| In this paper,the Chebyshev-spectral collocation method is adopted to the nonlinear aerosol dynamic equation.The paper is organized as follows.In Chapter 1,we briefly introduce the background of atmospheric aerosol particles and non-linear aerosol dynamic equation.Including,the concept of atmospheric aerosol,the classi-fication of particles and the movement mode of particles.And we briefly introduce the impor-tance of studying the non-linear aerosol dynamic equation,some classical numerical simulation methods and the Chebyshev-spectral collocation method used in this paper.In Chapter 2,we introduce the the nonlinear aerosol dynamic equations.In this paper,we considere the nonlinear aerosol dynamic equations of condensation,aggregation and settling:In Section 2.1,we give a brief introduction to the logarization of process and equation param-eters.In Section 2.2,we introduce the basic knowledge,lemmas and definitions that will be adopted in this paper.In Chapter 3,we propose the Chebyshev-spectral collocation method to study the non-linear aerosol dynamic equation.Firstly,we get the stability and convergence analysis of the semi-discrete schemes of the Chebyshev-spectral collocation method for the nonlinear aerosol dynamic equation.Secondly,we get the error estimates for the semi-discrete schemes.Finally,we derive the error estimate for the full discrete scheme of the Chebyshev-spectral collocation method for the nonlinear aerosol dynamic equation.In Chapter 4,we adopt the Chebyshev-spectral collocation model to some numerical ex-amples.In example 1,we test the error estimate of l? based on Chebyshev-spectral collocation method for the non-linear aerosol dynamic equation in condensation process.In example 2,we consider the effects of aerosol particles on the processes of condensation and aggregation during rainfall.From the particle size distribution of coagulation and aggregation,we can get the influence of each process on the particle size distribution intuitively. |
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