fabiana de fátima giacomini - PG-Mec Programa de Pós-Graduação ...

ABSTRACT
The focus of this work is the verification of the effect on the error discretization and its order
caused by the boundary conditions application methodology, in problems solved with the
finite volume method. In order to do this, the following aspects are considered: the Poisson,
the adveccion-diffusion and the Burgers equations; one-dimensional domain; uniform grids;
seven variables of interest with numerical interpolation schemes of first and second accuracy
order; Dirichlet boundary conditions; tridiagonal solver; grids with up to millions of volumes;
quadruple precision; and a number of iterations large enough to reach the machine round-off
error. The boundary condition application methodologies considered are four: without and
with ghost volumes; half-volume; and volume of zero thickness. The variables of interest are:
the primary variable obtained in x = 1/ 2 ; the average of the primary variable; the norm
average; and the first order derivative. The main result is the fact that the half-volume
boundary condition methodology had the smallest numeric error. Besides, the influence of the
presence of the advective effect was verified in the adveccion-diffusion and the Burgers
equations. Finally, it was verified that the concept of pollution error is implicit at the roundoff
error, which changed the order of the numeric error of the first order derivative, of the
three studied problems: without and with ghost volumes and with volume of zero thickness.
Keywords: Computational fluid dynamics. Finite volume method. Boundary conditions
application methodologies. Discretization error. Error order.