Legendre-galerkin Spectral Methods For Non-linear Aerosol Dynamic Equations

Aerosols are now an important part of the atmosphere.They can absorb incoming solar radiation to cause warming and even affect human health.Therefore,the study and simulation of aerosol dynamic behavior in atmospheric environment is a key field in environmental science.In this paper,the Legendre-Galerkin spectral method is used to solve the aerosol dynamic equations and theoretical analysis of the error,which consists of the following four chapters.The first chapter briefly introduces the background of atmospheric aerosol particles,in-cluding the concept of atmospheric aerosol,particle classification and particle movement mode.Then some classical numerical simulation methods and the Legendre-Galerkin spectral method used in this paper are introduced.The second chapter firstly introduces the aerosol model,which includes three processes of condensation,coagulation and removal.It is a nonlinear integral-differential equation:Then the particle distribution logarithmic coordinates,interval projection transformation and the treatment of boundary are briefly introduced.Finally,the relevant knowledge of Legendre-Galerkin spectral method is introduced,and the derivation process of solving the aerosol dy-namic equations based on Legendre-Galerkin spectral method is given.The third chapter,the errors of the Legendre-Galerkin spectral method for nonlinear aerosol dynamic equations are analyzed.In theory,the convergence errors of spectral accuracy can be obtained by the above two schemes.The fourth chapter Legendre-Galerkin spectral method is applied to numerical examples.Example 1 and 2 are used to test the error estimate L₂of solving the aerosol dynamic equations with the Legendre-Galerkin spectral method for the process of condensation and removal,and the error graphs of the variation of the error with the number of spatial subdivision are given.Finally,the particle size distribution figure of the condensation and removal processes were drawn,from which we can directly see the condensation and removal process to the influence of aerosol particle size distribution.