全球日冕演化的自适应数据驱动模式和日冕磁场外推
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摘要
太阳日冕是空间天气事件发生的上层区,其中丰富的结构及其演化是空间物理研究的重要内容.数据驱动的日冕模拟,是指在日冕底边界上连续时序地输入观测数据(如磁场)来驱动日冕数值模式,以模拟日冕真实的动力学演化;是研究日冕大尺度结构演变和太阳爆发活动的有力工具.本文侧重于计算技术层面,基于时空守恒数值格式(CESE)和自适应网格方法(AMR),开发了一个新型的日冕–太阳风自适应模式;并联合光球磁流输运模型,建立了首个由时变光球磁图驱动的全球日冕动态演化MHD模式.
作用一种新型高效的数值格式, CESE方法已成功地应用于多种空间物理问题的模拟研究.基于一般曲线坐标理论,本文通过把物理空间下的主控方程变换到计算空间并保持守恒形式,首先将CESE格式推广到了一般曲线坐标下.然后借助于并行自适应软件包PARAMESH,并克服了CESE格式和自适应网格系统的各种不兼容性(如时空交错问题,库朗数敏感问题等),将一般曲线CESE格式成功实现于块状自适应网格上,建立了一个MHD数值模拟的新方法AMR-CESE-MHD.
为精确刻画日冕底部球型边界面而不引入两极奇点问题,采用一种基于球坐标的重叠型网格(Yin-Yang网格)以克服其他网格系统的各种弱点,并利用高精度的插值保证重叠边界信息相互无障碍的传递.自适应的日冕–太阳风模型即建立于该网格系统和AMR-CESE-MHD方法上.时变自洽的底面边界条件基于投影特征线方法和一个描述光球磁图演化的模型–表面磁流输运(SFT)模型.SFT模型采用观测的综合磁图作为输入,能够很好的再现长达几个月的日面磁流的变化,而且避免了直接采用观测磁图而导致的不兼容性.通过模拟长达三个太阳自转周的动态演化并与多观测日冕图像进行比较,展示了该日冕动态模式模拟全球日冕基本结构如冕流,冕洞位置和活动区磁场及其演化的能力.
此外,由于日冕的三维磁场尚不能直接观测.作为一种替代办法,磁场外推(重构)也是研究日冕活动的一种重要方法.通过考察外推磁场的拓扑结构,可以发掘导致太阳爆发活动的不稳定磁场位形.本文针对于重构日冕磁场的松弛法,提出了一种新的实现方式.不同于以往的仅求解无力场模型的办法,我们采用全磁流体模型,并利用简洁而高效的CESE格式来求解.光球(底面)边界条件类似于挤压–松弛(stress-and-relax)方法,使初始的势场分布逐渐逼近于观测的矢量磁图.计算区域的其他人工边界全部采用基于投影特征线方法的无反射边界条件.我们将这个方法外推了无力场的两个经典解析解.结果证明了方法的有效性并且细致的分析发现和目前国际上最好的方法相当.
Solar corona is the upper region for the space-weather events. The diversestructures and evolutions in the corona are fundamental for the space physics. Ina data-driven corona model, the dynamic evolution of the corona is simulated bycontinuously inputting the observed data (e.g., the magnetic fleld) at the coronalbottom to drive the model. It provides a powerful numerical tool for study ofthe large-scale coronal structures and the solar eruptions. In this thesis withthe bias on numerical-technique aspect, we have developed a new adaptive solarcorona-solar wind model basing on the space-time conservation-element/solution-element (CESE) scheme and the adaptive-mesh-reflnement (AMR) technique.Then by combining with a photospheric magnetic-flux transport model, we de-velop the flrst dynamic model for the evolution of the global corona driven bythe time-varying photospheric magnetogram.
As a novel and high-performance numerical scheme, the CESE method hasalready been successfully applied to the fleld of space-physic simulation. Basingon the theory of general curvilinear coordinates, in this thesis we flrst establish acurvilinear-coordinate version of the CESE method for MHD, by transform thegoverning MHD equations from the physical space (x,y,z) to the computationalspace (ξ,η,ζ) while retaining the form of conservation. Then utilizing a parallel-AMR package PARAMESH and overcoming various incompatibles of the CESEscheme with the AMR grid system (e.g., the problems of space-time staggeringand the Courant number sensitive), we present the flrst implementation of theCESE method on block-AMR grid for MHD (the AMR-CESE-MHD code) inboth Cartesian and curvilinear coordinates.
To precisely characterize the bottom sphere of the global corona and avoidthe grid-convergence problems at two poles, a new kind of overlapping grid, theso-called Yin-Yang grid, is borrowed here to overcome various weaknesses of othergrid systems. High-accuracy interpolation is used for transparent transferring ofsolution information at the overlapping boundaries. The adaptive model of the solar corona-solar wind is built on the AMR-CESE-MHD code and the Yin-Yanggrid under the framework of PARAMESH.
The time-varying and self-consistent boundary conditions at the coronalbottom is based on the projected-characteristic method and a surface transport(SFT) model. With observed synoptic map as input, the SFT model can repro-duce well the long-term evolution of the photospheric fleld for several months,and avoid the inconsistency of using directly the global magnetogram from obser-vation. By modeling the dynamic evolution for a long time interval of three Car-ringtion rotation (from CR1913 to CR1915) and comparing with multi-observedcoronal images, we show that the model is able to simulate the general structuresof the global corona, e.g., the coronal streamers, the locations of coronal holes,the magnetic fleld of the active regions and their evolutions.
Besides, magnetic fleld extrapolation is a common and accurate way to over-come the problem of unavailable direct measurement of the three-dimensionalfleld in the corona. In this thesis, we also present a new implementation ofthe MHD relaxation method for reconstruction of the nearly force-free coronalmagnetic fleld from a photospheric vector magnetogram. Unlike most of the ex-trapolation methods that focus on a nonlinear force-free-fleld model, we solve thefull MHD equations directly by using the CESE method. The bottom boundarycondition is prescribed in a similar way as in the stress-and-relax method, i.e., bychanging the transverse fleld incrementally to match the magnetogram, and otherboundaries of the computational box are set by the nonreflecting boundary con-ditions. Applications to the well-known benchmarks for nonlinear force-free-fleldreconstruction, the Low & Lou force-free equilibria, validate the method and con-flrm its capability for future practical application, with observed magnetogramsas inputs.
作用一种新型高效的数值格式, CESE方法已成功地应用于多种空间物理问题的模拟研究.基于一般曲线坐标理论,本文通过把物理空间下的主控方程变换到计算空间并保持守恒形式,首先将CESE格式推广到了一般曲线坐标下.然后借助于并行自适应软件包PARAMESH,并克服了CESE格式和自适应网格系统的各种不兼容性(如时空交错问题,库朗数敏感问题等),将一般曲线CESE格式成功实现于块状自适应网格上,建立了一个MHD数值模拟的新方法AMR-CESE-MHD.
为精确刻画日冕底部球型边界面而不引入两极奇点问题,采用一种基于球坐标的重叠型网格(Yin-Yang网格)以克服其他网格系统的各种弱点,并利用高精度的插值保证重叠边界信息相互无障碍的传递.自适应的日冕–太阳风模型即建立于该网格系统和AMR-CESE-MHD方法上.时变自洽的底面边界条件基于投影特征线方法和一个描述光球磁图演化的模型–表面磁流输运(SFT)模型.SFT模型采用观测的综合磁图作为输入,能够很好的再现长达几个月的日面磁流的变化,而且避免了直接采用观测磁图而导致的不兼容性.通过模拟长达三个太阳自转周的动态演化并与多观测日冕图像进行比较,展示了该日冕动态模式模拟全球日冕基本结构如冕流,冕洞位置和活动区磁场及其演化的能力.
此外,由于日冕的三维磁场尚不能直接观测.作为一种替代办法,磁场外推(重构)也是研究日冕活动的一种重要方法.通过考察外推磁场的拓扑结构,可以发掘导致太阳爆发活动的不稳定磁场位形.本文针对于重构日冕磁场的松弛法,提出了一种新的实现方式.不同于以往的仅求解无力场模型的办法,我们采用全磁流体模型,并利用简洁而高效的CESE格式来求解.光球(底面)边界条件类似于挤压–松弛(stress-and-relax)方法,使初始的势场分布逐渐逼近于观测的矢量磁图.计算区域的其他人工边界全部采用基于投影特征线方法的无反射边界条件.我们将这个方法外推了无力场的两个经典解析解.结果证明了方法的有效性并且细致的分析发现和目前国际上最好的方法相当.
Solar corona is the upper region for the space-weather events. The diversestructures and evolutions in the corona are fundamental for the space physics. Ina data-driven corona model, the dynamic evolution of the corona is simulated bycontinuously inputting the observed data (e.g., the magnetic fleld) at the coronalbottom to drive the model. It provides a powerful numerical tool for study ofthe large-scale coronal structures and the solar eruptions. In this thesis withthe bias on numerical-technique aspect, we have developed a new adaptive solarcorona-solar wind model basing on the space-time conservation-element/solution-element (CESE) scheme and the adaptive-mesh-reflnement (AMR) technique.Then by combining with a photospheric magnetic-flux transport model, we de-velop the flrst dynamic model for the evolution of the global corona driven bythe time-varying photospheric magnetogram.
As a novel and high-performance numerical scheme, the CESE method hasalready been successfully applied to the fleld of space-physic simulation. Basingon the theory of general curvilinear coordinates, in this thesis we flrst establish acurvilinear-coordinate version of the CESE method for MHD, by transform thegoverning MHD equations from the physical space (x,y,z) to the computationalspace (ξ,η,ζ) while retaining the form of conservation. Then utilizing a parallel-AMR package PARAMESH and overcoming various incompatibles of the CESEscheme with the AMR grid system (e.g., the problems of space-time staggeringand the Courant number sensitive), we present the flrst implementation of theCESE method on block-AMR grid for MHD (the AMR-CESE-MHD code) inboth Cartesian and curvilinear coordinates.
To precisely characterize the bottom sphere of the global corona and avoidthe grid-convergence problems at two poles, a new kind of overlapping grid, theso-called Yin-Yang grid, is borrowed here to overcome various weaknesses of othergrid systems. High-accuracy interpolation is used for transparent transferring ofsolution information at the overlapping boundaries. The adaptive model of the solar corona-solar wind is built on the AMR-CESE-MHD code and the Yin-Yanggrid under the framework of PARAMESH.
The time-varying and self-consistent boundary conditions at the coronalbottom is based on the projected-characteristic method and a surface transport(SFT) model. With observed synoptic map as input, the SFT model can repro-duce well the long-term evolution of the photospheric fleld for several months,and avoid the inconsistency of using directly the global magnetogram from obser-vation. By modeling the dynamic evolution for a long time interval of three Car-ringtion rotation (from CR1913 to CR1915) and comparing with multi-observedcoronal images, we show that the model is able to simulate the general structuresof the global corona, e.g., the coronal streamers, the locations of coronal holes,the magnetic fleld of the active regions and their evolutions.
Besides, magnetic fleld extrapolation is a common and accurate way to over-come the problem of unavailable direct measurement of the three-dimensionalfleld in the corona. In this thesis, we also present a new implementation ofthe MHD relaxation method for reconstruction of the nearly force-free coronalmagnetic fleld from a photospheric vector magnetogram. Unlike most of the ex-trapolation methods that focus on a nonlinear force-free-fleld model, we solve thefull MHD equations directly by using the CESE method. The bottom boundarycondition is prescribed in a similar way as in the stress-and-relax method, i.e., bychanging the transverse fleld incrementally to match the magnetogram, and otherboundaries of the computational box are set by the nonreflecting boundary con-ditions. Applications to the well-known benchmarks for nonlinear force-free-fleldreconstruction, the Low & Lou force-free equilibria, validate the method and con-flrm its capability for future practical application, with observed magnetogramsas inputs.
引文
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