APPLICATION OF THE REGULARIZED DIRECT INTEGRATION TECHNIQUE OF THE OF BOUNDARY ELEMENT METHOD IN DIFFUSION-ADVECTIVE STATIONARY PROBLEMS

Vitor Pancieri Pinheiro¹; Carlos Friedrich Loeffler¹; Raphael Laquini¹

¹ Universidade Federal do Espírito Santo

doi:10.20906/CPS/CILAMCE2017-1064

Resumo

The most usual formulations of the boundary element method for solving the diffusive-advective problems present significant difficulties in the treatment of the transport term, for various reasons. While the classical formulation, which uses the diffusive-advective fundamental solution, is limited in variable velocity fields, the dual reciprocity formulation presents precision problems, being unable to produce satisfactory results even for only moderate Peclét numbers. This work applies the recent regularized direct interpolation technique with radial basis functions (DIBEM) to model the advective term, thus allowing good accuracy in problems with variable velocity fields and other complexities. The DIBEM was superior to the formulation with dual reciprocity in several applications, as in the cases governed by the Poisson and Helmholtz equations, and thus, its extension to diffusive-advective problems is a natural consequence of its development. In order to evaluate performance, this paper solves test problems with known analytical solution and already simulated by the formulations previously mentioned, in order to expose the applicability and adequacy of DIBEM in this context.

Palavras-chave: Direct Integration Boundary Element Method; Regularization Process; Diffusive-Advective Problems