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

COSTA, C. P. DA; RUI, K.; PÉREZ-FERNÁNDEZ, L. D.

doi:10.5540/tema.2018.019.01.0043

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Articles • TEMA (São Carlos) 19 (1) • Jan-Apr 2018 • https://doi.org/10.5540/tema.2018.019.01.0043 copy

Different Numerical Inversion Algorithms of the Laplace Transform for the Solution of the Advection-Diffusion Equation with Non-local Closure in Air Pollution Modeling ^† † Paper presented at the National Congress of Applied and Computational Mathematics 2016.

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

In this paper, a three-dimensional solution of the steady-state dvection-diffusion equation is obtained applying the so-called generalized integral advection-diffusion multilayer technique, considered non-local closure for turbulent flow. Two different parametrizations were considered for the countergradient coefficient and three 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 indexes to analyze the solution of the equation through the methods of numerical inversion. Different parametrizations 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 almost the same accuracy.

Keywords:
Non-local closure; numerical inversion; pollutant dispersion

Method	Parameter
FT	M^* = 100			M^* = 200			M^* = 500			M^* = 1000
	Time	Cp	Na	Time	Cp	Na	Time	Cp	Na	Time	Cp	Na
	70,67	3,27	31	115,30	3,27	26	648,22	3,27	62	1383,73	3,27	67
FS	N^* = 100			N^* = 200			N^* = 500			N^* = 1000
	Time	Cp	Na	Time	Cp	Na	Time	Cp	Na	Time	Cp	Na
	72,86	3,60	31	141,88	3,82	32	342,81	3,72	32	741,24	3,73	32
GQ	Np = 4			Np = 8			Np = 10
	Time	Cp	Na	Time	Cp	Na	Time	Cp	Na
	9,76	5,42	38	11,99	3,82	32	13,11	3,52	31
	Np = 12			Np = 16			Np = 20
	Time	Cp	Na	Time	Cp	Na	Time	Cp	Na
	14,41	3,50	31	17,02	3,64	31	20,09	3,75	31

K _z ū	Inversion method	NMSE		Cor		Fa2		Fb		Fs
K _z ū	Inversion method	β₁	β₂	β₁	β₂	β₁	β₂	β₁	β₂	β₁	β₂
1	Gauss	0.34	0.42	0.811	0.814	0.739	0.696	0.31	0.40	0.10	0.17
	Talbot	0.36	0.37	0.820	0.823	0.783	0.739	0.35	0.36	0.15	0.17
	Fourier	0.26	0.32	0.834	0.838	0.826	0.826	0.24	0.32	0.05	0.13
2	Gauss	0.30	0.36	0.808	0.811	0.783	0.739	0.24	0.33	0.02	0.10
	Talbot	0.31	0.32	0.815	0.819	0.783	0.783	0.28	0.29	0.08	0.10
	Fourier	0.24	0.28	0.830	0.834	0.826	0.826	0.18	0.26	-0.02	0.06
3	Gauss	0.31	0.39	0.840	0.846	0.783	0.739	0.31	0.41	0.14	0.22
	Talbot	0.36	0.37	0.841	0.844	0.783	0.783	0.37	0.38	0.21	0.23
	Fourier	0.25	0.31	0.853	0.860	0.826	0.739	0.26	0.35	0.10	0.19
4	Gauss	0.26	0.33	0.834	0.841	0.826	0.696	0.24	0.34	0.05	0.15
	Talbot	0.30	0.31	0.837	0.840	0.826	0.783	0.30	0.32	0.13	0.15
	Fourier	0.22	0.26	0.847	0.855	0.826	0.826	0.19	0.28	0.03	0.12
5	Gauss	0.22	0.25	0.853	0.855	0.826	0.826	0.20	0.27	0.06	0.11
	Talbot	0.22	0.22	0.860	0.863	0.826	0.826	0.22	0.23	0.07	0.08
	Fourier	0.17	0.19	0.871	0.873	0.913	0.870	0.13	0.19	-0.02	0.03
6	Gauss	0.19	0.22	0.851	0.854	0.913	0.913	0.13	0.20	-0.02	0.04
	Talbot	0.20	0.19	0.856	0.859	0.913	0.913	0.16	0.17	0.00	0.01
	Fourier	0.17	0.17	0.867	0.869	0.957	0.913	0.07	0.19	-0.09	-0.04

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[1] *Corresponding author: Camila Pinto da Costa - E-mail: camila.costa@ufpel.edu.br.

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Different Numerical Inversion Algorithms of the Laplace Transform for the Solution of the Advection-Diffusion Equation with Non-local Closure in Air Pollution Modeling † † Paper presented at the National Congress of Applied and Computational Mathematics 2016.

ABSTRACT

Different Numerical Inversion Algorithms of the Laplace Transform for the Solution of the Advection-Diffusion Equation with Non-local Closure in Air Pollution Modeling ^† † Paper presented at the National Congress of Applied and Computational Mathematics 2016.