198
Air Pollution and Turbulence: Modeling and Applications
variables. For such, we circumvent the disability of the Laplace transform to handle
this sort of problems by the application of decomposition method (Adomian, 1988).
By doing so, we reduce the advection–diffusion equation with the velocity fi eld
depending on time variable into a set of recursive diffusion equations with source
carrying the time information, which has a well-known solution. The motivation
for this procedure comes from the fact that the resulting recursive problems can be
straightly solved by the methodology discussed in this chapter. Bearing in mind
the aptness of the decomposition method to solve, analytically, nonlinear problems, we are also confi dent to affi rm that this methodology is a promising approach
to handle nonlinear problems of pollutant dispersion in atmosphere appearing in
problems with pollutants subject to chemical reaction. We hope that with the formulation reported we paved the road to update the GILTT formulation to simulate
pollutant dispersion in the described scenarios. We shall focus our future attention
in these directions.
REFERENCES
Abate, J. and Valkó, P.P., 2004. Multi-precision Laplace transform inversion. Int. J. Num.
Methods Eng. 60, 979–993.
Adomian, G., 1988. A review of the decomposition method in applied mathematics, J. Math.
Anal. Appl. 1(135), 501–544.
Arya, P., 1995. Modeling and parameterization of near-source diffusion in weak winds.
J. Appl. Meteor. 34, 1112–1122.
Barad, M.L., 1958. Project Prairie Grass’. Geophysical Research Paper, No. 59, vols. I and
II, GRD, Bedford, MA.
Bechtold, P., Bazile, E., Guichard, F., Mascart, P., and Richard, E., 2001. A mass fl ux convection scheme for regional and global models. Quart. J. Roy. Meteor. Soc. 127, 869–886.
Biagio, R., Godoy, G., Nicoli, I., Nicoli, D., and Thomas, P., 1985. First Atmospheric Diffusion
Experiment Campaign at the Angra Site—KfK 3936. Karlsruhe and CNEN 1201, Rio
de Janeiro.
Blackadar, A.K., 1997. Turbulence and Diffusion in the Atmosphere: Lectures in Environmental
Sciences, Springer-Verlag, Berlin, Germany, p. 185.
Buske, D., Vilhena, M.T., Moreira, D.M., and Tirabassi, T., 2006. Analytical solution for the
transient two-dimensional advection-diffusion equation considering nonlocal closure of
the turbulent diffusion. In: K. Hanjalic, Y. Nagano, S. Jakirlic (eds.), Turbulence, Heat,
and Mass Transfer 5. Begel House Inc., New York, pp. 705–708.
Buske, D., Vilhena, M.T., Moreira, D.M., and Tirabassi, T., 2007a. An analytical solution of
the advection-diffusion equation considering non-local turbulence closure. Environ.
Fluid Mech. 7, 43–54.
Buske, D., Vilhena, M.T., Moreira, D.M., and Tirabassi, T., 2007b. Simulation of pollutant
dispersion for low wind conditions in stable and convective planetary boundary layer.
Atmos. Environ. 41, 5496–5501.
Buske, D., Costa, C., Tirabassi, T., Moreira, D.M., and Vilhena, M.T., 2007c. An unsteady analytical solution of advection-diffusion equation for low wind conditions, Proceedings do
XXVIII CILAMCE, Porto, Portugal.
Buske, D., Vilhena, M.T., Moreira, D.M., and Bodmann, B., 2008. An analytical solution
for the steady-state two-dimensional diffusion-advection-deposition model by the
GILTT approach. In: C. Constanda, S. Potapenko (eds.), Integral Methods in Science
and Engineering: Techniques and Applications, XVI ed. Birkhauser, Boston, MA, pp.
27–36.
© 2010 by Taylor and Francis Group, LLC
Air Pollution and Turbulence: Modeling and Applications
variables. For such, we circumvent the disability of the Laplace transform to handle
this sort of problems by the application of decomposition method (Adomian, 1988).
By doing so, we reduce the advection–diffusion equation with the velocity fi eld
depending on time variable into a set of recursive diffusion equations with source
carrying the time information, which has a well-known solution. The motivation
for this procedure comes from the fact that the resulting recursive problems can be
straightly solved by the methodology discussed in this chapter. Bearing in mind
the aptness of the decomposition method to solve, analytically, nonlinear problems, we are also confi dent to affi rm that this methodology is a promising approach
to handle nonlinear problems of pollutant dispersion in atmosphere appearing in
problems with pollutants subject to chemical reaction. We hope that with the formulation reported we paved the road to update the GILTT formulation to simulate
pollutant dispersion in the described scenarios. We shall focus our future attention
in these directions.
REFERENCES
Abate, J. and Valkó, P.P., 2004. Multi-precision Laplace transform inversion. Int. J. Num.
Methods Eng. 60, 979–993.
Adomian, G., 1988. A review of the decomposition method in applied mathematics, J. Math.
Anal. Appl. 1(135), 501–544.
Arya, P., 1995. Modeling and parameterization of near-source diffusion in weak winds.
J. Appl. Meteor. 34, 1112–1122.
Barad, M.L., 1958. Project Prairie Grass’. Geophysical Research Paper, No. 59, vols. I and
II, GRD, Bedford, MA.
Bechtold, P., Bazile, E., Guichard, F., Mascart, P., and Richard, E., 2001. A mass fl ux convection scheme for regional and global models. Quart. J. Roy. Meteor. Soc. 127, 869–886.
Biagio, R., Godoy, G., Nicoli, I., Nicoli, D., and Thomas, P., 1985. First Atmospheric Diffusion
Experiment Campaign at the Angra Site—KfK 3936. Karlsruhe and CNEN 1201, Rio
de Janeiro.
Blackadar, A.K., 1997. Turbulence and Diffusion in the Atmosphere: Lectures in Environmental
Sciences, Springer-Verlag, Berlin, Germany, p. 185.
Buske, D., Vilhena, M.T., Moreira, D.M., and Tirabassi, T., 2006. Analytical solution for the
transient two-dimensional advection-diffusion equation considering nonlocal closure of
the turbulent diffusion. In: K. Hanjalic, Y. Nagano, S. Jakirlic (eds.), Turbulence, Heat,
and Mass Transfer 5. Begel House Inc., New York, pp. 705–708.
Buske, D., Vilhena, M.T., Moreira, D.M., and Tirabassi, T., 2007a. An analytical solution of
the advection-diffusion equation considering non-local turbulence closure. Environ.
Fluid Mech. 7, 43–54.
Buske, D., Vilhena, M.T., Moreira, D.M., and Tirabassi, T., 2007b. Simulation of pollutant
dispersion for low wind conditions in stable and convective planetary boundary layer.
Atmos. Environ. 41, 5496–5501.
Buske, D., Costa, C., Tirabassi, T., Moreira, D.M., and Vilhena, M.T., 2007c. An unsteady analytical solution of advection-diffusion equation for low wind conditions, Proceedings do
XXVIII CILAMCE, Porto, Portugal.
Buske, D., Vilhena, M.T., Moreira, D.M., and Bodmann, B., 2008. An analytical solution
for the steady-state two-dimensional diffusion-advection-deposition model by the
GILTT approach. In: C. Constanda, S. Potapenko (eds.), Integral Methods in Science
and Engineering: Techniques and Applications, XVI ed. Birkhauser, Boston, MA, pp.
27–36.
© 2010 by Taylor and Francis Group, LLC