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A numerical simulation on a two-dimensional atmospheric diffusion equation of an air pollution measurement model is proposed. The considered area is separated into two parts that are an industrial zone and an urban zone. In this research, the air pollution measurement by releasing the pollutant from multiple point sources above an industrial zone to the other area is simulated. The governing partial differential equation of air pollutant concentration is approximated by using a finite difference technique. The approximate solutions of the air pollutant concentration on both areas are compared. The air pollutant concentration levels influenced by multiple point sources are also analyzed.

A rapid growth of industrial sector can explain that air pollution affects the health of human being who lives around industrial areas. The air pollution has become a major problem of human life and environment. The purpose of this research was to study the air pollution assessment problem in two adjacent zones: industrial and urban zones by using the atmospheric diffusion model. In [

The source that is smokestack of industrial factory or power plant discharges the air pollution into the system. The genesis of air pollution is the cause of problems. In this research, the simple finite difference methods are used for solving the atmospheric diffusion equation.

The diffusion model generally uses Gaussian plume idea, which is the well-known atmospheric diffusion equation. It represents the behavior of air pollution in industrial areas. The dispersion of pollutant concentration from multiple point sources is described by the following three-dimensional advection-diffusion equation:

The assumptions of (

Now, we introduce the dimensionless form of equation (

We use the finite difference methods for calculating the nondimensional form of the atmospheric diffusion equation. In (

The first method, we use the forward difference in transient term that is

The second method, we use the backward difference in transient term that is

The two-dimensional atmospheric diffusion equation (

In Figure

Model of the problem.

Domain of solutions.

The air pollutant emission from multiple point sources above an industrial zone to the urban area is presented. The finite difference techniques introduced two methods for calculating the air pollutant concentrations. Figures

The air pollutant concentration levels after 2 hours passed which are computed by the forward time central space scheme (

The air pollutant concentration levels after 2 hours passed which are computed by the backward time central space scheme (

The air pollutant concentration levels after 2 hours passed which are computed by the forward time central space scheme (

The air pollutant concentration levels after 2 hours passed which are computed by the backward time central space scheme (

The air pollutant concentration between the forward time central space and the backward time central space schemes (

The air pollutant concentration between the forward time central space and the backward time central space schemes (

Figures

Computing time comparison of forward time central space and backward time central space schemes.

Simulation Time | FTCS (sec.) | BTCS (sec.) |
---|---|---|

30 minutes | 1.49 | 22.48 |

1 hour | 1.68 | 42.66 |

2 hours | 2.05 | 84.18 |

The air pollutant concentration between 2 cases: added sink and without sink (computed by the forward time central space scheme) at

The air pollutant concentration between 2 cases: added sink and without sink (computed by the forward time central space scheme) at

The air pollutant concentration with the variant values of sink rate (computed by the forward time central space scheme) at

The simple air pollution measurement models which are released air pollutants by a single point source and coupled point sources are proposed. The traditional finite difference methods such as forward time central space and backward time central space schemes can be used to approximate the air pollutant levels for each points and times. The results of this study show that the air pollutant concentrations of forward time central space are close to the air pollutant concentrations of backward time central space. In the case of a coupled point sources problem, the overall concentration levels of air pollution are less than a single point source problem. Therefore, the influence of multiple point sources and the variable rate of sink are also considered. It obtains that the higher sink rate does decrease pollutant levels around human living. The both finite difference methods are used to compute the numerical solutions of air pollution by MATLAB. The forward time central space has advantages that the method gives less computing time than the backward time central space computing time. On the other hand, the forward time central space also has disadvantages that are the limitation of the grid spacing due to the stability condition.

The calculated air pollution measurement data used to support the findings of this study are available from the corresponding author upon request.

A part of the research has been presented as an oral presentation in ACFPTO 2016.

The authors declare no conflicts of interest.

This research is supported by the Centre of Excellence in Mathematics, the Commission on Higher Education, Thailand.