Simulação Computacional Para Problemas De Difusão Transiente 2d Pelo Método Dos Elementos De Contorno Utilizando A Solução Fundamental Independente Do Tempo.

Abstract

The present work has for objective to present an alternative computational
implementation of the Boundary Element Method, with time independent fundamental
solution, applied time to Transient heat Diffusion problems. The formulation uses the
fundamental solution that is the solution of the Poisson equation for an unitary source applied
in the point source 
i. The geometric approach uses linear elements with double nodes
alternative, and the time discretization it is done by finite differences. The mathematical
formulation obtains the boundary integral equation starting from the sentence of weighted
residual. The explicit presence of the domain integral is maintained in the equation turning
obligatory the discretization of the domain in internal cells. The time marching process starts
from a known value of potential, u0 in the time t0. Values of potential u in following time
are calculated then, in an enough number of internal points, and they are used as initial
condition for the next step of time. In this way, the potentials at internal points are calculated
together with boundary the unknowns (potential and derived normal). The results of the
obtained numeric solutions are compared with analytical, F.E.M. and time dependent B.E.M
solutions to verify the quality of the solutions..