日冕亮度图。
最后数值模拟CME在日冕内的传播特征。CME传播所需的背景结构是采用时间松弛方法计算得到的，这保证背景结构是自洽和稳定的。触发CME时采用具有同心圆磁场位形的触发模式，触发的CME事件具有和磁云横截面磁场相似的结构。模拟结果给出在太阳表面不同位置触发CME事件在太阳子午面内的传播特征，数值上验证了CME向电流片的偏转传播效应。
在两冕流间CME事件的数值模拟过程中，采用偶极子场和六极子场适当迭加得到初始猜解磁场，由猜解磁场和太阳风流动相互作用计算出稳态自洽解，稳态自洽解的背景磁场在太阳南北极符号相反，这符合观测。在两个冕流间采用具有同心圆磁场位形的触发模型触发CME事件，研究CME的日冕传播特征。模
拟结果表明，CME被约束在两冕流间传播，CME闭磁场位形和磁云横截面磁场位形相似，可以解释1AU处观测磁云的部分特征；在CME附近，存在压力和Lorentz起主要作用的区域，这可以为分析1AU处CME的观测数据提供帮助
The ideal Magnetohydrodynamic equations(MHD), the governing equations of the solar atmosphere dynamical process, are taken to numerically simulate Coronal Mass Ejection(CME) phenomena.
At first, we develop suitable numerical algorithms corresponding to the features of different forms of MHD equations. We generalize Non-oscillatory, Non-free parameter Discrete scheme(NND) for the first time and apply it to the conservative form of MHD equations. The work lies in two main aspects: 1) To effectively reduce the error of Lorentz force caused by the non-zero numerical value of magnetic field divergence, we divided magnetic field into two parts, one is potential field invariant of time and the other is non-potential field varying with time and get an improved conservative form of MHD equations. 2) Considering MHD equation features, we put forward a flux splitting method applicable for the conservative form of MHD equations. With the method we can apply NND scheme to MHD equation effectively. About non-conservative form of MHD equations, we apply second order accuracy MacCormackII scheme to three dimensional MHD equations and apply non-reflective projected characteristic boundary condition to inner boundary for the first time in this three-dimensional case, which effectively stabilize computation. With the numerical model, we get a stable and self-consistent background solar wind of Carrington rotation 1935 at May 1998. This makes a foundation for simulating CME events.
Second, in order to eliminate geometry singularity related to usual two-dimensional MHD governing equations in solar meridian plane at solar poles, we
introduce a new two-dimensional MHD model. With the model, we succeed in simulating LACO-C2 image observed at May 2 1998.
Finally, we simulate CME propagation features in corona numerically. Background structure for CME propagation is obtained by the time relaxation method, which guarantees it stable and self-consistent. CME triggering model has concentric circular magnetic field profiles to make CME magnetic field structure similar to that in the section of the magnetic cloud structure. Numerical results present propagation features in meridian plane of CME events triggered at different places of solar surface and numerically testify the effect of propagating CME deflecting to current sheet.
When numerically simulating CME events between two streamers, we construct a potential magnetic field by properly combining a dipole and a hexadpole and calculate a stable and self-consistent background after a long time interaction between the potential magnetic field and solar wind flow. Agreeing with observation, the polarity at two solar-magnetic poles are opposite in the background of the stable and self-consistent solution. With this background, we trigger CME with the triggering model between two streamers to make research about propagation features of CMEs. Numerical results tell us that CMEs are confined by two streamers to propagate between them. CME magnetic field profiles are similar to those in the section of magnetic cloud, which can explain partial features of magnetic cloud observed at 1AU. Near CMEs, there exist areas that pressure and Lorentz force play a central role, which can help for analysis of CME observational data at 1AU
首先，根据不同形式MHD方程组的特点，发展与之相适应的数值算法。首次推广了无振荡、无自由参数格式（NND），把它应用于守恒形式的MHD方程组。主要做了两个方面的工作，第一，为了降低由磁场散度数值上不为零造成的Lorentz力误差，把磁场分解成两部分，一部分为势场，不随时间变化，另一部分为非势场，随时间变化，得到改进的守恒形式MHD方程组。第二，针对MHD方程组的特点 提出了一种适用于守恒型MHD方程组的通量分裂方法，这种方法能够把NND格式有效地应用于MHD方程组。对非守恒形式的MHD方程组，把二阶精度的MacCormackII格式推广应用到三维MHD方程组，首次把无反射投影特征线边界条件应用于三维情况下的内边界，有效地稳定了数值计算。采用这种数值模式进行计算，得到了1998年5月1935卡林顿周稳定和自洽的背景太阳风，这为模拟CME事件打下了基础。
其次，为消除一般两维MHD模式在太阳子午面内极区的几何奇异性，引入两维MHD方程组的新模式，采用这种模式成功地模拟了98年5月2日观测到的子午面内日冕亮度图。
最后数值模拟CME在日冕内的传播特征。CME传播所需的背景结构是采用时间松弛方法计算得到的，这保证背景结构是自洽和稳定的。触发CME时采用具有同心圆磁场位形的触发模式，触发的CME事件具有和磁云横截面磁场相似的结构。模拟结果给出在太阳表面不同位置触发CME事件在太阳子午面内的传播特征，数值上验证了CME向电流片的偏转传播效应。
在两冕流间CME事件的数值模拟过程中，采用偶极子场和六极子场适当迭加得到初始猜解磁场，由猜解磁场和太阳风流动相互作用计算出稳态自洽解，稳态自洽解的背景磁场在太阳南北极符号相反，这符合观测。在两个冕流间采用具有同心圆磁场位形的触发模型触发CME事件，研究CME的日冕传播特征。模
拟结果表明，CME被约束在两冕流间传播，CME闭磁场位形和磁云横截面磁场位形相似，可以解释1AU处观测磁云的部分特征；在CME附近，存在压力和Lorentz起主要作用的区域，这可以为分析1AU处CME的观测数据提供帮助
The ideal Magnetohydrodynamic equations(MHD), the governing equations of the solar atmosphere dynamical process, are taken to numerically simulate Coronal Mass Ejection(CME) phenomena.
At first, we develop suitable numerical algorithms corresponding to the features of different forms of MHD equations. We generalize Non-oscillatory, Non-free parameter Discrete scheme(NND) for the first time and apply it to the conservative form of MHD equations. The work lies in two main aspects: 1) To effectively reduce the error of Lorentz force caused by the non-zero numerical value of magnetic field divergence, we divided magnetic field into two parts, one is potential field invariant of time and the other is non-potential field varying with time and get an improved conservative form of MHD equations. 2) Considering MHD equation features, we put forward a flux splitting method applicable for the conservative form of MHD equations. With the method we can apply NND scheme to MHD equation effectively. About non-conservative form of MHD equations, we apply second order accuracy MacCormackII scheme to three dimensional MHD equations and apply non-reflective projected characteristic boundary condition to inner boundary for the first time in this three-dimensional case, which effectively stabilize computation. With the numerical model, we get a stable and self-consistent background solar wind of Carrington rotation 1935 at May 1998. This makes a foundation for simulating CME events.
Second, in order to eliminate geometry singularity related to usual two-dimensional MHD governing equations in solar meridian plane at solar poles, we
introduce a new two-dimensional MHD model. With the model, we succeed in simulating LACO-C2 image observed at May 2 1998.
Finally, we simulate CME propagation features in corona numerically. Background structure for CME propagation is obtained by the time relaxation method, which guarantees it stable and self-consistent. CME triggering model has concentric circular magnetic field profiles to make CME magnetic field structure similar to that in the section of the magnetic cloud structure. Numerical results present propagation features in meridian plane of CME events triggered at different places of solar surface and numerically testify the effect of propagating CME deflecting to current sheet.
When numerically simulating CME events between two streamers, we construct a potential magnetic field by properly combining a dipole and a hexadpole and calculate a stable and self-consistent background after a long time interaction between the potential magnetic field and solar wind flow. Agreeing with observation, the polarity at two solar-magnetic poles are opposite in the background of the stable and self-consistent solution. With this background, we trigger CME with the triggering model between two streamers to make research about propagation features of CMEs. Numerical results tell us that CMEs are confined by two streamers to propagate between them. CME magnetic field profiles are similar to those in the section of magnetic cloud, which can explain partial features of magnetic cloud observed at 1AU. Near CMEs, there exist areas that pressure and Lorentz force play a central role, which can help for analysis of CME observational data at 1AU
引文
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