One-dimensional modeling of aquifer contamination using a meshless method

Water is one of the most important and fundamental needs in the lives of all living creatures. Owing to the recent drought around the world and reduction of surface water resources, groundwater resources are gaining more significance. Distribution and spread of contamination in groundwater resources make them unusable and thus aggravate the drought crisis in arid and semi-arid regions. Therefore, it is of utmost importance to protect groundwater resources from the input of pollutants and to reduce the amount of contaminants in them.
In this research, the transmission of pollution, identification of transmission and diffusion processes, and its modeling were studied in order to assist the practitioners in adopting appropriate strategies. Also, the Meshless Local Petrov-Galerkin method was used to solve the transmission equation of the porous medium, while moving the least squares was used as its approximation function. For verification purposes, the results of the numerical solution were compared with the exact solution. This comparison indicated the acceptable accuracy of the Meshless Local Petrov-Galerkin method for solving the transmission equation for porous media.
The results of the numerical solution were compared with the calculated values of Agata's exact solution at different times for the one-dimensional equation of pollution in the porous medium. The calculated total error was 0.03, indicating that the Meshless Local Petrov-Galerkin method has an acceptable precision in simulating one-dimensional contamination in the aquifer.
This study showed that the numerical method of Meshless Local Petrov-Galerkin is suitable for modeling the transmission of pollutants in groundwater in one-dimensional mode and has acceptable accuracy.