Numerical Simulation of a Two-Dimensional Groundwater Pollute Transport Problem Using Incompressible Steady-State Navier-Stokes Equations and Diffusion-Convection Equations

Abstract

Most of the real contaminant problems are defined domains that are geometrically complex and can have different boundary conditions in different areas. Therefore, it is usually difficult to find a solution analytically, so we use the approximate method to generate an approximate function. One answer to this problem is the finite element approach (FEM). This study presents a partial differential equation (PDE) simulation system that uses numerical techniques for the distribution of pollutant concentrations in groundwater in space and time. The movement of the liquid is described by the incompressible steady-state Navier-Strokes equation, while the transport of pollutants is described by the diffusion-convention equation. The variation formulation that forms the basis of FEM and MATLAB is discussed along with the selection of the abstract approximation space and the welfare of the weak formulation. The motivation for this study comes from a specific and considered water body with the discharge of factory effluents on the ground that ends up reducing the quality of groundwater. First, the fluid flow equation is solved to obtain velocity and pressure profiles. Steady-state concentration profiles were obtained for various values of diffusion coefficient ( $D$ ), baseline, and input concentrations. The results showed that decreasing the diffusion coefficient $D$ increased the number of pollutants for convective transport and decreased the number of pollutants that diffused from the entrance. Although groundwater is not completely safe, it is concluded that experimental studies are necessary decision-making basis for water resource protection, especially in water pollution emergencies.