The Time Second-Order Characteristic FEM for Nonlinear Multicomponent Aerosol Dynamic Equations in Environment

Abstract

An efficient time second-order characteristic finite element method for solving the nonlinear multi-component aerosol dynamic equations is developed. While a highly accurate characteristic method is used to treat the advection multi-component condensation/evaporation process, a time high-order extrapolation along the characteristics is applied to approximate the nonlinear multi-component coagulation terms. The scheme is of second order accuracy in time for the multi-component problems. We study the theoretical analysis and obtain the time second-order error estimate of the scheme. Numerical experiments are further given to confirm the theoretical results. The dynamic behaviours of multi-component aerosol distributions are also simulated for the multi-component aerosol problems of aerosol water, black carbon and sulfate components with different tri-modal log-normal initial distributions.