Finite-infinite element analysis for flow simulation in a phreatic aquifer

Abstract

Groundwater and surface water interaction is a common process of the hydrologic cycle but still challenging to be addressed in a general context. A special case of groundwater-surface water interaction is the seepage from a river/stream or canal into an adjacent phreatic aquifer, where the groundwater flow in the vicinity of the stream is crucial while the aquifer is supposed to extend to infinity, especially for the mathematical analysis. Herein, numerical solutions of 1-D Boussinesq equation and 2-D Richards equation are presented by embedding infinite elements in the finite element analysis to discretise only the key subsurface flow region close to the stream. By using the infinite elements, which extend to infinity to one direction according to appropriate shape functions, the total number of elements required to discretise the simulation area is substantially reduced. As a result, computationally efficient solutions are obtained, which is particularly important for the two-dimensional saturated-unsaturated groundwater flow described by the Richards equation, as well as sufficiently accurate, both in terms of groundwater recharge and water table in the vicinity of the stream. The finite-infinite element approach could be useful to derive accurate and fast numerical solutions under the investigation of several scenarios.