  In this work, we present a class of new efficient models for water flow in
shallow unconfined aquifers, giving an alternative to the classical but less
tractable 3D-Richards model. Its derivation is guided by two ambitions: any new
model should be low cost in computational time and should still give relevant
results at every time scale. We thus keep track of two types of flow occurring
in such a context and which are dominant when the ratio thickness over
longitudinal length is small: the first one is dominant in a small time scale
and is described by a vertical 1D-Richards problem; the second one corresponds
to a large time scale, when the evolution of the hydraulic head turns to become
independent of the vertical variable. These two types of flow are appropriately
modelled by, respectively, a one-dimensional and a two-dimensional system of
PDEs boundary value problems. They are coupled along an artificial level below
which the Dupuit hypothesis holds true (i.e. the vertical flow is
instantaneous) in a way ensuring that the global model is mass conservative.
Tuning the artificial level, which even can depend on an unknown of the
problem, we browse the new class of models. We prove using asymptotic
expansions that the 3D-Richards problem and each model of the class behaves the
same at every considered time scale (short, intermediate and large) in thin
aquifers. The results are illustrated by numerical simulations, showing
especially that the new models results fit well with the ones obtained with the
original 3d-Richards problem even in non-thin aquifers.
