Numerical Analysis Of Characteristic Finite Volume Methods For Non-linear Aerosol Dynamic Equations

Aerosol particles have an important effect on changing of climate and hu-man health, furthermore, aerosol modeling has been playing a significant role in terms of studying and simulating the behavior of aerosol dynamics. Thus it is very important and necessary to study the aerosol modeling. In this paper, we consider the non-linear aerosol dynamic equations, which contain convective-condensation and nonlinear coagulation process. The error estimates of finite volume method (FVM)and characteristic finite volume method (C-FVM) are given rigorously.Finite volume element method(L-FVM) based on linear interpolation for solving non-linear aerosol dynamic equations is studied in [9], and some nu-merical examples are proved that the scheme is of second order accuracy, but theoretical estimates are not given. In this paper, we analyze errors of con-tinuous time and discrete time linear finite volume methods, and proved the global existence and uniqueness of solution of continuous time linear finite volume method which is established for the nonlinear aerosol dynamics.Characteristic finite volume element methods based on linear interpolation and hcrmite interpolation are developed, and we study the theoretical analysis and obtain the second-order and four-order error estimates of the methods respectively. We can obtain that the linear C-FVM has a higher error accuracy By comparing L-FVM and linear C-FVM.At the end of the article, two numerrical experiments using L-FVM and linear C-FVM are given to verify the theoretical analysis.