tailieunhanh - Application of the Bessel function to compute the air pollutant with the stratification of the atmospheric

In this paper, present the analytic solutions of the atmospheric advection-diffusion equation with the stratification of the boundary condition. The solution has been found by applied the separation of variable method and Bessel’s equation. | SCIENCE & TECHNOLOGY DEVELOPMENT, Vol 18, 2015 Application of the Bessel function to compute the air pollutant with the stratification of the atmospheric Tran Anh Dung 1 Chu Thi Hang 1 Bui Ta Long 2 1 Industrial University of Ho Chi Minh city. 2 Ho Chi Minh city University of Technology, VNU-HCM (Manuscript Received on August 01st, 2015, Manuscript Revised August 27th, 2015) ABSTRACT: The Bessel differential equation with the Bessel function of solution has been applied. Bessel functions are the canonical solutions of Bessel's differential equation. Bessel's equation arises when finding separable solutions to Laplace's equation in cylindrical or spherical coordinates. Bessel functions are important for many problems of advection–diffusion progress and wave propagation. In this paper, authors present the analytic solutions of the atmospheric advection-diffusion equation with the stratification of the boundary condition. The solution has been found by applied the separation of variable method and Bessel’s equation. Keywords: Air pollutant, Bessel function, the separation of variable method 1. INTRODUCTION The air pollution modeling often leads to solving the general second order partial differential equations (PDE) [11]. The most commonly equation is steady state atmospheric advection – diffusion equation. The separation of variable method is used to solve the PDE. This method is simpler than the Green function method [8], [10], [9]. The atmospheric advection – diffusion equation is transformed to the Bessel equation, with the solution is Bessel function [1]. In this paper, the authors introduce the applications of Bessel equations to solve atmospheric advection - diffusion. The boundary conditions considering the factors of atmospheric stratification and divided into four main types: Dirichlet (total absorption), Neumann (total reflection), Mixed type I (reflections at the Page 14 ground, absorption at inversion layer) and Mixed Type II .