论文标题
连续的立方样条插值，在一般多面体中的迭代量界面界面定位
Iterative Volume-of-Fluid interface positioning in general polyhedrons with Consecutive Cubic Spline interpolation
论文作者
论文摘要
提出了一种直接且计算上有效的连续三次样条（CCS）迭代算法，用于在任意形状的细胞中定位非结构化几何量量量方法的平面界面。 CCS算法是一种专为VOF接口定位问题设计的两点根找到算法，其中体积分数函数在搜索间隔的末端具有减小的导数。作为两点迭代算法，CCS从以前的迭代中重新使用函数值和衍生物，并且不依赖间隔括号。 CCS算法平均仅需要两次迭代，即使在数字上非常具有挑战性的体积分数值，例如，即使是$ 10^{ - 12} $的界面，例如。接近$ 10^{ - 9} $或$ 1-10^{ - 9} $。 提出的CCS算法非常简单地实现，因为其输入已经通过每种几何VOF方法计算出来。它基于并显着改善了预测性牛顿方法，并且与细胞的几何模型和相关的相交算法无关。完全避免了其他当代方法使用的截短体积的几何参数化。计算效率与迄今为止报告的最快方法的迭代次数相比。参考文献在CCS算法的开源实现和性能测量数据的结果部分中提供。
A straightforward and computationally efficient Consecutive Cubic Spline (CCS) iterative algorithm is proposed for positioning the planar interface of the unstructured geometrical Volume-of-Fluid method in arbitrarily-shaped cells. The CCS algorithm is a two-point root-finding algorithm specifically designed for the VOF interface positioning problem, where the volume fraction function has diminishing derivatives at the ends of the search interval. As a two-point iterative algorithm, CCS re-uses function values and derivatives from previous iterations and does not rely on interval bracketing. The CCS algorithm only requires only two iterations on average to position the interface with a tolerance of $10^{-12}$, even with numerically very challenging volume fraction values, e.g. near $10^{-9}$ or $1-10^{-9}$. The proposed CCS algorithm is very straightforward to implement because its input is already calculated by every geometrical VOF method. It builds upon and significantly improves the predictive Newton method and is independent of the cell's geometrical model and related intersection algorithm. Geometrical parametrizations of truncated volumes used by other contemporary methods are completely avoided. The computational efficiency is comparable in terms of the number of iterations to the fastest methods reported so far. References are provided in the results section to the open-source implementation of the CCS algorithm and the performance measurement data.
