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

A variety of algorithms have been proposed to cope with issues associated with local refinements of numerical grids typically employed to cope with subsurface flow driven by sources acting on diverse scales (e.g., pumping wells, channels or ditches or abrupt changes in hydraulic conductivity distributions). In this context, here we focus on grid refinement associated with nonmatching grids, which still pose significant challenges in terms of accuracy. We propose a numerical modeling scheme based on a new algorithm that has an improved accuracy when compared against approaches that are typically used in conjunction with nonmatching grids. Our approach is based on the vertex-centred finite-volume method (VCFVM), the key feature of the algorithm resting on setting all unknowns on vertices of the mesh elements while the flux crossing a lateral surface of the control volume centred around a mesh vertex is expressed as a function of the hydraulic heads at the vertices of the element containing the lateral surface. A given row of the stiffness matrix of the system includes the entries associated with mass conservation formulated for the control volume associated with a corresponding grid node. Since the algorithm sets all unknowns on element vertices and a control volume can be defined for each vertex, our scheme readily embeds treatment of nonmatching grids in the presence of local grid refinement. Hydraulic heads evaluated through our algorithm are benchmarked against (a) results obtained from the widely used and tested MODFLOW and MODFLOW6 groundwater modeling suites in the presence of a variety of boundary conditions and considering high resolution matching (for MODFLOW) and nonmatching (for MODFLOW6) grids, and (b) a test analytical solution. Our results show that the average value of relative root mean square error (RRMSE) resulting from comparing our approach against the analytical solution and the MODFLOW simulations performed on the highly resolved grid (which we consider as reference) was always lower than 0.50%, thus imbuing us with confidence with respect to the accuracy of our proposed scheme. Additionally, while the requirement of CPU time associated with our algorithm is of the same order (on average) as the one associated with MODFLOW6 (benefits being noted mainly for settings involving flow in confined groundwater scenarios), our scheme is highly flexible in terms of spatial discretization and is characterized by higher accuracy for a given discretization.