| Aerosol modelling is very important to study and simulate the behavior of aerosol dynamics in the atmosphere. In this thesis, we consider the general aerosol dynamic equation which describes the spatial-temporal evolution of the aerosol distribution on size, time and space. The model is a nonlinear integro-partial differential equation including different processes of condensation, coagulation, deposition, nucleation as well as spatial convection and diffusion. A splitting wavelet-Galerkin method is proposed for solving the general aerosol dynamic equation. Wavelet-Galerkin method is designed in size direction due to the fact that aerosol distribution changes strongly along this direction and the wavelet technique can solve it very effectively. We adopt the class of Daubechies wavelets in the Galerkin scheme as the trial and weight functions based on its advantage of both compact support and orthonormality. Numerical experiments and simulations are taken for both spatially homogeneous and inhomogeneous aerosol dynamics. Numerical tests indicate the developed method to be accurate and effective. |
