Aerosol dynamics are described by the population balance equation (PBE). In principle, three typical methods (i.e., direct discretization, method of moments, and stochastic method) have been widely used to solve the PBE. Stochastic method is the most flexible among the three methods. However, stochastic method is computationally expensive. Recently, an operator splitting Monte Carlo (OSMC) method has been developed so as to improve the numerical efficiency while preserving the flexibility of the stochastic method. Within the OSMC, nucleation and surface growth are handled with deterministic means, while coagulation is simulated with a stochastic method (the Marcus‐Lushnikov stochastic process). The stochastic and deterministic treatments of various aerosol dynamic processes are synthesized under the framework of operator splitting. Here, the operator splitting errors of various schemes are analyzed rigorously, combined with concrete numerical examples. The analyses not only provide sound theoretical bases for selecting the most efficient operator splitting scheme for the usage of the OSMC, but also shed lights on how to adopt operator splitting in other PBE solving methods, i.e., direct discretization, method of moments, etc.
Part of the book: Aerosols