Efficacy of an Adaptive Integration Scheme on the Numerical Performance of DIBEM applied to the Solution of Compressible Diffusive-Advective Problems

Resumo

Advection-diffusion models can adequately describe several industrial applications in relevant areas such
as heat and mass transfer, fluid flow, metallurgy, pollutant dispersion among a wide spectrum of engineering
problems. This class of problems presents challenging numerical aspects to the boundary element method (BEM),
in special for formulations that employ radial basis functions to approximate the advective domain integral as
occurs in the Direct Interpolation technique (DIBEM). Furthermore, the representation of variable velocity fields
and the reproduction of compressibility effects in low to moderate Peclet flows also require a more robustness
numerical model. For definition, BEM formulations generates singular and quasi-singular integrals that demand
an adequate treatment. Specifically, the application of DIBEM requires a greater number of interpolation poles in
the domain for a better accuracy. As the internal points are also source points, more refined meshes require the
use of adaptive schemes to handle the quasi-singular integrals that arise from locating the source points closer to
the boundary. In the present article, the performance of the Telles’s self-adaptive integration scheme is compared
to the classical Gaussian quadrature, in a two-dimensional diffusive-advective application with variable velocity.
DIBEM results are compared with Dual Reciprocity technique (DRBEM) and the available analytical solution.
These preliminar results indicate that the use of the adaptive scheme provides more significant improvements in
accuracy for DRBEM when compared to DIBEM.