A 2d Fea for Aquifer Boundary Inverse Problem: Co-Simulating Groundwater Flow in Lebna Watershed-Tunisia Using Comsol-Matlab
This study was conducted in the Lebna side of Plio-quaternary aquifer belonging to Cape Bon in the Northeastern side of Tunisia. This coastal aquifer is often inaccessible and does not have enough information about its parameters such as hydraulic head and hydraulic fluxes.
This paper aims to treat the Partial Differential Equations (PDE) of groundwater flow problem. Variational method based Finite Elements (FE) has been used to solve the Cauchy problem or inverse problem. This problem accommodate an inverse algorithm developed by Andrieux et al. in order to identify the missing data as hydraulic head and hydraulic fluxes on a part of an aquifer boundaries where data are non-available.
Cauchy problem, which is known as an ill-posed problem, has been divided into two well-posed sub-problems. Then the role of the inverse algorithm is shortly solutions optimization; it works on solving those sub problems; each one is supposed to find out specific data, one for hydraulic head and the other for hydraulic fluxes. Only the nearly equivalent to exact data have been considered as optimal solutions, which are determined based on minimizing an energy like-error in each simulation.
In this case of study, a forward problem of Darcy Flow has been solved using measurement data as input through Comsol Multiphysics, a FE based modeling software. The outputs of the forward simulation have been utilized as the entry data written within the inverse algorithm in Matlab for the aim of simulating data where requested.
In the general context of aquifer, modeling the data completion problem is very helpful to understand the boundary conditions, which are determined in the resolution.
Authors and others have studied this kind of problem in an academic framework but to our knowledge, it is the first work with a real case of aquifer
Computed results have been compared to measurement data, exact ones and similarity has been noticed which could prove the efficiency of the method used in this context since 2006. Thus, RMSE is about 0.055 and a percent error varies between 0 and 14 % for hydraulic head.
