Short Communication: Semi-analytical solution of the asymptotic Langevin Equation by the Picard Iterative Method

  • Authors:

  • Charles R. P. Szinvelski;Marco T. M. B. Vilhena;Jonas C. Carvalho;Gervásio A. Degrazia

  • Affiliations:

  • Universidade Federal de Santa Maria, Departamento de Física, Santa Maria, RS, Brazil;Universidade Federal do Rio Grande do Sul, Instituto de Matemática, PPGMAp, Porto Alegre, RS, Brazil;Universidade Luterana do Brazil, Engenharia Ambiental, PPGEAM, Canoas, RS, Brazil;Universidade Federal de Santa Maria, Departamento de Física, Santa Maria, RS, Brazil

  • Venue:
  • Environmental Modelling & Software
  • Year:
  • 2006

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Abstract

In this work, a semi-analytical solution for the asymptotic Langevin Equation (Random Displacement Equation) applied to the pollutant dispersion in the Planetary Boundary Layer (PBL) is developed and tested. The solution considers as starting point the first-order differential equation for the random displacement, on which is applied the Picard Iterative Method. The new model is parameterized by a turbulent eddy diffusivity derived from the Taylor Statistical Diffusion Theory and a model for the turbulence spectrum, assuming the hypothesis of linear superposition of the mechanical and thermal turbulence mechanisms. We report numerical simulations and comparisons with experimental data and other diffusion models. The main motivation for this work comes from the fact that the round-off error influence and computational time can be reduced in the new method.