### 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..

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..

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**