A time-driven constant-number Monte Carlo method for the GPU-simulation of particle breakage based on weighted simulation particles

Abstract

Monte Carlo (MC) simulations based on weighted particles offer novel and more precise techniques for the solution of the population balance equation for particulate systems. A recent constant-number approach named stochastic weighted algorithm (SWA) (Lee et al. (2015), J. Comput. Phys. (303) 1–18) has been developed, which renders the breakage of a simulation particle by an alteration of its properties, without the creation of novel simulation particles. The theoretic justification of the general formulation for all possible SWAs is limited to binary breakage kernels. We present a novel approach for the derivation of the properties of the MC particles representing fragments, which is applicable for all sorts of breakage kernels. This general scheme encompasses the already introduced SWA schemes, especially a number-based (SWA1, named NBS in this paper) and volume-based (SWA2, named VBS in this paper) breakage scheme, and it makes novel formulations possible: the low volume scheme (LVS), which renders preferably lower fragment sizes, and the combination of LVS with the NBS (LVS-NBS) or VBS (LVS-VBS). The implementation of these breakage schemes in the context of a GPU-based time-driven method is presented and the gained results are validated by comparison with results of the analytic solutions of a homogeneous binary breakage kernel. It is found, that the SWA methods (NBS and VBS) are only able to render large particle sizes, and that LVS, NBS-LVS and VBS-LVS are able to render the whole spectrum of particle sizes. Smaller noise levels are found for VBS and specific VBS-LVS schemes, making both more suitable for prolonged simulations than the other presented methods.