Refining the reconstruction-based Monte Carlo methods for solving breakage population balance equation

This work presents a class of refinement reconstruction-based Monte Carlo methods dedicated to solving a generic breakage population balance equation. The focus is on enhancing the precision and computational speed of the existing reconstruction scheme by incorporating two refinement strategies, including effective-breakage ratios and population scaling rules with local coarsening/refinement based on adaptive subdomain meshes. A comparative analysis of the performances of the proposed methods is conducted for the benchmark breakage case with a known analytical solution. The results indicate that the accuracy can be significantly increased by a stepwise-varying breakage ratio and the local refinement scaling rule, whereas the cost can be reduced by properly tuning parameters related to the refinement strategies. In addition, multi-objective optimization is introduced to achieve optimal simulation with the least systematic and statistical errors and CPU time, offering further insights into the combination of conditions required for the Monte Carlo methods to yield the best possible efficiency.