计算电动力学自适应网格细化的系统方法

IF 1.8 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC
Dinshaw S. Balsara;Costas D. Sarris
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引用次数: 0

摘要

迫切需要在自适应网格上解决CED问题;这里称为AMR-CED。该问题被认为易受“长期不稳定性”的影响,并采用参数化方法来控制不稳定性。在本文中,我们提出了一类新的AMR-CED方法,它们没有这种不稳定性,因为它们基于对麦克斯韦方程中的约束的更仔细的理解以及它们在单个控制体积上的保存。这些新方法的重要组成部分是:1)子网格相对于父网格的时间步子循环。2)当两种网格及时同步时,细网格面部数据限制为粗网格。3)保持散度约束的粗网格解扩展到新建的细网格或已存在的细网格的幽灵区域。4)细粗界面电场和磁场强度校正策略。通过实例,我们证明了所得到的AMR-CED算法没有“长期不稳定性”。与以前的方法不同,没有可调参数。该方法具有固有的稳定性,因为在AMR网格层次结构的所有层次上都采用了严格的算法一致性。我们还证明了该方法保留了阶精度,因此AMR-CED的高阶方法确实是可能的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Systematic Approach to Adaptive Mesh Refinement for Computational Electrodynamics
There is a great need to solve CED problems on adaptive meshes; referred to here as AMR-CED. The problem was deemed to be susceptible to “long-term instability” and parameterized methods have been used to control the instability. In this paper, we present a new class of AMR-CED methods that are free of this instability because they are based on a more careful understanding of the constraints in Maxwell's equations and their preservation on a single control volume. The important building blocks of these new methods are: 1) Timestep sub-cycling of finer child meshes relative to parent meshes. 2) Restriction of fine mesh facial data to coarser meshes when the two meshes are synchronized in time. 3) Divergence constraint-preserving prolongation of the coarse mesh solution to newly built fine meshes or to the ghost zones of pre-existing fine meshes. 4) Electric and magnetic field intensity-correction strategy at fine-coarse interfaces. Using examples, we show that the resulting AMR-CED algorithm is free of “long-term instability”. Unlike previous methods, there are no adjustable parameters. The method is inherently stable because a strict algorithmic consistency is applied at all levels in the AMR mesh hierarchy. We also show that the method preserves order of accuracy, so that high order methods for AMR-CED are indeed possible.
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来源期刊
CiteScore
4.30
自引率
0.00%
发文量
27
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