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Lattice Boltzmann method (LBM) has emerged as a fast, precise, and efficient numerical solution to solve differential equations. There seems to be a dearth of research regarding the solution for groundwater flow in unconfined aquifer using LBM. Accordingly, in this study, an innovative numerical solution based on LBM was introduced to solve groundwater flow in unconfined aquifers, taking into account D2Q9 scheme. The solutions obtained from the proposed LBM were compared to results stemmed from three different unconfined groundwater problems with known solutions.Both steady and transient conditions for groundwater flow were considered in simulations. It was deduced that the proposed LBM could simulate the unconfined groundwater flow satisfactorily.

Excessive exploitation of groundwater has led to a significant subsidence in Darab plain, located in Fars province, Iran. The compaction of aquifer layers especially in fine-grain sediments leads to changes in aquifer parameters including hydraulic conductivity, specific yield, and compressibility which consequently changes the permeability and storage of the aquifer. Accordingly, a precise estimation of aquifer parameters are essential for both future water resources planning and management. The main objective of this paper is to determine the most optimum values of aquifer parameters based on the groundwater information and subsidence measurements spanning from 2010 to 2016. The proposed approach for inverse solution of groundwater flow is based on Lattice Boltzmann Method (LBM) integrated with Genetic Algorithm for optimization (GA). Subsidence measurements made by previous studies as well as the initial values of unknown parameters obtained from piezometric information are incorporated into the inverse modeling. The whole process of inverse modeling is repeated from 2010 to 2016 which leads to annually estimation of the aquifer parameters. Due to the compaction occurring in the aquifer system, a decreasing temporal trend is observed in the aquifer parameters in most parts of the plain. By fitting a function to time-dependent aquifer parameters, their corresponding values and consequently the amount of subsidence in 2017 are predicted. The small average relative error (~3.5%) between the predicted land subsidence and the measurements demonstrates the high performance of the proposed inverse modeling approach.