三维空间液滴运动模型数值解法研究

提出了数值求解三维空间液滴运动模型的算子分裂算法（OS算法），并与常用的显式单步长Runge-Kutta（RK）算法进行了比较。简述了三维空间液滴运动模型的具体形式，提出了求解该模型的OS算法，以求解不同直径液滴在波形板汽水分离器内的运动轨迹作为算例，从OS算法的相容性、稳定性、计算精度和计算效率（CPU耗时）等方面，与4级4阶显式单步长RK算法进行了比较。结果表明，OS算法所构造的离散格式与液滴运动模型相容，采用此算法计算得到的液滴运动轨迹与RK算法得到的结果相似，而OS算法的稳定性和计算效率均优于RK算法。因此，OS算法的提出为数值计算波形板的分离效率提供了较为稳定、高效的算法。

Study on Numerical Algorithm of Droplet Motion Model in Three-dimensional Space

An algorithm called operator-splitting (OS) to solve the model of a single droplet moving in three-dimensional space was developed. At the same time, the algorithm was compared with the frequently used explicit single step Runge-Kutta (RK) algorithm. The droplet motion model in three-dimensional space was briefly introduced. The OS algorithm was showed in detail. Then the trajectories of droplets with different diameters in the wave-type plate separator were calculated numerically. In this example, the OS algorithm and the 4th order 4-step RK algorithm were both tested from the aspects of consistency, stability, numerical precision and calculating efficiency. The results show that the trajectories acquired by these two algorithms are almost the same. However, the stability and the calculating efficiency of the OS algorithm are both better than those of the RK algorithm. Therefore, the OS algorithm is a relatively stable and efficient algorithm to numerically calculate the droplet separation efficiency of wave-type plate separator.