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同时发生的颗粒凝并和沉积所导致的离散系统动力学演变过程数学上可由通用动力学方程描述.MonteCarlo算法是求解通用动力学方程的一类重要方法.然而,常体积法由于模拟颗粒数目的波动而存在着计算代价和计算精度无法协调的矛盾,常数目法由于计算区域的不断收缩或扩展而难以工程实际应用和科学定量分析,且这些MonteCarlo算法均依赖于子系统概念而大大限制了其扩展性和应用范围.发展一种多重MonteCarlo算法求解同时考虑凝并和沉积的通用动力学方程.该算法引入加权虚拟颗粒的概念,基于时间驱动,在颗粒尺度分布时间演变过程中同步保持恒定的虚拟颗粒数目和稳定的计算区域体积,这使得MMC算法具有考虑边界条件、颗粒尺度分布空间扩散、甚至颗粒-流体动力学的可扩展性.利用多重MonteCarlo算法对几种特殊工况进行数值模拟,结果与理论分析解符合很好,表明该算法具备较高且稳定的计算精度和较低的计算代价,这是由于虚拟颗粒数目稳定且较少的缘故.最后分析了该算法的误差源以及相对误差.
The simultaneous evolution of discrete system dynamics caused by the coalescence and deposition of particles can be mathematically described by a generalized kinetic equation. Monte Carlo algorithms are an important class of methods for solving general kinetic equations. However, the normal volume method, due to the number of simulated particles However, the contradiction between the computational cost and the calculation accuracy can not be reconciled because of the fluctuation. The constant value method is hard to be applied to engineering and scientific quantitative analysis due to the constant contraction or expansion of the calculation area. These MonteCarlo algorithms are greatly dependent on the subsystem concept, Scalability and application scope, a multi-Monte Carlo algorithm is developed to solve the general dynamic equation which considers both condensation and sedimentation. The algorithm introduces the concept of weighted virtual particles based on time-driven and keeps constant at the same time during the evolution of particle-scale distribution The number of virtual particles and the stable calculation of the volume of the region, which makes the MMC algorithm consider the boundary conditions, the spatial distribution of particle size distribution, and even the particle-fluid dynamics scalability.Using Monte Carlo algorithm to simulate several special conditions, The result is in good agreement with the theoretical analysis. The algorithm includes a clear and stable high accuracy and low computational cost, due to the number of virtual particles and less stable sake. Finally the source of the error and the relative error algorithm.