Radial Basis Function Method for Predicting the Evolution of Aerosol Size Distributions for Coagulation Problems

Abstract

The dynamic evolution of particle size distributions (PSDs) during coagulation is of great importance in many atmospheric and engineering applications. To date, various numerical methods have been developed for solving the general dynamic equation under different scenarios. In this study, a radial basis function (RBF) method was proposed to solve particle coagulation evolution. This method uses a Gaussian function as the basis function to approximate the size distribution function. The original governing equation was then converted to ordinary differential equations (ODEs), along with numerical quadratures. The RBF method was compared with the analytical solutions and sectional method to validate its accuracy. The comparison results showed that the RBF method provided almost accurate predictions of the PSDs for different coagulation kernels. This method was also verified to be reliable in predicting the self-preserving distributions reached over long periods and for describing the temporal evolution of moments. For multimodal coagulation, the RBF method also accurately predicted the temporal evolution of a bimodal distribution owing to scavenging effects. Moreover, the computational times of the RBF method for these cases were usually of the order of seconds. Thus, the RBF method is verified as a reliable and efficient tool for predicting PSD evolution during coagulation.