A new splitting wavelet method for solving the general aerosol dynamics equation

In this paper, a new and robust splitting wavelet method has been developed to solve the general aerosol dynamics equation. The considered models are the nonlinear integro-partial differential equations on time, size and space, which describe different processes of atmospheric aerosols including condensation, nucleation, coagulation, deposition, sources as well as turbulent mixing. The proposed method reduces the complex general aerosol dynamic equation to two one-dimensional splitting equations in each time interval, and further the wavelet method and the upstream finite difference method are proposed for solving the particle size directional and the spatial directional splitting equations. By the method, the aerosol size spectrum is represented by a combination of Daubechies’ wavelets and substituted into the size-directional splitting equation at each time step. The class of Daubechies’ wavelets in the wavelet-Galerkin scheme as trial and weight functions has the advantages of both compact support and orthonormality which can efficiently simulate the sharp shape distribution of aerosols along the particle size direction. Numerical experiments are given to show the efficient performance of the method.