Research Article
Transmissivity Identification by Combination of CVFEM and
Genetic Algorithm: Application to the Coastal Aquifer
Hassan Smaoui ,
1,2
Abdelkabir Maqsoud,
3
and Sami Kaidi
1,2
1
CEREMA/DTecEMF, 134, Rue de Beauvais, CS 60039, 60280 Margny-L` es-Compi` egne, France
2
Sorbonne Universit´ e, Universit´ e de Technologie de Compi` egne, Laboratoire Roberval/LHN, FRE-CNRS 2012,
CS 60319, 60203 Compi` egne, France
3
Universit´ e du Qu´ ebec en Abitibi-T´ emiscamingue (UQAT) 675, 1
` ere
Avenue, Val-d’Or (QC) J9P 1Y3, Canada
Correspondence should be addressed to Hassan Smaoui; hassan.smaoui@cerema.fr
Received 31 December 2018; Accepted 11 June 2019; Published 29 July 2019
Academic Editor: Saeed Efekhar Azam
Copyright © 2019 Hassan Smaoui et al. Tis is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Te solution of inverse problems in groundwater fow has been massively invested by several researchers around the world. Tis
type of problem has been formulated by a constrained optimization problem and this constraint is none other than the direct
problem (DP) itself. Tus, solving algorithms are developed that simultaneously solve the direct problem (Darcy’s equation) and
the associated optimization problem. Several papers have been published in the literature using optimization methods based on
computation of the objective function gradients. Tis type of method sufers from the inability to provide a global optimum.
Similarly, they also have the disadvantage of not being applicable to objective functions of discontinuous derivatives. Tis paper is
proposed to avoid these disadvantages. Indeed, for the optimization phase, we use random search-based methods that do not use
derivative computations, but based on a search step followed only by evaluation of the objective function as many times as necessary
to the convergence towards the global optimum. Among the diferent algorithms of this type of methods, we adopted the genetic
algorithm (GA). On the other hand, the numerical solution of the direct problem is accomplished by the CVFEM discretization
method (Control Volume Finite Element Method) which ensures the mass conservation in a natural way by its mathematical
formulation. Te resulting computation code HySubF-CVFEM (Hydrodynamic of Subsurface Flow by Control Volume Finite
Element Method) solves the Darcy equation in a heterogeneous porous medium. Tus, this paper describes the description of the
integrated optimization algorithm called HySubF-CVFEM/GA that has been successfully implemented and validated successfully
compared to a schematic fow case ofering analytical solutions. Te results of this comparison are qualifed of excellent accuracy.
To identify the transmissivity feld of the realistic study area, the code HySubF-CVFEM/GA was applied to the coastal “Chaouia”
groundwater located in Western of Morocco. Tis aquifer of high heterogeneity is essential for water resources for the Casablanca
region. Results analysis of this study has shown that the developed code is capable of providing high accuracy transmissivity felds,
thus representing the heterogeneity observed in situ. However, in comparison with gradient method optimization the HySubF-
CVFEM/GA code converges too slowly to the optimal solution (large CPU-time consuming). Despite this disadvantage, and given
the high accuracy of the obtained results, the HySubF-CVFEM/GA code can be recommended to solve in an efcient and efective
manner the identifcation parameters problems in hydrogeology.
1. Introduction
Te coastal aquifers play an important role in the socioe-
conomic development of the coastal plains [1–4]. Tese
costal aquifers are particularly exposed to over-exploitation
problems that can induce aquifer salinization [5–7]. Also, as
presented in the Intergovernmental Panel on climate change
(IPCC, 2007), climate changes will provide variations in the
sea level, temperature and rate and intensity of precipitation.
All these changes will afect freshwater resources, in terms of
both quantity and quality [8].
Te climate change impacts are mainly evaluated using
numerical groundwater modeling for both fow and trans-
port phenomenon (Moustadraf et al., 2008). Te numer-
ical groundwater modeling requires many hydrodynamic
parameters such as the water budget, the storativity, the
Hindawi
Mathematical Problems in Engineering
Volume 2019, Article ID 3463607, 14 pages
https://doi.org/10.1155/2019/3463607