A new method for solving population balance equations using a radial basis function network

Abstract

This study presents a new method for solving the population balance equation (PBE) for particle coagulation. The method introduces a radial basis function network to approximate the number density function. The approximate solution should satisfy the PBE at the collocation points in a continuous manner. The coagulation terms in the PBE are directly handled using the Gaussian quadrature techniques. The final solution is a bivariant analytical function of particle volume and time, which can be easily used in any subsequent calculation. Then the method is validated by comparing with analytical solutions and the sectional method for four numerical test problems. These problems are selected to vary in coagulation kernels and initial conditions. The comparative results show that the present method can accurately predict the time evolution of the number density function. Moreover, the computational efficiency of the present method is quite acceptable considering the high accuracy. Copyright © 2020 American Association for Aerosol Research.