CONVERGENCE ANALYSIS OF THE GILTT METHOD FOR PROBLEMS IN POLLUTANT DISPERSION IN THE ATMOSPHERE

Daniela Buske, Cláudio Zen Petersen, Régis Sperotto de Quadros, Glênio Aguiar Gonçalves, Juliana Ávila Contreira

Abstract


In this paper, we present a convergence analysis of the GILTT method for pollutant dispersion problems consolidating the solution of the problem in analytical representation. There have been many advances in the GILTT technique over the past few years. The advection-diffusion equation was solved for the multidimensional case and applied to various situations, mainly in pollutant dispersion. The theorem of Cauchy-Kowalewsky guarantees the existence and uniqueness of an analytic solution for the advection-diffusion equation. In this paper, we present a convergence analysis for the GILTT method to pollutant dispersion problems. Numerical results are presented.


Keywords


Analytical solution. GILTT. Convergence analysis.

References


Buske, D., Vilhena, M.T., Tirabassi, T., Bodmann, B. (2012). Air Pollution Steady-State Advection-Diffusion Equation: The General Three-Dimensional Solution. J. Env. Protection, 3, 1124-1134.

Carvalho, J. C., Moreira, D. M. (2007). Evaluation of two semi-analytical techniques in air quality applications. Rev. Brasileira de Meteorologia, 22, 10–20.

Costa, C.P., Vilhena, M.T., Moreira, D.M., Tirabassi, T. (2006). Semi-analytical solution of the steady three-dimensional advection-diffusion equation in the planetary boundary layer. Atmos. Environ., 40 (29), 5659-5669.

Cotta, R., Mikhaylov, M. (1997). Heat conduction lumped analysis, integral transforms, symbolic computation, John Wiley Sons, Baffins Lane, Chinchester, England.

Courant, R., Hilbert, D. (1989). Methods of Mathematical Physics , John Wiley & Sons.

Degrazia, G.A., Campos Velho, H.F., Carvalho, J.C. (1997). Nonlocal exchange coefficients for the convective boundary layer derived from spectral properties. Contr. Atmos. Phys., 57-64.

Hanna, S.R., Briggs, G.A., Hosker Jr., R.P. (1982). Handbook on Atmospheric Diffusion. Oak Ridge, Tenessee: U. S: Department of Energy, Technical Information Center, 102p.

Irwin, J.C. (1979). A theoretical variation of the wind profile power-law exponent as a function of surface roughness and stability. Atm. Environ., 13, 191-194.

Mangia,C., Moreira,D.M., Schipa,I., Degrazia, G.A., Tirabassi,T. (2002). Evaluation of a new eddy diffusivity parameterization from turbulent Eulerian spectra in different stability conditions. Atm. Environ, 36, 67-76.

Moreira, D.M., Tirabassi, T. (2004). Modelo matemático de Dispersão de

poluentes na atmosfera: um instrumento técnico para gestão ambiental. Ambiente & Sociedade, 7 (2), 169-171.

Moreira, D.M, Vilhena, M.T., Tirabassi, T., Costa, C., Bodmann, B. (2006). Simulation of pollutant dispersion in atmosphere by the Laplace transform: the ADMM approach. Water, Air and Soil Pollution, 177, 411-439.

Moreira, D.M., Vilhena, M.T., Buske, D., Tirabassi, T. (2009). The State-of-art of the GILTT Method to Simulate Pollutant Dispersion in the Atmosphere. Atm. Research., 92, 1-17.

Panofsky, A.H., Dutton, J.A. (1984). Atmosferic Turbulence. John Wiley & Sons, New York.

Wortmann, S., Vilhena, M.T., Moreira, D.M., Buske, D. (2005). A new analytical approach to simulate the pollutant dispersion in the PBL. Atmos. Environ., 39, 2171-2178.




DOI: https://doi.org/10.5902/2179460X20156

Copyright (c) 2016



Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.