Modeling of the Saltwater Intrusion Using the Level Set Method. Application to Henry’s Problem ()
ABSTRACT
The salt intrusion phenomenon is caused by overexploitation of
aquifers in coastal areas. This physical phenomenon has been the subject of
numerous studies and numerous methods have been
proposed, with the aim of protecting the quality of the water in these
aquifers. This work proposes a two-dimensional saline intrusion model
using the sharp interface approach and the level set method. It consists of a
parabolic equation modeling the underground flow and a hyperbolic Equation (the
level set equation) which makes it possible to track the evolution of the
interface. High-order numerical schemes such as the space scheme WENO5 and the
third-order time scheme TVD-RK were used for the numerical
resolution of the hyperbolic equation. To limit the tightening of the contour
curves of the level set function, the redistanciation or reinitialization algorithm proposed by Sussma et al. (1994) was used. To ensure the effectiveness and reliability of the proposed
method, two tests relating to the standard Henry problem and the modified Henry
problem were performed. Recall that Henry’s problem uses the variable density
modeling approach in a confined and homogeneous aquifer. By comparing the
results obtained by the level set method with reinitialization (LSMR)
and those obtained by Henry (1964), and by Simpson and Clement (2004), we see
in the two test cases that the level set method reproduces well the toe, the
tip and the behaviour of the interface. These results correspond to the
results obtained by Abarca for Henry’s problem with constant dispersion
coefficients. The results obtained with LSMR, reproduced the interface
with a slight spacing compared to those obtained by Henry. According to Abarca (2006), this spacing is due to the absence of the longitudinal and transversal dispersion coefficients in the model.
Share and Cite:
Loua-Bouayi, J. , Tathy, C. and Manounou, A. (2022) Modeling of the Saltwater Intrusion Using the Level Set Method. Application to Henry’s Problem.
Computational Water, Energy, and Environmental Engineering,
11, 11-33. doi:
10.4236/cweee.2022.111002.
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