Application of stochastic weighted algorithms to a multidimensional silica particle model

• Stochastic weighted algorithms (SWAs) are developed for a detailed silica model.
• An implementation of SWAs with the transition kernel is presented.
• The SWAs’ solutions converge to the direct simulation algorithm’s (DSA) solution.
• The efficiency of SWAs is evaluated for this multidimensional particle model.
• It is shown that SWAs can be used for coagulation problems in industrial systems.

This paper presents a detailed study of the numerical behaviour of stochastic weighted algorithms (SWAs) using the transition regime coagulation kernel and a multidimensional silica particle model. The implementation in the SWAs of the transition regime coagulation kernel and associated majorant rates is described. The silica particle model of Shekar et al. [S. Shekar, A.J. Smith, W.J. Menz, M. Sander, M. Kraft, A multidimensional population balance model to describe the aerosol synthesis of silica nanoparticles, Journal of Aerosol Science 44 (2012) 83–98] was used in conjunction with this coagulation kernel to study the convergence properties of SWAs with a multidimensional particle model. High precision solutions were calculated with two SWAs and also with the established direct simulation algorithm. These solutions, which were generated using large number of computational particles, showed close agreement. It was thus demonstrated that SWAs can be successfully used with complex coagulation kernels and high dimensional particle models to simulate real-world systems.