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首页> 外文期刊>Journal of Computational Physics >An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics
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An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics

机译：多维磁流体动力学的非分裂交错网格方案

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摘要

We introduce an unsplit staggered mesh scheme (USM) for multidimensional magnetohydrodynamics (MHD) that uses a constrained transport (CT) method with high-order Codunov fluxes and incorporates a new data reconstruction-evolution algorithm for second-order MHD interface states. In this new algorithm, the USM scheme includes so-called "multidimensional MHD terms", proportional to del.B, in a dimensionally-unsplit way in a single update. This data reconstruction-evolution step, extended from the corner transport upwind (CTU) approach of Colella, maintains in-plane dynamics very well, as shown by the advection of a very weak magnetic field loop in 2D. This data reconstruction-evolution algorithm is also of advantage in its consistency and simplicity when extended to 3D. The scheme maintains the del.B = 0 constraint by solving a set of discrete induction equations using the standard CT approach, where the accuracy of the computed electric field directly influences the quality of the magnetic field solution. We address the lack of proper dissipative behavior in the simple electric field averaging scheme and present a new modified electric field construction (MEC) that includes multidimensional derivative information and enhances solution accuracy. A series of comparison studies demonstrates the excellent performance of the full USM-MEC scheme for many stringent multidimensional MHD test problems chosen from the literature. The scheme is implemented and currently freely available in the University of Chicago ASC FLASH Center's FLASH3 release. (C) 2008 Elsevier Inc. All rights reserved.
机译：我们为多维磁流体动力学（MHD）引入了未拆分的交错网格方案（USM），该方案使用具有高阶Codunov通量的约束传输（CT）方法，并为二阶MHD接口状态合并了新的数据重构-演化算法。在这种新算法中，USM方案在一次更新中以尺寸未拆分的方式包含了与del.B成比例的所谓的“多维MHD项”。从Colella的转角上风（CTU）方法扩展而来的这一数据重构-演化步骤很好地保持了平面内动力学，如2D中非常弱的磁场环的平流所表明的那样。当扩展到3D时，这种数据重建-演化算法在其一致性和简单性方面也具有优势。该方案通过使用标准CT方法求解一组离散感应方程来维持del B = 0约束，其中计算出的电场的精度直接影响磁场解的质量。我们解决了简单电场平均方案中缺乏适当耗散行为的问题，并提出了一种新的改进的电场构造（MEC），其中包括多维导数信息并提高了求解精度。一系列比较研究表明，对于从文献中选择的许多严格的多维MHD测试问题，完整的USM-MEC方案具有出色的性能。该方案已实施，目前可在芝加哥大学ASC FLASH中心的FLASH3版本中免费获得。 （C）2008 Elsevier Inc.保留所有权利。

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