考虑颗粒碰撞的多重Monte Carlo算法

从减少计算代价和改进碰撞算法出发, 提出了考虑颗粒碰撞的多重Monte Carlo算法, 它采用直接模拟Monte Carlo算法来考虑颗粒碰撞, 并与求解颗粒拉氏Langevin方程的Monte Carlo算法耦合起来, 跟踪比实际颗粒数目小得多的虚拟颗粒. 提出了时间步长选定标准、虚拟碰撞伙伴所在控制容积的判断准则、颗粒碰撞发生的判 断准则、虚拟碰撞伙伴的选择、基于随机碰撞角度的碰撞动力学, 构成了考虑颗粒碰撞的完整多重Monte Carlo算法. 对理想工况的细微颗粒流和粗重颗粒流进行了数值模拟, 颗粒碰撞率的模拟结果与理论分析解和DNS结果均符合很好, 颗粒场演变的细节信息, 如时间平均和特定时刻的颗粒数密度, 速度和颗粒湍动能等, 均与DNS结果符合很好. 数值模拟结果证明该算法不仅具有较低的计算代价, 而且能够达到足够的计算精度.

Multi-Monte Carlo Methods for Inter-particle Collision

In the interest of improving collision arithmetic and decreasing computation cost, a new Multi-Monte Carlo (MMC) method for inter-particle collision is promoted. The particle motion is described by the Langevin equations, which are solved by Monte Carlo (MC) method. On the same time, inter-particle collision is modeled by Direct Simulation Monte Carlo (DSMC) method, which is coupled with the forenamed MC method. The simulation particles of MMC method are fictitious particles, the number of which is far less than that of real particles. In order to found an integrated MMC method for inter-particle collision, a series of methods are developed, which include the setting of time step, the judgment of control volume in which fictitious collision partner lies, the judgment of the occurrence of inter-particle collision event, the choice of fictitious collision partner, and particle collision dynamics based on stochastic collision angle. Fine particles flows and heavy coarse particles flows are chosen as standard cases to validate MMC method. The simulation results of MMC method are in good agreement with that of both analytical solution and Direct Numerical Simulation (DNS), not only on macroscopical facets such as particle collision frequency, but also on microcosmic facets such as time-averaged or special-time-point particle number density, particle velocity and particle turbulent kinetic energy etc. The results of numerical simulation show that MMC method for inter-particle collision has not only enough low computation cost but also enough high computation precision.