Application of Meshless local Petrov-Galerkin approach for steady state groundwater flow modeling

The complicated behavior of groundwater system in an arid aquifer is generally studied by solving the governing equations using either analytical or numerical methods. In this regard, analytical methods are just for some aquifers with regular boundaries. Numerical methods used for this aim are finite difference (FDM) and finite element methods (FEM) which are engaged for some simple aquifers. Using them in the complex cases with irregular boundaries has some shortcomings, depended on meshes. In this study, meshless local Petrov-Galerkin (MLPG) method based on the moving kriging (MK) approximation function is used to simulate groundwater flow in steady state over three aquifers, two standard and a real field aquifer. Moving kriging function known as new function which reduces the uncertain parameter. For the first aquifer, a simple rectangular aquifer, MLPG-MK indicates good agreement with analytical solutions. In the second one, aquifer conditions get more complicated. However, MLPG-MK reveals results more accurate than FDM. RMSE for MLPG-MK and FDM is 0.066 and 0.322 m respectively. In the third aquifer, Birjand unconfined aquifer located in Iran is investigated. In this aquifer, there are 190 extraction wells. The geometry of the aquifer is irregular as well. With this challenging issues, MLPG-MK again shows satisfactory accuracy. As the RMSE for MLPG-MK and FDM are 0.483 m and 0.566 m. therefore, planning for this aquifer based on the MLPG-MK is closer to reality.