标题： 在直线涡丝方法中使用的核心和曲率修正 显示英文标题

标题： On Core and Curvature Corrections used in Straight-Line Vortex Filament Methods

摘要： 两种粘性核心修正在直线分割方法中的收敛特性被严格分析。 这些是 \emph{曲率修正}用于考虑由于局部曲率而在涡丝上某一点引起的速度贡献，以及\emph{核心修正}用于消除涡丝附近不现实的高诱导速度。 研究了后一种修正的两种替代版本：Scully 引入的原始版本以及作者最近引入的改进版本。 该问题通过一个粘性涡环进行分析。 提出了一种高阶数值丝方法，该方法使用有理 B 样条曲线精确建模涡环几何结构。 首先，使用数值丝方法研究了这两种修正对诱导速度值的单独影响。 随后，这四种不同的组合情况使用分割方法进行研究。 发现为了在粗网格离散化下获得准确的结果，不能忽略曲率修正。 当与原始核心修正模型结合使用时，对于小于约十度的离散化，结果开始偏离参考值。 将曲率修正与改进的核心修正结合，使找到准确结果的离散化区域向下扩展了一个数量级。 最后，表明使用原始核心修正模型而没有曲率修正的分割方法完全无法收敛到参考值。 显示英文摘要

摘要： The convergence characteristics of two viscous core corrections as used in straight-line segmentation methods are rigorously analysed. These are \emph{curvature corrections} that account for the induced velocity contribution at a point on a vortex filament due to local curvature and \emph{core corrections} that remove unrealistically high induced velocities near vortex segments. Two alternative versions of the latter correction are studied: the original as introduced by Scully and a recently introduced improved correction by the authors. The problem is analysed using a viscous vortex ring. A high-order numerical filament method is presented that uses rational B-spline curves to model the vortex ring geometry exactly. First, the separate influence of the two corrections on induced velocity values are studied using the numerical filament method. Afterwards, the corrections are combined in four separate cases that are studied using the segmentation method. It is found that in order to get accurate results at coarse discretisations, curvature corrections cannot be neglected. When used together with the original core correction model, results start to diverge from the reference values for discretisations smaller than approximately ten degrees. Combining the curvature correction with the improved core correction extends the discretisation region for which accurate results are found down by approximately one order. Finally, it is shown that segmentation methods that use the original core correction model without curvature correction completely fail to converge to the reference values.