Formulações do método de elementos de contorno com interpolação direta em problemas difusivo-advectivo-reativos estacionários - Pinheiro, Vitor Pancieri (2023)
The occurrence of advective-diffusive-reactive models in the description of engineering phenomena is recurrent in different industrial areas, such as oil and gas, metallurgy, paper and cellulose, energy, pollutant dispersion, among others. In the context of the development of numerical methods capable of dealing with such models, the treatment of the advective transport term stands out, as it constitutes a relevant obstacle to the performance of most of these techniques, which significantly lose their precision with the increase in the relative magnitude of this term. There is a classic formulation of the boundary element method (BEM), which uses a Green’s solution associated with the correlated differential operator, which consistently represents only problems with a uniform velocity field, although with fewer limitations regarding the intensity of advective effects. The dual reciprocity formulation (DRBEM), proposed later, removes the restriction on the mathematical shape of the velocity field and is capable of dealing with variable hydrodynamic fields, however, with satisfactory precision only when advective effects are weak. More recently, a new technique has emerged, called direct interpolation (DIBEM), which is mainly characterized by the approximation of the entire kernel of the remaining domain integrals and by a regularization process that avoids singularities generated in the coincidence between source and field points. The robust performance of the DIBEM proposal in several relevant scalar field problems, such as Poisson, Helmholtz and wave propagation problems, underlies the interest in more systemic tests also in advective-diffusive models to determine potentialities and limitations. To this end, this thesis proposes two DIBEM formulations to approach advective-diffusive-reactive models, a classic one, as a continuation of the format already tested in other scalar field problems and an alternative proposal, which uses an approach analogous to that used in DRBEM to approximate the derivatives of the potential field. Both proposed formulations are tested and contrasted with the dual reciprocity technique as a relative reference. In general terms, the classic DIBEM formulation appears to be the most accurate and robust in cases of uniform velocity field. In cases of variable velocity field, the alternative DIBEM formulation is more accurate than the classic DIBEM and the DRBEM, concomitantly, which attests to the quality of the new formulation. Both DIBEM formulations proposed in this thesis, classic and alternative, exhibited satisfactory accuracy, and are considered reliable tools in the numerical treatment of advective-diffusive-reactive models in scenarios with moderate advective effects.