Shallow aquifers without 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 meet three objectives. 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 follows the velocity field. In particular, it is not based on the Dupuit hypothesis, which can be naturally considered in the context of shallow aquifers. The model can be used in the presence of wells and in aquifers with variable bedrock. We illustrate this effectiveness with numerical simulations in a not particularly shallow geometry and in the presence of sources (pumping and injection). Third, the new model allows for a numerical treatment that reduces the high computational cost associated with the Richards model. We present an efficient numerical scheme that exploits a formulation of the model as the coupling of several 1d-vertical Richards problems with a 2d-elliptic one.
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