Fast Monte Carlo simulation for particle coagulation in population balance

• We propose a fast random simulation scheme based on the differentially weighted PBMC.
• We introduce majorant to estimate the maximum coagulation kernel by a single looping.
• The CPU time increases with particle number linearly rather than quadratically.
• The fast PBMC yields reasonably closer prediction to normal PBMC.
• The fast PBMC attains an optimal combination of high accuracy and high efficiency.

The Monte Carlo (MC) method for population balance modeling (PBM) has become increasingly popular because the discrete and stochastic nature of the MC method is especially suited for particle dynamics. However, for the two-particle events (typically, particle coagulation), the double looping over all simulation particles is required in normal MC methods, and the computational cost is O(Ns2), where Ns is the simulation particle number. This paper proposes a fast random simulation scheme based on the differentially-weighted Monte Carlo (DWMC) method. The majorant of coagulation kernel was introduced to estimate the maximum coagulation rate by a single looping over all particles rather than the double looping. The acceptance–rejection process then proceeded to select successful coagulation particle pairs randomly, and meanwhile the waiting time (time-step) for a coagulation event was estimated by summing the coagulation kernels of rejected and accepted particle pairs. In such a way, the double looping is avoided and computational efficiency is greatly improved as expected. Five coagulation cases for which analytical solutions or benchmark solutions exist were simulated by the fast and normal DWMC, respectively. It is found the CPU time required is orders of magnitude lower and only increases linearly with Ns; at the same time the computational accuracy is guaranteed very favorably.

The fast DWMC method approximates the maximum coagulation rate by weighted majorant kernel and estimates the waiting time of coagulation events through the acceptance–rejection process. The fast PBMC can attain very favorable improvement in cost (computational time is only O(Ns)) as well guarantee in accuracy (almost same results as normal PBMC).Figure optionsDownload high-quality image (89 K)Download as PowerPoint slide