Modeling of shallow aquifers in interaction with overland water

•A new class of flow models for unconfined aquifers is proposed.•The models couple the fast and slow components of the flows.•The 3D-Richards equation is properly approached in a wide range of time scales.•The validity of the models is specified using a non-conventional asymptotical analysis.•The pe...

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Bibliographic Details
Published in:Applied Mathematical Modelling 2020-05, Vol.81, p.727-751
Main Authors: Bourel, Christophe, Choquet, Catherine, Rosier, Carole, Tsegmid, Munkhgerel
Format: Article
Language:English
Subjects:
Analysis of PDEs
Aquifers
Asymptotic analysis
Asymptotic series
Boundary value problems
Computer simulation
Dupuit hypothesis
Fluid flow modeling
Mathematical models
Mathematics
Numerical simulations
Saturated and unsaturated porous media
Time
Two dimensional models
Vertical Richards equations
Water flow
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Summary:•A new class of flow models for unconfined aquifers is proposed.•The models couple the fast and slow components of the flows.•The 3D-Richards equation is properly approached in a wide range of time scales.•The validity of the models is specified using a non-conventional asymptotical analysis.•The performances and the tractability of the models are illustrated by numerical simulations. In this paper, we present a new class of efficient models for water flow in shallow unconfined aquifers, providing an alternative to the classical but less tractable 3d-Richards model. Its derivation is guided by two objectives: to obtain a model that has low computational cost and yields relevant results on every time scale. Thus, we keep track of two types of flow that occur in such a context and are dominant when the ratio of thickness to longitudinal length is small: the first is dominant on a small time scale and is described by a vertical 1d-Richards problem; the second corresponds to a large time scale, when the evolution of the hydraulic head becomes independent of the vertical variable. These two types of flow are appropriately modeled by a one-dimensional and two-dimensional system of PDE boundary value problems, respectively. They are coupled at an artificial level below which the Dupuit hypothesis holds true (i.e., the vertical flow is instantaneous) so that the global model is mass conservative. Tuning the artificial level, which can even depend on an unknown of the problem, we obtain the new class of models. Using asymptotic expansions, we prove that the 3d-Richards model and each model in the class behave identically on every considered time scale (short, intermediate, and large) in thin aquifers. The results are illustrated by numerical simulations, and it is demonstrated that they fit well with those obtained by the original 3d-Richards model even in non-thin aquifers.
ISSN:0307-904X
1088-8691
0307-904X
1872-8480
DOI:10.1016/j.apm.2020.01.011