约束输运（CT）方法反映了最先进的数值技术，用于在Godunov型或迎风保守代码进行的多维MHD模拟中将磁场的无发散条件保持到机器精度。通过计算单元边缘处的电场分量，以必须与用于更新界面处以单元为中心的流体量的黎曼解算器一致的方式，实现了使用交错表示法位于区域界面处的不同磁场分量的演变。尽管已经采取了几种方法，但这项工作的目的是，一方面，在鲁棒性和准确性方面比较现有方法，另一方面，扩展Londrillo \& Del Zanna（2004）和Del Zanna等人（2007）的\emph{upwind contrained transport}（UCT）方法，以系统地构建新的平均方案。特别是，我们提出了一个一般公式的迎风通量的感应方程，其中简单地涉及到的信息，从基础黎曼求解器采用的流体部分，只要它不需要全谱分解，和一维重建的速度和磁场组件从附近的intercell面临的细胞边缘。我们的结果在这里的背景下，二阶计划的经典MHD，但它们可以很容易地推广到高于二阶计划，无论是基于有限体积或有限差分，和其他物理系统保留相同的结构的方程，如相对论或广义相对论MHD。
英文摘要：
The constrained transport (CT) method reflects the state of the art numerical technique for preserving the divergence-free condition of magnetic field to machine accuracy in multi-dimensional MHD simulations performed with Godunov-type, or upwind, conservative codes. The evolution of the different magnetic field components, located at zone interfaces using a staggered representation, is achieved by calculating the electric field components at cell edges, in a way that has to be consistent with the Riemann solver used for the update of cell-centered fluid quantities at interfaces. Albeit several approaches have been undertaken, the purpose of this work is, on the one hand, to compare existing methods in terms of robustness and accuracy and, on the other, to extend the \emph{upwind contrained transport} (UCT) method by Londrillo \& Del Zanna (2004) and Del Zanna et al. (2007) for the systematic construction of new averaging schemes. In particular, we propose a general formula for the upwind fluxes of the induction equation which simply involves the information available from the base Riemann solver employed for the fluid part, provided it does not require full spectral decomposition, and 1D reconstructions of velocity and magnetic field components from nearby intercell faces to cell edges. Our results are presented here in the context of second-order schemes for classical MHD, but they can be easily generalized to higher than second order schemes, either based on finite volumes or finite differences, and to other physical systems retaining the same structure of the equations, such as that of relativistic or general relativistic MHD.
A partially dimensionally-split approach to numerical MHD
我们修改现有的磁流体力学算法，使其更兼容的维度分裂（DS）框架。它基于标准的重建-求解-平均策略（使用黎曼解算器），并依赖于受约束的传输来确保磁场保持无发散（div B = 0）。DS方法，结合使用一个单一的，细胞为中心的网格（流体量和磁场），意味着该算法可以很容易地添加到现有的DS流体动力学代码。这使得它对成熟的天体物理代码特别有用，这些代码通常在底层DS流体动力学引擎之上模拟更复杂的物理效应，因此不能轻易重构。几个测试问题已被列入，以证明算法的准确性，说明性的源代码已免费提供在线。
A Stable, Accurate Methodology for High Mach Number, Strong Magnetic Field MHD Turbulence with Adaptive Mesh Refinement: Resolution and Refinement Studies
Systematic Comparison between Constrained Transport and Mixed Divergence Cleaning Methods for Astrophysical Magnetohydrodynamic Simulations
Astronomical Institute, Tohoku University（东北大学天文学研究所）；École Normale Supérieure de Lyon, Centre de Recherche Astrophysique de Lyon（里昂高等师范学校，里昂天体物理研究中心）；Humanities and Sciences/Museum Careers, Musashino Art University（武藏野美术大学人文科学与博物馆职业）；Center for Computational Astrophysics, National Astronomical Observatory of Japan（日本国立天文台计算天体物理学中心）
A High-Order Relativistic Two-Fluid Electrodynamic Scheme with Consistent Reconstruction of Electromagnetic Fields and a Multidimensional Riemann Solver for Electromagnetism
