A non-linear finite volume method coupled with a higher order MUSCL- type formulation for the numerical simulation of groundwater solute trans- port

Resumo

A groundwater solute transport model can predict the process of contaminant migration and play an im-
portant role in groundwater contamination control and remediation. In groundwater solute transport simulation, for

example, reliable prediction of fluid dynamics requires a simulator that can rigorously handle highly heterogeneous
and anisotropic permeability tensors on nonorthogonal grids dictated by complex aquifer geology. In this sense,
to solve the equations that constitute the flow model, it is necessary to make simplifying assumptions about the
aquifer and the physical processes governing groundwater flow. In this study, we applied an improved numerical
formulation which deals with highly heterogeneous and anisotropic medium, that can handle distorted meshes. The
governing equations are solved via an implicit pressure and explicit concentration procedure, where the dispersion
term is discretized by a non-linear Two-Point Flux Approximation Method (NL-TPFA), this method is very robust
and capable of reproducing piecewise linear solutions exactly by means of a linear preserving interpolation with
explicit weights that avoids the solution of locally defined systems of equations. A Monotonic Upstream Centered
Scheme for Conservation Laws (MUSCL) type method is adapted for the solution of the advection term. This

method is based on a gradient reconstruction obtained by a least square technique in which monotonicity is rein-
forced by an appropriate slope limiter. The methods can be used with general polygonal meshes, even though we

restrict ourselves to conforming triangular and quadrilateral grids. In order to validate the formulations adopted,

some benchmark problems found in literature are solved. These numerical experiments suggest that our formu-
lations can provide robust solutions for simulating groundwater solute transport processes, especially in aquifer

systems with complex physical and geological properties.