Water flow in shallow aquifers without the Dupuit hypothesis

Abstract

In this paper, we present a new model as an alternative to the classical 3D Richards model for the description of water flow in shallow aquifers. The new model is designed to achieve three goals. First, it provides a good approximation to the Richards model over a wide range of time scales. More specifically we show that both models characterize a flow with the same dominant components when the ratio of the horizontal length to the depth of the aquifer is small. Second, the new model accurately describes the velocity field. In particular, it is not based on the Dupuit hypothesis, which is often used in the context of shallow aquifers. This allows the new model to be well accurate even in the presence of wells and in aquifers with variable bedrock. Third, the new model can be viewed as a coupling of numerous 1D vertical Richards problems with a 2D elliptic one. In practice, this coupling is treated numerically using a Picard fixed point scheme, avoiding the need to solve any three-dimensional problem. This results in a significant reduction in computational cost compared to solving the 3D Richards problem directly.