A Brief Performance Analysis of Direct Interpolation Technique applied on Bidimensional Advective-Diffusive Problems with Variable Velocity Fields

Resumo

Research efforts directed to advective-diffusive equation have resurfaced, strongly motivated by the
recent use of these mathematical models in pollutant dispersion applications, within the scope of environmental
engineering. In the context of the Boundary Element Method (BEM), the treatment of the advective transport term
characterizes a technical challenge. The BEM classic formulation, which uses the problem’s inherent fundamental
solution, is capable of handling high Peclet numbers phenomena, however it is limited to uniform velocity fields.
In parallel, the Dual Reciprocity technique, which is more robust and versatile, offers flexibility in describing
variable flow velocity fields, nevertheless it remains restricted to representing creeping flows. The recent Direct
Interpolation technique provides a balanced alternative to the two previous approaches, as it is able to deal with
variable velocity fields, such as Dual Reciprocity, despite that, it maintains stability up to moderate Peclet number.
This article aims to expose a preliminary performance of the of Direct Interpolation technique comparing it to
the well-established Dual Reciprocity approach, in physical situations with spatial variation of the velocity field,
while the effects of advection are gradually increased. Focusing on determining the relative performance of the
formulations, in terms of precision and stability, the numerical results are evaluated using benchmark problems
with widely known analytical solutions.