To predict the clustering of inclusions at the liquid steel and inert gas interface, it is essential to calculate the pairwise attractive (inertial) force on the inclusions correctly. In most of the studies, the inertial force is calculated from three successive inter-particle distances with a certain time interval, in which the inertial force is assumed to be identical at the first two distances. Considering the nature of the attractive force, a new iteration scheme is proposed where the inertial force is assumed to be non-identical from point to point. However, both the identical and non-identical force schemes tend to give an unreasonably oscillating force when the measured inter-particle distance is less accurate. Moreover, the curve fitting function is also considered in this study including the use of polynomial, exponential, sum of sines, rational, Gaussian functions and Fourier series. Among these functions, the 4th order polynomial and the 2nd order sine are the most robust functions in predicting the inertial force on particles, even when the measured distance is less accurate.

为了预测钢水和惰性气体界面处夹杂物的聚集，必须正确计算夹杂物上的成对吸引力（惯性）力。在大多数研究中，惯性力是根据具有特定时间间隔的三个连续粒子间距离计算得出的，其中假设惯性力在前两个距离处相同。考虑到吸引力的性质，提出了一种新的迭代方案，其中假设惯性力从点到点不相同。然而，当测量的粒子间距离不太准确时，相同和不同的力方案往往会产生不合理的振荡力。此外，本研究还考虑了曲线拟合函数，包括使用多项式、指数、正弦和、有理、高斯函数和傅立叶级数。在这些函数中，4 阶多项式和 2 阶正弦是预测粒子惯性力的最稳健的函数，即使测量的距离不太准确。