verificação de funções de interpolação em advecção-difusão 1d ...

ABSTRACT
This work is based on Computacional Fluid Dynamics. Among the possibilities of this area,
the focus was the study of discretization error generated by interpolation functions (IF`s). To
achieve this aim was considered the one-dimensional advection-diffusion problem, in one
dimensional space, without source term. Other considerations were: steady-state flow,
constant properties, Dirichlet boundary condition, finite volume method and ghost cell on
boundaries. For the approximation of the advection term were adopted two IF of 1 st order,
seven of 2 nd order and one of 3 rd order. To approximate diffusive term were used one 2 nd
order IF and one 4 th order IF. To each of those pairs of IF`s (advective term/difusive term),
simulations for 15 distinct grids were performed, beginning with 5 control volumes (CV`s)
and refining till 23.914.845 CV`s, with refine rate of 3. Four variables of interest were
defined: variable T c (value of variable T at middle point of domain, got by the nodal value of
the central volume in an odd grid), variable T m (medium value of variable T get with
rectangle interpolation rule), variable I ( flux of variable T at the face of east boundary of
domain); and finally variable L (average value of norm l 1 ). A priori error analysis of each
variable were conducted, getting the true orders (p V ) and asymptotic order (p L ) for each one
of four variables. After simulations the effective (p E ) and apparent (p U ) orders were defined,
and the results of priori analysis were confirmed, except for variable I. Using the method of
multiples Richardson extrapolation (MER) could be obtained better magnitude of
discretization error. Comparing the performance of interpolation functions, could be seen
better performance of QUICK/CDS-4 when the error was obtained without MER, and CDS-2
for error obtained using MER. And finally could be confirmed all results achieved before with
other values of Peclet number.
Key Words: Finite Volume, a priori errors, a posteriori errors, advection-diffusion, MER,
CFD.