论文标题
测量磁场建模的发散
On measuring divergence for magnetic field modeling
论文作者
论文摘要
物理磁场的发散为零。但是，在构建模型字段和计算差异时的数值误差会引入这些计算中的有限差异。测量分歧的流行度量是平均分数通量$ \ langle | f_ {i} | \ rangle $。我们表明$ \ langle | f_ {i} | \ rangle $缩放计算网格的大小，并且可能是差异的差异，因为它在增加网格分辨率的情况下任意很小，而没有差异实际上减小。我们定义了该指标的修改版本，该版本不会以网格尺寸扩展。我们将新指标应用于Derosa等人的结果。 （2015年），测量$ \ langle | f_ {i} | \ rangle $用于基于在不同空间分辨率下归入的太阳边界数据的冠状磁场的一系列非线性力场（NLFFF）模型。我们计算了DeRosa等人的许多差异指标。 （2015）使用非参数方法数据并分析空间分辨率对这些指标的影响。我们发现DeRosa等人报道的一些趋势。 （2015年）是由于$ \ langle | f_ {i} | \ rangle $。我们还发现，不同的指标为相同的数据集提供了不同的结果，因此通过几个指标测量差异是有价值的。
A physical magnetic field has a divergence of zero. Numerical error in constructing a model field and computing the divergence, however, introduces a finite divergence into these calculations. A popular metric for measuring divergence is the average fractional flux $\langle |f_{i}| \rangle$. We show that $\langle |f_{i}| \rangle$ scales with the size of the computational mesh, and may be a poor measure of divergence because it becomes arbitrarily small for increasing mesh resolution, without the divergence actually decreasing. We define a modified version of this metric that does not scale with mesh size. We apply the new metric to the results of DeRosa et al. (2015), who measured $\langle |f_{i}| \rangle$ for a series of Nonlinear Force-Free Field (NLFFF) models of the coronal magnetic field based on solar boundary data binned at different spatial resolutions. We compute a number of divergence metrics for the DeRosa et al. (2015) data and analyze the effect of spatial resolution on these metrics using a non-parametric method. We find that some of the trends reported by DeRosa et al. (2015) are due to the intrinsic scaling of $\langle |f_{i}| \rangle$. We also find that different metrics give different results for the same data set and therefore there is value in measuring divergence via several metrics.
