Assessment of Radial Basis Function Network Method for Fractal-Like Agglomerate Dynamics

Abstract

During physical and chemical processes, aerosol particles often undergo coagulation to form Agglomerates. Agglomerates are fractal-like in a statistical sense, whose dynamical evolution of particle size distribution is governed by the population balance equation (PBE). In this study, the Radial Basis Function (RBF) method RBF is firstly extended to the solution of fractal-like agglomerate dynamics problems. The applicable conditions, and advantages and disadvantages of this method are studied. Two dynamic processes of fractal-like agglomerates, namely Brownian coagulation in the continuum regime and Brownian coagulation in the free molecular regime, are investigated. As a comparison, the sectional method (SM) is utilized as the referenced method. The initial geometric standard deviation (GSD) and the fractal dimension (\(D_{f}\)) of agglomerates are found to be the two main key factors affecting the accuracy and efficiency of the RBF. The RBF method is more suitable for calculating cases with larger GSD. As the GSD increases (i.e., GSD > 1.2), the computational efficiency and accuracy of the RBF increase accordingly. The RBF method is more suitable for calculating cases with larger \(D_{f}\). As the \(D_{f}\) decreases, the calculation error of RBF method becomes further larger, which is more obvious in the free molecular regime. Compared with the SM method, the calculation efficiency of RBF method increases by 3–4 orders of magnitude. This study provides excellent application of RBF method to the solution of the PBE.