The conservative characteristic FD methods for atmospheric aerosol transport problems

In the paper, we develop the new conservative characteristic finite difference methods (C-CFD) for the atmospheric aerosol transport problems. We propose the time second-order and spatial high-order conservative characteristic finite difference methods for the aerosol vertical advection-diffusion process and the two-dimensional conservative characteristic finite difference methods for aerosol horizontal transport process in the second-order splitting algorithm. Based on the characteristic form of advection-diffusion equations tracking back along the characteristic curve, we treat the integrals over the tracking cells at the previous time level by the conservative interpolations and propose to treat the diffusion terms by the average along the characteristics, where the high-order discrete fluxes are obtained by approximating the cumulative mass function and are continuous at the tracking points. The important feature is that the proposed C-CFD schemes preserve mass and have second-order accuracy in time and high-order accuracy in space. Numerical tests are taken to show the accuracy in time and space and mass conservation of our C-CFD schemes, compared with the standard CFD method. A real case of air quality modelling during the 2008 Beijing Olympics and a severe haze in North China are further simulated and analyzed by using our C-CFD algorithm. Simulated results are in good agreement with observations. The developed C-CFD algorithm can be used for efficiently solving large scale atmospheric aerosol transport problems.