Leslie D. Pérez-Fernández

Combinação do ADMM com Homogeneização Matemática na Modelagem da Dispersão de Poluentes na Atmosfera

The advection-diffusion multilayer method (ADMM) produces accurate semi-analytical solutions of initial/boundaryvalue problems for advection-diffusion equations with variable coefficients that model pollutant dispersion in the atmosphere, and exhibits lower computational cost in comparison to other integral transform-based methods. However, in operative situations such as natural/industrial disasters resulting in the release of pollutants to the atmosphere, it is necessary to assess rapidly and accurately the ground-level distribution of pollutant concentration in order to minimize 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, whose use in pollutant dispersion modeling seems to be new. The proposed approach is compared with the direct application of the ADMM and to the observations of the Hanford experiment in order to access both its accuracy and computational cost, for stable atmospheric conditions and considering the influence of deposition velocity. The results show that the combination of the ADMM and mathematical homogeniRevista Brasileira de Meteorologia, v. 33, n. 2, 329-335, 2018 rbmet.org.br DOI: http://dx.doi.org/10.1590/0102-7786332014

Effective Coefficients and Local Fields of Periodic Fibrous Piezocomposites with 622 Hexagonal Constituents

The asymptotic homogenization method is applied to a family of boundary value problems for linear piezoelectric heterogeneous media with periodic and rapidly oscillating coefficients.We consider a two-phase fibrous composite consisting of identical circular cylinders perfectly bonded in a matrix. Both constituents are piezoelectric 622 hexagonal crystal and the periodic distribution of the fibers follows a rectangular array. Closed-form expressions are obtained for the effective coefficients, based on the solution of local problems using potential methods of a complex variable. An analytical procedure to study the spatial heterogeneity of the strain and electric fields is described. Analytical expressions for the computation of these fields are given for specific local problems. Examples are presented for fiber-reinforced and porous matrix including comparisons with fast Fourier transform (FFT) numerical results.

Uma Solução Assintótica Formal de um Problema de Advecção-Difusão-Reação Não Linear sobre um Meio Micro-heterogêneo e Periódico

O metodo de homogeneizacao assintotica e empregado na obtencao de uma solucao assintotica formal de um problema de adveccao-difusao-reacao nao linear sobre um meio unidimensional micro-heterogeneo e periodico.

Homogeneização Assintótica de um Problema Eíptico Multidimensional sobre um Meio Linear Microperiódico

O metodo de homogeneizacao assintotica e aplicado ao problema da distribuicao de um campo termico estacionario sobre um meio micro-heterogeneo e periodico com comportamento constitutivo linear e na presenca de uma fonte de calor. Obtem-se os coeficientes efetivos da condutividade e os problemas locais e homogeneizado, os quais permitem construir uma solucao assintotica formal do problema original. Mediante um exemplo, ilustra-se a proximidade entre as solucoes assintotica e homogeneizada.

Computation of the Effective Conductivity of Fibrous Composites with Imperfect Thermal Contact by Combination of Asymptotic Homogenization, Domain Decomposition and Finite Elements Methods

The methods of asymptotic homogenization, domain decomposition and finite elements are combined for the computation of the effective thermal conductivity of periodic biphasic fibrous composites with interfacial thermal resistance. The asymptotic homogenization method is used to obtain the so-called local problems on the periodic cell whose solution allows the calculation of the effective conductivity tensor. The numerical solution of the local problems requires a special treatment because of the temperature discontinuity on the interfaces due to the thermal barrier. In the present work these problems are decomposed into two, one for each phase, linked via a coupling condition. The finite element method, implemented in the software FreeFEM++, is employed to solve the resulting problems on each phase. FreeFEM++, which is based on the variational formulation of the problems, potentially allows to consider arbitrary shapes for both the fiber and the periodic cell cross sections. Numerical results for a square periodic cell with fibers of circular cross-section are presented and compared with results from other reported approaches.