A long-term numerical groundwater quality assessment model using a modified fourth-order finite difference method with Saulyev scheme

Abstract

Mathematical models are required for long-term groundwater quality assessment around landfill sites. The long-term groundwater-quality prediction is used to report the environmental impact assessment of landfill site projects. In this research, a one- dimensional transient advection-diffusion equation is used to describe groundwater pollutant concentration measurement. Numerical simulations of groundwater quality measurement for long periods of time are proposed. The traditional and modified finite difference techniques are used to approximate the solutions. The traditional explicit forward time central space and the standard fourth-order finite difference methods are introduced. The standard fourth-order finite difference methods with Saulyev Scheme and a modified fourth-order finite difference methods with Saulyev Scheme are proposed. The approximated solutions are compared with the exact solutions in a specified case. The proposed modified new fourth-order finite difference technique gives accurate approximated solutions. The proposed numerical simulation can be applied to several types of soil physics.