Abstract View
Radial Basis Neural Network Method for Solving Population Balance Equations for Particle Coagulation
KAIYUAN WANG, Pei Wang, Suyuan Yu, Wei Peng, Institute of Applied Physics and Computational Mathematics
Abstract Number: 175
Working Group: Aerosol Physics
Abstract
Many engineering applications and environmental processes involve population balances of particles, such as flame synthesis of nanoparticles, crystallization, polymerization, soot formation, atmospheric aging, and radioactive aerosols. The governing equation to describe the evolution of the number density function is called the population balance equation (PBE). The highly nonlinear nature and partial integral-differential characteristics of the PBE bring great challenges to the solution of this equation. Thus, it is of great theoretical and practical significance to study the numerical solution of the PBE. This study presents a radial basis neural network (RBNN) method for solving the PBE for particle coagulation. The new method approximates the number density function using an RBNN. The solution process of the PBE is comparable to the training process of a neural network. The final solution has an RBNN structure, which is also a bivariant analytical function of particle volume and time. Then the method is validated by comparing with analytical solutions and the sectional method for four numerical test problems. The comparison results show that the present method can almost accurately predict the time evolution of the number density function. The convergence analysis shows that the quality of the solution increases significantly with the increased number of center points.