CONTINUOUS GROUNDWATER VELOCITY-FIELDS AND PATH LINES IN LINEAR, BILINEAR, AND TRILINEAR FINITE-ELEMENTS

Darcy velocity fields obtained from finite element solutions of heads in groundwater flow exhibit discontinuities at element boundaries, thus giving rise to inaccuracies in path line construction. Several methods have been developed to resolve those inaccuracies including global postprocessing of velocity fields, mixed hybrid finite element formulations, and stream function formulations. All of these techniques either lead to a considerable increase in the computational effort or are not general enough for all purposes. The point of view taken here is that standard finite element flow models yield exact water balances, which in the usual approach to path line computation are not fully used. By starting out from patches with flux-conserving boundaries, a new postprocessing procedure is derived that allows construction of a continuous flux distribution over the whole model domain. In this procedure only the head gradients of adjacent elements are used, thus avoiding the solution of another global system of equations. Furthermore. application of a stream function interpolation inside each patch allows the fast computation of path lines without any time stepping. The path lines computed with the proposed procedure are compared to path lines computed by usual particle tracking and examples are presented showing that the new method is vastly superior to traditional particle tracking.