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

Resumo

A groundwater solute transport model that predicts the process of contaminant migration plays an impor-
tant role in the control and remediation of groundwater contamination. For example, in simulating solute transport

in groundwater, reliable prediction of fluid dynamics requires a simulator capable of correctly handling highly het-
erogeneous and anisotropic permeability tensors on nonorthogonal grids due to the complex geology of the aquifer.

To solve the equations that constitute the flow model, simplifying assumptions must be made about the aquifer and
the physical processes that govern groundwater flow. In this study, we applied an improved numerical formulation

that deals with highly heterogeneous and anisotropic media and can handle distorted grids. The governing equa-
tions are solved via an implicit pressure and explicit concentration procedure, where the advective term is solved

using a Monotonic Upstream Centered Scheme for Conservation Laws (MUSCL) type method. This method is
based on a gradient reconstruction obtained by a least square technique in which the monotonicity is enhanced by a
multidimensional limiting process (MLP). The essence of the present limiting strategy is to control the distribution
of both cell-centered and cell-vertex concentration in a multidimensional way to flow physics. Is showed in the
literature that this strategy satisfies the local extremum diminishing condition in a truly multidimensional manner.
The dispersion term is discretized by a nonlinear two-point flux approximation method (NL-TPFA). This method
is very robust and able to exactly reproduce piecewise linear solutions through a linear-preserving interpolation
with explicit weights. The methods can be used with general polygonal meshes, although we restrict ourselves
to conformal triangular and quadrilateral grids. To validate the adopted formulations, some benchmark problems

found in literature are solved. These numerical experiments indicate that our formulations can provide robust so-
lutions for simulating groundwater solution processes, especially in aquifer systems with complex physical and

geological properties.