Groundwater flow simulation using a finite volume method based on harmonic points

Código

I-EBHE0088

Autores

FERNANDO RAUL LICAPA CONTRERAS, Darleson Luiz Alves de Oliveira, Alessandro Romario Echevarria Antunes

Tema

WG 1.12: Development & application of river basin simulators

Resumo

Before simulating an aquifer, a model must be created that characterizes the aquifer by describing its geometry, its architecture, its stratigraphy, and its distribution of properties such as porosity and hydraulic conductivity. The latter property is very heterogeneous and anisotropic and can vary by several orders of magnitude in a small section of the aquifer. The detailed geometrical representation of the geological features can only be achieved with flexible meshes (corner-point, unstructured and/or distorted), otherwise some of these large-scale features such as faults, fractures or pinchouts may be lost and consequently the accuracy of the simulation is compromised. On the other hand, the geological complexity, and the presence of multi-component fluids mean that the mathematical models describing the behavior of aquifers are highly nonlinear and coupled and have no analytical solutions. Therefore, to understand the behavior of aquifers in detail, accurate, robust, and computationally efficient numerical methods that can handle flexible meshes and consistently discretize the mathematical models must be used, but finding this numerical method is still a challenge. Currently, there are several commercial simulators that are capable of simulating flow in saturated and unsaturated aquifers, namely FEFLOW, FEMWATER, FE3DGW and HYDRUS use the conventional finite element (FE) method and the simulators MODFLOW6, ParFlow, PFLOTRAN and MIKE SHE use the conventional control volume finite difference (CVFD) method. The FE method, which approximates the mathematical model, in its conventional form does not fulfill the Discrete Maximum Principle (DMP) and Linearity-Preserving (LP) criteria and does not preserve the physical properties at the local level. It is more adaptable to areas with irregular contours and the accuracy of its results is highly dependent on the quality of the mesh used. On the other hand, the CVFD method is easy to code, computationally efficient and consists only of K-orthogonal meshes. In this method, the template is compact since the flow is approximated by only two points and the global matrix is symmetric and diagonally dominant, which makes it an M-matrix, so the method satisfies the DMP and LP criterion. In this work, we propose a non-conventional finite volume method with multipoint flux approximation based in harmonic points (MPFA-H) to solve the hydraulic head equation in aquifers highly heterogeneous and anisotropic with full hydraulic conductivity tensor, which can be easily adapted to irregular contours and preserves the physical properties both locally and globally. In this method, the total flux is approximated by a convex combination of the one-sided fluxes, where these fluxes depend only on cell-centered variables and variables centered on harmonic points (auxiliary variables). The auxiliary variables are interpolated as a convex combination of cell-centered variables that are adjacent to the edge.