Locally conservative groundwater flow in the continuous Galerkin method using 3-D prismatic patches

A new procedure has been developed to improve the velocity field computed by the continuous Galerkin finite element method (CG). It enables extending the postprocessing algorithm proposed by Cordes and Kinzelbach (1992) to three-dimensional (3-D) models by using prismatic patches for saturated groundwater flow. This approach leverages a dual mesh to preserve local mass conservation and provides interpolated velocities based on consistent fluxes. To develop this 3-D approach, a triangular conservative patch is introduced by computing not only advection fluxes, but also vertical infiltrations, storage changes, and other sink or source terms. This triangular patch is then used to develop a prismatic patch, which consists of subprisms in two layers. By dividing a single two-layer patch into two separate one-layer patches, two dimensional (2-D) algorithms can be applied to compute velocities. As a consequence, each subelement is able to preserve local mass conservation. A hypothetical 3-D model is used to evaluate the precision of streamlines and flow rates generated by this approach and the FEFLOW simulation program.