Dezembro 2021 vol. 8 num. 4 - VII Simpósio Internacional de Inovação e Tecnologia

Original Article - Open Access.

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UMA NOVA METODOLOGIA PARA A SOLUÇÃO DA EQUAÇÃO DE DIFUSÃO-ADVECÇÃO NA CAMADA LIMITE PLANETÁRIA USANDO DERIVADA CONFORMÁVEL

A NEW METHODOLOGY FOR THE SOLUTION OF THE ADVECTION-DIFFUSION EQUATION IN THE PLANETARY BOUNDARY LAYER USING CONFORMABLE DERIVATIVE

Silva, José Roberto Dantas da ; Xavier, Paulo Henrique Farias ; Palmeira, Anderson da Silva ; Soledade, André Luiz Santos da ; Moreira, Davidson Martins ;

Original Article:

O objetivo deste trabalho é descrever uma proposta metodológica para o desenvolvimento de uma solução da equação difusão-advecção bidimensional fracionária, considerando uma camada limite planetária não homogênea (CLP). Utiliza-se o método ADMM (Advection-Diffusion Multilayer Method) que fornece uma solução semianalítica baseada na discretização da CLP em subcamadas e a equação de advecção-difusão é resolvida pela aplicação da técnica da transformada de Laplace, agora incluindo como novidade a derivada conformável. Este procedimento gera uma nova metodologia denominada alpha- ADMM.

Original Article:

"The objective of this work is to describe a methodological proposal for the development of a solution of the fractional two-dimensional diffusion-advection equation considering a non-homogeneous planetary boundary layer (PBL). The method ADMM (Advection-Diffusion Multilayer Method) is used, which provides a semi-analytical solution based on the discretization of the PBL in sublayers, and the advection-diffusion equation is solved by applying the Laplace transform technique, now including the novelty of the conformable derivatives. This procedure generates a new methodology called alpha-ADMM."

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Palavras-chave: Modelagem matemática; Equação de difusão-advecção; Método ADMM; Camada Limite Planetária,

Palavras-chave: Mathematical modeling; Advection-diffusion equation; ADMM method; Planetary Boundary Layer,

DOI: 10.5151/siintec2021-208187

Referências bibliográficas
  • [1] "1 VILHENA, M. T. B.; RIZZA, U., DEGRAZIA, G., MANGIA, C., MOREIRA, D., and TIRABASSI, T., 1998. “An analytical air pollution model: Development and evaluation”, Contrib. Atmos. Phys, vol. 71, pp. 818-827.
  • [2] 2 MOREIRA, D.M., RIZZA, U., VILHENA, M.T., GOULART, A., 2005. Semi-analytical model for pollution dispersion in the planetary boundary layer. Atmospheric Environment 39 (14), 2689–2697.
  • [3] 3 KHALIL, Roshdi, et al. 2014. A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264: 65-70.
  • [4] 4 ORTIGUEIRA, M.D. and MACHADO, J.A.T., 2015. What is a fractional derivative? Journal of Computational Physics 293, 4-13.
  • [5] 5 TARASOV, V.E., 2018. No nonlocality. No fractional derivative. Communications in Nonlinear Science and Numerical Simulation 62, 157-163.
  • [6] 6 CAPUTO, M. and FABRIZIO, 2015. M. Prog. Fract. Differ. Appl.1, 73 (2015).
  • [7] 7 XAVIER, P.H.F.; NASCIMENTO, Erick Giovani Sperandio; MOREIRA, Davidson Martins. 2019. A model using fractional derivatives with vertical eddy diffusivity depending on the source distance applied to the dispersion of atmospheric pollutants. Pure and Applied Geophysics, 176.4: 1797-1806
  • [8] 8 SILVA, J.R.D.; XAVIER, Paulo Henrique Farias; PALMEIRA, Anderson da Silva; MOREIRA, Davidson Martins. 2020. ""Fractional calculus: an approach to the atmospheric dispersion equation using conformable derivative"", p. 594-602. In: Anais do VI Simpósio Internacional de Inovação e Tecnologia. São Paulo: Blücher, ISSN 2357-7592, ISBN:2357-7592, doi:10.5151/siintec2020-fractionalcalculus.
  • [9] 9 SILVA, J.R.D. 2021. Fractional calculus: historical, philosophical aspects and relevance in modeling and problem solving / José Roberto Dantas da Silva, 73-fl, Dissertation (Master’s in computational modeling and industrial technology) – PPG-MCTI – Centro Universitário SENAI-CIMATEC, Salvador-Ba.
  • [10] 10 PALMEIRA, Anderson; Xavier, PAULO; MOREIRA, Davidson. Simulation of atmospheric pollutant dispersion considering a bi-flux process and fractional derivatives. Atmospheric Pollution Research, 2020, 11.1: 57-66.
  • [11] 11 GOMEZ-AGUILAR, J.F., MIRANDA-HERNANDEZ, M., LOPEZ-LOPEZ, M.G., ALVARADO-MARTINEZ, V.M. e BALEANU, D., 2016. Modeling and simulation of the fractional space-time diffusion equation. Commun. Nonlinear Sci. Numer. Simul. 30, 115-127.
  • [12] 12 MOREIRA, D.M. and VILHENA, M.T., 2009. Air Pollution and Turbulence: Modeling and Applications. CRC Press, Boca Raton, Florida, 354 pp.
  • [13] 13 TALBOT, A. 1979. The accurate numerical inversion of Laplace transforms. IMA Journal of Applied Mathematics, 23(1), 97-120.
  • [14] 14 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. Atmospheric Environment, 40 (29), 5659-5669.
  • [15] 15 ARYA, S.P., 2003. A review of the theoretical bases of short-range atmospheric dispersion and air quality models. Proceedings of the Indian National Science Academy 69A (6), 709–724.
  • [16] 16 DEGRAZIA, G.A., MOREIRA, D.M., VILHENA, M.T., 2001. Derivation of an eddy diffusivity depending on source distance for vertically inhomogeneous turbulence in a convective boundary layer. Journal of Applied Meteorology 40, 1233–1240.
  • [17] 17 GRYNING, S.E., LYCK, E., 1984. Atmospheric dispersion from elevated sources in an urban area: comparison between tracer experiments and model calculations. American Meteorological Society 23, 651–660.
  • [18] 18 HANNA, S.R., 1989. Confidence limit for air quality models as estimated by bootstrap and jacknife resampling methods. Atmospheric Environment 23, 1385–1395.
  • [19] 19 LIN, J.S., HILDEMANN, L.M., 1997. Analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities. Atmospheric Environment 30, 239–254.
  • [20] 20 MOREIRA, D.M., VILHENA, M.T., TIRABASSI, T., BUSKE, D., COTTA, R.M., 2005b. Near source atmospheric pollutant dispersion using the new GILTT method. Atmospheric Environment 39 (34), 6290–6295.
  • [21] 21 MOREIRA, D.M., TIRABASSI, T., CARVALHO, J.C., 2005c. Plume dispersion simulation in low wind conditions in stable and convective boundary layers. Atmospheric Environment 39 (20), 3643–3650.
  • [22] 22 MOREIRA, Davidson; MORET, Marcelo. A New Direction in the Atmospheric Pollutant Dispersion inside the Planetary Boundary Layer. Journal of Applied Meteorology and Climatology, 2018, 57.1: 185-192.
  • [23] 23 OETTL, D., ALMBAUER, R.A., STURM, P.J., 2001. A new method to estimate diffusion in stable, low-wind conditions. Journal of Applied Meteorology 40, 259–268.
  • [24] 24 TIRABASSI, T., 1989. Analytical air pollution advection and diffusion models. Water, Air and Soil Poll 47, 19–
  • [25] 25 ZANNETTI, P., 1990. Air Pollution Modeling. Computational Mechanics Publications, Southampton, 444pp."
Como citar:

Silva, José Roberto Dantas da; Xavier, Paulo Henrique Farias; Palmeira, Anderson da Silva; Soledade, André Luiz Santos da; Moreira, Davidson Martins; "UMA NOVA METODOLOGIA PARA A SOLUÇÃO DA EQUAÇÃO DE DIFUSÃO-ADVECÇÃO NA CAMADA LIMITE PLANETÁRIA USANDO DERIVADA CONFORMÁVEL", p. 369-376 . In: VII International Symposium on Innovation and Technology. São Paulo: Blucher, 2021.
ISSN 2357-7592, DOI 10.5151/siintec2021-208187

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