Flow Computation and Mass Balance in Galerkin Finite-Element Groundwater Models

Abstract

In most groundwater modeling studies, quantification of the flow rates at domain and subdomain boundaries is as important as the computation of the groundwater heads. The computation of these flow rates is not a trivial task when a finite-element method is chosen to solve the groundwater equation. Generally, it is believed that finite-element methods do not conserve mass locally. In this paper, a postprocessing technique is developed to compute mass-conserving flow rates at element faces. It postprocesses the groundwater head field obtained by the Galerkin finite-element method, and the calculated flow rates conserve mass locally and globally. The only requirement for the postprocessor to be applicable is the irrotationality of the flow field, i.e., the curl of the Darcy flux should be zero. The accuracy and the mass conservation properties of the new postprocessor are demonstrated using several test problems that include one-, two-, and three-dimensional flow systems in both homogeneous and heterogeneous aquifer conditions.