A computational scheme of air pollutant transfer and diffusion with a finite difference method.

Abstract

In order to represent or predict concentrations of air pollutants continuously, a finite difference model was offered to solve the nonlinear diffusion equation on the assumption that variable winds and diffusion parameters were given in all meshes at any time in some way. Insecurities and errors of finite difference calculation were avoided with adopting Lax-Wendroff method for horizontal transfer, backward step for vertical transfer, forward step for horizontal diffusion and Clank-Nicolson method for vertical diffusion after examination of various difference schemes. Restrictive conditions were confirmed also for steps of time and space. Verification of the model was conducted with comparison between analytical solutions of the diffusion equation for uniform wind and constant diffusion coefficients in the field and numerical solution for the same wind and diffusivity. As an analytical solution, a puff model was adopted for calm and breezy conditions and a plume model was used for windy condition. The verification in various stability categories showed sufficient accuracy to justify practical use, except a few cases that the concentration peak with the numerical model distributed slightly flatter than that with the puff model in the limited periods of breezy condition. Noise undulations in the leeward boundary and their extensions to windward in windy condition were removed with such a regulation that Δc/Δx≈0 was satisfied in the leeward boundary.