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Problemas difusivos bidimensionais em regime permanente com fonte arbitrária: soluções exatas Steady two-dimensional diffusion problems with arbitrary sources: exact solutions

By Jorge Rodolfo Silva Zabadal, Daniel Beck, Renato Letizia Garcia, Elenara Corrêa Lersch and César Xavier Hoffmann

Abstract

Neste trabalho são apresentados métodos híbridos para solução de problemas difusivos relativos à dispersão de poluentes em meio aquático. Estes métodos aplicam variáveis complexas a fim de executar mapeamentos sobre a equação diferencial a ser resolvida bem como sobre o domínio considerado. O mapeamento sobre a equação diferencial converte o operador laplaciano bidimensional em uma derivada cruzada de segunda ordem na variável espacial. O mapeamento do domínio transforma regiões de formato complexo em regiões retangulares. Ambos mapeamentos são usados a fim de reduzir o tempo total requerido de processamento para solução de problemas difusivos não-homogêneos. Resultados numéricos são apresentados.<br>In this work hybrid methods for solving diffusion problems related to pollutants dispersion in water bodies are presented. These methods employ complex variables in order to perform mappings over the differential equation to be solved as well as over the considered domain. The mapping over the differential equation converts the two dimensional laplacian operator into a second order mixed derivative in the complex variables. The mapping of the domain transforms complex-shaped regions into rectangular ones. Both mappings are used in order to reduce the total time proccessing required for solving non-homogeneous diffusion problems. Numerical results are reported

Topics: Problemas difusivos, equação de poisson, variáveis complexas, transformações conformes, Diffusion problems, poisson equation, complex variables, conformal mapping, Environmental engineering, TA170-171, Engineering (General). Civil engineering (General), TA1-2040, Technology, T, DOAJ:Environmental Engineering, DOAJ:Technology and Engineering, Environmental technology. Sanitary engineering, TD1-1066
Publisher: Brazilian Association of Sanitary and Environmental Engineering
Year: 2006
DOI identifier: 10.1590/S1413-41522006000200005
OAI identifier: oai:doaj.org/article:049f8218fc9d458e8df823145643790a
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