An Alternative Numerical Approach to Solve the Langevin Equation Applied to Air Pollution Dispersion

Authors: Carvalho, Jonas¹; Vilhena, Marco²; Moreira, Davidson²

Source: Water, Air, and Soil Pollution, Volume 163, Numbers 1-4, May 2005 , pp. 103-118(16)

Publisher: Springer

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Abstract:

In this work an alternative numerical approach to solve the three-dimensional stochastic Langevin equation applied to air pollution is proposed and tested. The method leads to a first-order differential equation whose solution is obtained through the method of successive approximations or Picard’s iteration method. Langevin models for Gaussian and non-Gaussian turbulence are obtained, considering Gaussian and bi-Gaussian probability density functions (PDF) of the turbulent velocity, respectively. The proposed approach is evaluated through the comparison with experimental data and results from three different models. A statistical analysis shows a good agreement between the comparisons.

Keywords: atmospheric dispersion; Lagrangian particle model; Langevin equation; model evaluation; Picard’s iteration method; probability density function

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s11270-005-8137-3

Affiliations: 1: Universidade Luterana do Brasil, Engenharia Ambiental, PPGEAM, 92420–280, Canoas, RS, Brazil, Email: jonas@ulbra.tche.br 2: Universidade Luterana do Brasil, Engenharia Ambiental, PPGEAM, 92420–280, Canoas, RS, Brazil,

Publication date: 2005-05-01