Resultados Numéricos do Método de Elementos Analíticos em Aglomerados de Inomogeneidades

ABSTRACT

An analytical solution for the interaction of cylindrical inhomogeneities in a complex potential was obtained using the analytical element method. This method utilizes expansions in the Laurent and Taylor series for the outer and inner parts, respectively, of each cylindrical inhomogeneity. The availability of individual solutions allowed the application of the superposition principle to obtain the solution of the flow problem in terms of discharge potential. This representation, however, required an iterative method for determining the coefficients of the series expansions, which used the minimum value for the absolute differences between successive iterations and a maximum number of iterations as a stop criterion. The implementation of the algorithm was performed in Python language v 3.6.7 and the numerical results after analysis of the convergence are presented in graphs containing the set of inhomogeneities used and their influence on the behavior of flow lines and potentials. These, through the precision and detail obtained, showed the ability of the MEA to characterize flow and identify preferred channels, evidencing its applicability to real situations.

Keywords:
analytical elements; flow equation; scientific computing; numerical integration; Python ^R