论文标题
MHD的上风限制运输方案的系统构建
Systematic construction of upwind constrained transport schemes for MHD
论文作者
论文摘要
受约束运输（CT）方法反映了最先进的数值技术的状态，用于保留磁场无差异条件与用Godunov-Type或Upwind，“保守代码”执行的多维MHD模拟中的机器精度。使用交错表示位于区域界面的不同磁场组件的演变是通过计算细胞边缘处的电场成分来实现的，这种方式必须与用于更新接口处细胞中心的流体的Riemann求解器一致。尽管已经采用了几种方法，但这项工作的目的一方面是用Londrillo \＆del Zanna（2004）和Del Zanna等人的\ emph {uct contress and contress and contrancy和准确性来比较现有方法。 （2007年）用于系统的新平均方案。特别是，我们提出了一个通用公式，用于感应方程的上风通量，只要它不需要完全的频谱分解，并且从附近的速度和磁场成分的1D重建到附近的Intercell Faces到细胞Edges。我们的结果在此处以经典MHD的二阶方案的背景介绍，但是可以很容易地将其推广到高于二阶方案，无论是基于有限的量或有限差异，以及其他物理系统保留了方程式相同结构的物理系统，例如相对论或一般相对论MHD。
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.
