A Local Grid-Refined Numerical Groundwater Model Based on the Vertex-centred Finite-Volume Method

Abstract

Many algorithms have been proposed to cope with groundwater numerical simulation associated with local grid refinements typically for subsurface flow driven by sources acting on diverse scales. In this context, we focus on establishing an efficient local grid refinement method with nonmatching grids for groundwater flow modelling. The new model is based on the vertex-centred finite-volume method (VCFVM). The core idea of the algorithm resting on set all unknowns on vertices, and the flux between two vertices (the numerical flux) is expressed as a function of the hydraulic heads at the vertices of the element containing the lateral surface. The total outflow of the control volume of a given vertex is expressed as the sum of numerical fluxes. Since the algorithm sets all unknowns on vertices and a control volume can be defined for each vertex, our scheme readily embeds treatment of arbitrary polygonal grids, including nonmatching grids, in the presence of local grid refinement, without additional treatment at the nonmatching nodes. Six test cases, including five assumed ones and a real-world case, were adopted to evaluate the accuracy and efficiency of the new algorithm. The hydraulic heads calculated by the new algorithm were compared with those by a widely used and tested numerical groundwater model, called MODFLOW, and the analytic solutions. The mass balance error and the CPU time were compared with those of the MODFLOW 6 model, which owns ability to cope with nonmatching grids. The results show that the new algorithm yields high accuracy and efficiency in simulating groundwater flows with local grid refinements.