A Multipoint Flux Approximation Method based on Harmonic Points to Simulate Highly Heterogeneous and Anisotropic Aquifers

Resumo

Currently, groundwater has become an essential natural resource for human consumption, particularly in arid regions. It is well-known that aquifers have very complex geological characteristics due to the presence of zones of low permeability, vugs and fractures. The geological complexity and the presence of strongly coupled terms in the mathematical models make it difficult, if not impossible, to obtain an analytical solution, and solving this class of problem is a challenge for the hydraulic engineer. In this sense, computer simulators supported by numerical methods have become a fundamental tool for dealing with these mathematical models. Currently, in the context of numerical simulation of fluid flow in aquifers, several classical numerical methods are used in most commercial simulators such as FEFLOW, MODFLOW, and HydroGeoSphere. However, it is well known that these classical methods cannot deal with complex physical phenomena and can lead to inconsistent approximate solutions. In this sense, in the present work, the hydraulic head equation of the aquifer is solved for the first time using a cell-centered finite volume method, where the spatial and temporal terms are solved using the multi-point flux approximation method based on harmonic points (MPFA-H) and the backward Euler or Crank-Nicolson schemes, respectively. In this context, the MPFA-H method is characterized by being globally and locally conservative, piecewise-linear, and able to deal with highly heterogeneous and anisotropic porous media. Moreover, the harmonic points are calculated from physical and geometrical parameters, which allows a piecewise-linear solution and guarantees the positivity of the interpolation weights of the hydraulic head on the control surface of the computational mesh. The results show that the proposed method provides high accuracy and efficiency in groundwater simulation.