Different Numerical Inversion Algorithms of the Laplace Transform for the Solution of the Advection-Diffusion Equation with Non-local Closure in Air Pollution Modeling

Camila Pinto da Costa, Karine Rui, Léslie Darien Pérez-Fernández


In this paper, a three-dimensional solution of the steady-state advection-diffusion equation is obtained applying the Generalized Integral Advection Diffusion Multilayer Technique (GIADMT), considering non-local closure for turbulent flow. Two different parameterizations were considering for the countergradient term and different methods of numerical inversion for inverse Laplace transform. The results were compared with the experimental data of Copenhagen experiment by an evaluation of statistical indices to analyse the solution of the equation through the methods of numerical inversion. Differents parameterizations for the vertical turbulent eddy diffusivity and wind profile were utilized. The results show a good agreement with the experiment and the methods of numerical inversion for inverse Laplace transform show same efficacy.




Non-local closure; numerical inversion; pollutant dispersion

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J. Abate, P. Valkó, Multi-precision Laplace transform inversion, Int. J. Numer. Methods Eng. , 60 (2004), 979-993.

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

R. M. Cotta, Integral transforms in computational heat and fluid fow, Boca Raton, Florida: CRC Press, 1993.

K. S. Crump, Numerical Inversion of Laplace Transforms Using a Fourier series approximation, J. ACM , 23 , No. 1 (1976), 89-96.

J. W. M. Cuijpers, A. A. M. Holtslag, Impact of skewness and nonlocal effects on scalar and buoyancy fluxes in convective boundary layers,

J. Atmos. Sci. , 55 (1998), 151-162.

J. W. Deardor, Theoretical expression for the countergradient vertical heat flux, J. Geophys. Res. , 77 (1972), 5900-5904.

G. A. Degrazia, D. M. Moreira, M. T. Vilhena, Derivation of an eddy diffusivity depending on source distance for vertically inhomogeneous turbulence in a convective boundary layer, J. Appl. Meteor. , (2001), 1233-1240.

G. A. Degrazia, U. Rizza, C. Mangia, T. Tirabassi, Validation of a new turbulent parameterization for dispersion models in convective conditions,

Boundary-Layer Meteor. , 85 , No. 2 (1997), 243-254.

S. E. Gryning, E. Lyck, The Copenhagen Tracer Experiments: Reporting of Measurements, Riso National Laboratory, 2002.

S. R. Hanna, Condence limits for air quality models, as estimated by bootstrap and jackknife resampling methods, Atmos. Environ. , 23 (1989), 1385-1395.

J. S. Irwin, A theoretical variation of the wind profile power-law exponent as a function of surface roughness and stability, Atmos. Environ. , 13 , No. 1 (1979), 191-194.

D. M. Moreira, M. T. Vilhena, T. Tirabassi, C. P. Costa, B. Bodmann, Simulation of pollutant dispersion in the atmosphere by the laplace transform: The ADMM approach, Water, Air, Soil Pollut. , 77 , No. 1-4 (2006), 411-439.

Moreira, D.M., Moraes, A.C., Goulart, A.G., Albuquerque, T.T.A., 2014. A contribution to solve the atmospheric diffusion equation with eddy diffusivity depending on source distance. Atmospheric Environment 83, 254-259.

A. H. Panofsky, A. J. Dutton, Atmospheric Turbulence, John Wiley & Sons, New York, 1984.

J. Pleim, J. Chang, A non-local closure model for vertical mixing in the convective boundary layer, Atmos. Environ. , 26A , No. 6 (1992), 965-981.

D. R. Roberti, H. F. Campos Velho, G. A. Degrazia, Identifing counter-gradient term in atmospheric convective boundary layer, Inverse Probl. Sci. Eng. , 12 , No. 3 (2004), 329-339.

Z. Sorbjan, Structure of the Atmospheric Boundary Layer, Prentice Hall, 1989.

A. H. Stroud, D. Secrest, Gaussian Quadrature Formulas, Prentice Hall, Inc., Englewood Clis, N. J., 1966.

R. B. Stull, An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, Dordrecht, Holanda, 1988.

DOI: https://doi.org/10.5540/tema.2018.019.01.43

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
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