Pollutant Dispersion Modeling via Mathematical Homogenization and Integral Transform-Based Multilayer Methods

Camila P. da Costa (), Leslie D. Pérez-Fernández () and Julián Bravo-Castillero ()
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Camila P. da Costa: Universidade Federal de Pelotas, Instituto de Física e Matemática
Leslie D. Pérez-Fernández: Universidade Federal de Pelotas, Instituto de Física e Matemática
Julián Bravo-Castillero: Universidad Nacional Autónoma de México, Instituto de Investigaciones en Matemáticas Aplicadas y Sistemas

A chapter in Towards Mathematics, Computers and Environment: A Disasters Perspective, 2019, pp 59-82 from Springer

Abstract: Abstract The advection–diffusion multilayer method (ADMM) provides accurate semi-analytical solutions of the two-dimensional boundary/initial-value problems for advection–diffusion equations with variable coefficients that model air pollutant dispersion, exhibiting the lowest computational cost among related integral transform-based methods. However, in operative situations such as industrial/natural disasters resulting in the escape of pollutants to the atmosphere, swifter and accurate assessment of the ground-level distribution of pollutant concentration is required for reducing the impact on health and economy. Here, in order to accelerate the availability of results with little loss of accuracy, the ADMM is combined with mathematical homogenization (MH). Such a combination is compared to the direct application of the ADMM and the Copenhagen experimental data for its accuracy and computational cost, considering various parameterizations of the wind velocity profile and vertical eddy diffusivity for unstable atmospheric conditions. Also, such a study is carried out for the generalized integral advection–diffusion multilayer technique (GIADMT), which extends the ADMM to three-dimensional models. Several computational experiments show that the runtimes of the combination of MH with the ADMM and the GIADMT are several orders of magnitude smaller that of the direct application of the multilayer methods with little loss of accuracy.

Date: 2019
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DOI: 10.1007/978-3-030-21205-6_4

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