Desenvolvimento e implementação do método difusional bidimensional transiente para solução numérica de problemas convectivos difusivos

Abstract

The study of groundwater contamination involves understanding the relevant mechanisms involved in the migration of pollutants (transport problems). Such problems are governed by convection-diffusion equations whose numerical solutions can be obtained through discrete techniques, when the problem is dominated by diffusion. However, when such problems are dominated by convection, classical numerical techniques present difficulties related to dispersion and numerical oscillations. The need for improving those methods, mainly in the study of convective problems, can be assessed by several methods and 'ad doc' techniques that have been developed to solve this kind of problems. Such techniques modify the parameters of the convective diffusive equation, fact that lead to solution mistakes and to doubts about which problem is really being solved. A recently developed technique, named diffusional method, proposes a modification of the convection-diffusion equation to a purely diffusive equation, through algebraic manipulation without losing the characteristics of the original equation, in such way that the resulting equation can be solved by means of the classical techniques of finite differences, finite volumes or finite elements. This work develops the diffusional method to solve two-dimensional transient convective diffusive problems by the finite volumes technique. The numeric algorithm had for base the adptação of an existent program in the literature for the solution of problems purely diffusives, CONDUCT developed by Patankar (1991). Tests with two benchmark problems, aiming to investigate the performance of the proposed technique were made. Also, the proposed technique was utilized to solve a real problem and the results obtained were compared against the literature values. The results show that the difusional method is an efficient tool and simple tool for solving transient two-dimensional convective diffusive problems