Acceleration of the dynamic simulation of grinding particle size distribution based on τ-leap method

Industrial grinding process shows strong discrete and stochastic properties. It is difficult to fully describe its dynamics in the particle-level with ordinary differential equations based on the population balance concept. Monte Carlo (MC: Monte Carlo) simulation algorithm, a kind of the so called stochastic simulation algorithms (SSA), can accurately describe the particle-level breakage process during grinding. But, the conventional MC method is too inefficient for practical use. This paper proposes an accelerated MC simulation algorithm based on the τ-leap method which is proposed by Gillespie for the simulation of chemical kinetics. This method treats multiple breakage events during each simulation cycle which is in contrast to that of the MC method where only one event is treated. Results show that with little loss of accuracy the τ-leap based method can speed up the grinding simulation remarkably.