A Finite Element Solution of the Mathematical Model for Smoke Dispersion from Two Sources
Smoke discharging is a main reason of air pollution
problem from industrial plants. The obstacle of a building has an
affect with the air pollutant discharge. In this research, a mathematical
model of the smoke dispersion from two sources and one source with
a structural obstacle is considered. The governing equation of the
model is an isothermal mass transfer model in a viscous fluid. The
finite element method is used to approximate the solutions of the
model. The triangular linear elements have been used for discretising
the domain, and time integration has been carried out by semi-implicit
finite difference method. The simulations of smoke dispersion in
cases of one chimney and two chimneys are presented. The maximum
calculated smoke concentration of both cases are compared. It is then
used to make the decision for smoke discharging and air pollutant
control problems on industrial area.
[1] Ciuperca, I., Hafidi, I. and Jai, M., Analysis of a parabolic compressible
first-order slip Reynolds equation with discontinuous coefficients, Nonlinear
Analysis: Theory, Methods & Applications, 69(4) (2008), 1219-1234.
[2] Crank, J., Nicolson, P., A practical method for numerical solution of
partial differential equations of heat conduction type, Proc. Cambridge
Philos. Soc., 43:50-67, 1947.
[3] Hassan, M.H.A., Eltayeb, I.A., Diffusion of dust particles from a point
source above ground level and a line source at ground level, Geophys.
J. Int., 142 (2000), 426-438.
[4] Kai, S., Chun-qiong, L., Nan-shan, A. and Xiao-hong, Z., Using three
methods to investigate time-scaling properties in air pollution indexes
time series, Nonlinear Analysis: Real World Applications, 9(2) (2008),
693-707.
[5] Konglok, S.A., Tangmanee, S., Numerical Solution of Advection-
Diffusion of an Air Pollutant by the Fractional Step Method, Proceeding
in the 3rd national symposium on graduate research, Nakonratchasrima,
Thailand, July, 18th - 19th, 2002.
[6] Konglok, S.A., A K-model for simulating the dispersion of sulfur dioxide
in a tropical area, Journal of Interdisciplinary Mathematics, 10:789-799,
2007.
[7] Konglok, S.A., Pochai, N, Tangmanee, S., A Numerical Treatment of
the Mathematical Model for Smoke Dispersion from Two Sources,
Proceeding in International Conference in Mathematics and Applications
(ICMA-MU 2009), Bangkok, Thailand, December 17th - 19th, 2009.
[8] Naresh, R., Sundar, S. and Shukla, J.B., Modeling the removal of
gaseous pollutants and particulate matters from the atmosphere of a city,
Nonlinear Analysis: Real World Applications, 8(1) (2007), 337-344.
[9] Ninomiya, H. and Onishi, K., Flow analysis using a PC, CRC Press,
1991.
[10] Pasquill, F., Atmospheric Diffusion, 2nd edn., Horwood, Chicsester,
1974.
[11] Prez-Chavela, E. , Uribe, F.J. and Velasco, R.M., The global flow
in the Chapman mechanism , Nonlinear Analysis: Theory, Methods &
Applications, 71(1-2) (2009), 88-95.
[12] Richtmyer, R.D., Morton, K.W., Difference methods for initial-value
problems, Interscience, New York, 1967.
[13] Yanenko, N.N., The Method of fractional Steps, Springer-Verlag, 1971.
[1] Ciuperca, I., Hafidi, I. and Jai, M., Analysis of a parabolic compressible
first-order slip Reynolds equation with discontinuous coefficients, Nonlinear
Analysis: Theory, Methods & Applications, 69(4) (2008), 1219-1234.
[2] Crank, J., Nicolson, P., A practical method for numerical solution of
partial differential equations of heat conduction type, Proc. Cambridge
Philos. Soc., 43:50-67, 1947.
[3] Hassan, M.H.A., Eltayeb, I.A., Diffusion of dust particles from a point
source above ground level and a line source at ground level, Geophys.
J. Int., 142 (2000), 426-438.
[4] Kai, S., Chun-qiong, L., Nan-shan, A. and Xiao-hong, Z., Using three
methods to investigate time-scaling properties in air pollution indexes
time series, Nonlinear Analysis: Real World Applications, 9(2) (2008),
693-707.
[5] Konglok, S.A., Tangmanee, S., Numerical Solution of Advection-
Diffusion of an Air Pollutant by the Fractional Step Method, Proceeding
in the 3rd national symposium on graduate research, Nakonratchasrima,
Thailand, July, 18th - 19th, 2002.
[6] Konglok, S.A., A K-model for simulating the dispersion of sulfur dioxide
in a tropical area, Journal of Interdisciplinary Mathematics, 10:789-799,
2007.
[7] Konglok, S.A., Pochai, N, Tangmanee, S., A Numerical Treatment of
the Mathematical Model for Smoke Dispersion from Two Sources,
Proceeding in International Conference in Mathematics and Applications
(ICMA-MU 2009), Bangkok, Thailand, December 17th - 19th, 2009.
[8] Naresh, R., Sundar, S. and Shukla, J.B., Modeling the removal of
gaseous pollutants and particulate matters from the atmosphere of a city,
Nonlinear Analysis: Real World Applications, 8(1) (2007), 337-344.
[9] Ninomiya, H. and Onishi, K., Flow analysis using a PC, CRC Press,
1991.
[10] Pasquill, F., Atmospheric Diffusion, 2nd edn., Horwood, Chicsester,
1974.
[11] Prez-Chavela, E. , Uribe, F.J. and Velasco, R.M., The global flow
in the Chapman mechanism , Nonlinear Analysis: Theory, Methods &
Applications, 71(1-2) (2009), 88-95.
[12] Richtmyer, R.D., Morton, K.W., Difference methods for initial-value
problems, Interscience, New York, 1967.
[13] Yanenko, N.N., The Method of fractional Steps, Springer-Verlag, 1971.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59805", author = "Nopparat Pochai", title = "A Finite Element Solution of the Mathematical Model for Smoke Dispersion from Two Sources", abstract = "Smoke discharging is a main reason of air pollution
problem from industrial plants. The obstacle of a building has an
affect with the air pollutant discharge. In this research, a mathematical
model of the smoke dispersion from two sources and one source with
a structural obstacle is considered. The governing equation of the
model is an isothermal mass transfer model in a viscous fluid. The
finite element method is used to approximate the solutions of the
model. The triangular linear elements have been used for discretising
the domain, and time integration has been carried out by semi-implicit
finite difference method. The simulations of smoke dispersion in
cases of one chimney and two chimneys are presented. The maximum
calculated smoke concentration of both cases are compared. It is then
used to make the decision for smoke discharging and air pollutant
control problems on industrial area.", keywords = "Air pollution, Smoke dispersion, Finite element
method, Stream function, Vorticity equation, Convection-diffusion
equation, Semi-implicit method", volume = "5", number = "12", pages = "2044-5", }