Comparison between numerical and analytical solution of solute transport models

Abstract

The fate and movement of dissolved substances in soils and groundwater has generated considerable concern for the quality of the subsurface environment. Many analytical solutions for the partial differential equations that describe solute and pollutant movement exist. Numerical solutions are more general, and often more difficult to verify. In order to determine the model error, the examination of the ability of numerical methods compared to analytical methods is strongly recommended. The objective of the study is to make a comparison between numerical and analytical solution models for solute transport equation. In this study, the numerical solution calculated with the WAVE-model is compared with the analytical solution calculated with CXTFTT-model. The study scenarios considered variables such as compartment depth, applied flux at the top and soil dispersivity under steady-state conditions. The simulations depend on 27 solute infiltration scenarios. The solute concentrations were calculated with the WAVE-model and the CXTFIT-model for each scenario. The WAVE-model error was evaluated with three methods: absolute average maximum error, relative average maximum error and relative average area error. The study implied that the WAVE-model error increased with the increase of the compartment depth, decreasing soil dispersivity, and decrease in flux. The study leads to the recommendation to use compartment depth as thin as possible to minimise the WAVE-model error. Furthermore, it is more useful to use several numerical solution models, such as SWMS-2D model, to evaluate and examine the WAVE-model.