SUMMARYThis work is concerned with the development of different domain-BEM (D-BEM) approaches to the solution of two-dimensional diffusion problems. In the first approach, the process of time marching is accomplished with a combination of the finite difference and the Houbolt methods. The second approach starts by weighting, with respect to time, the basic D-BEM equation, under the assumption of linear and constant time variation for the temperature and for the heat flux, respectively. A constant time weighting function is adopted. The time integration reduces the order of the time derivative that appears in the domain integral; as a consequence, the initial conditions are directly taken into account. Four examples are presented to verify the applicability of the proposed approaches, and the D-BEM results are compared with the corresponding analytical solutions.
A modelagem matemática pode ser utilizada como recurso didático pedagógico no ensino de matemática em vários níveis, tanto no ensino básico como no ensino superior. Este trabalho tem como foco, apresentar como pode se dar a aplicação da metodologia de modelagem matemática na avaliação do impacto ambiental causado pelo lançamento de uma carga poluidora em um rio em aulas da disciplina de Cálculo III para o curso de Engenharia Ambiental. Desta forma, apresenta-se um modelo matemático que descreve o transporte de poluente sobre um eixo que pode ser resolvido numericamente. Os resultados obtidos mostram que a modelagem matemática é uma ferramenta muito útil na avaliação de impacto ambiental e podem auxiliar na tomada de decisão quanto a medidas a serem tomadas para minimização dos impactos causados pelo lançamento de cargas poluidoras em rios, ao mesmo tempo em que se configura como uma metodologia de ensino motivadora no ensino superior.
This work is concerned with development of an alternative finite difference method approach to the solution of the transient diffusion equation. In this approach is assumed that the potential function has a linear variation in some time interval. Thus an integral with respect to time is carried out in the initial diffusion equation. A constant time weighting function is adopted. The time integration reduces the order of the time derivative that appears in the initial equation. Two numerical examples are presented to verify the accuracy and applicability of the proposed approaches. The results are compared with the standard corresponding analytical solutions.
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