SIMULAÇÃO NUMÉRICA DE TRAÇADORES APLICADOS EM MEIOS POROSOS UTILIZANDO UM MÉTODO DE VOLUMES FINITOS DO TIPO MULTIPOINT FLUX APPROXIMATION QUASI-LOCAL (MPFA-QL)

Resumo

Numerical simulation of solutes (e.g.: tracers and contaminants) in porous media remain a challenge
for numerical analysts, particularly due to the complex geological characteristics of the medium. The use of
tracers allows to characterize hydrodynamically the porous media covered by a certain volume of fluid
previously marked by these substances. The mathematical model that determines the concentration of tracers in
porous medium is given by the advection-dispersion-reaction (ADR) equation. The numerical solution of this
equation is usually obtained by the finite difference method, therefore, there are limitations to treat problems
with anisotropic tensors, and it is not suitable for the use of unstructured meshes. On the other hand, an
alternative solution is the use of Galerkin finite element method, however, this method in the most classical form
does not produce locally conservative solutions, which can be a serious problem for numerical modeling
involving conservation laws. In this context, the present work presents a finite volume method (FVM) to

discretize the ADR equation, where the discretization of the advective-dispersive term is performed using a non-
orthodox FVM, known as multipoint flux approximation quasi-local (MPFA-QL), that was originally used to

solve diffusion problems with heterogeneous and anisotropic coefficients on unstructured and distorted meshes.