摘要：提出一种基于有限元的虚拟区域法,可在亚颗粒尺度上实现对三维颗粒群运动的高效直接数值模拟;基于虚拟区域法的思想将颗粒视为浸入在背景网格中的有限大小区域而非零维点,在有限元方法的离散方程中引入体现颗粒作用的动量方程源项以保证颗粒的刚体运动;给出了三维虚拟区域法的实现方式与数值检验结果,并对管道中的颗粒群实际运动过程进行了直接数值模拟,得到了颗粒群与流场相互作用的非稳态结果。结果表明,虚拟区域法不仅能够处理三维颗粒运动的颗粒边界条件,不需要重新划分网格,而且还可以用于进行多颗粒运动系统的亚颗粒尺度直接数值模拟,最终得到详细的速度场和受力结果。

关键词：颗粒群运动；虚拟区域法；直接数值模拟；亚颗粒尺度

Abstract： A three dimensional fictitious domain method was proposed to perform direct numerical simulation of complex particulate flows efficiently. Based on the fictitious domain point of view, the three dimensional particles were immersed in the background mesh, and the source terms were added to impose rigid body movement constraint of solid particles, incorporating the finite element discretization of background mesh equations. The detail of implementing three dimensional fictitious domain method was discussed and the method was validated. A particle cluster movement problem was solved and the results were illustrated. The results show that the fictitious domain method is proved to be able to handle the moving particles boundary conditions, and is suitable to simulate movements of multi-particle system in sub-particle scale. Detailed velocity and force results are obtained. 

Keywords: particulate flows；fictitious domain method； direct numerical simulation；sub-particle scale