Numerical Errors Associated with Groundwater Models and Improving the Reliability of Models in Environmental Management Issues

Abstract

Improving numerical accuracy of the finite difference (FD) models of groundwater transport is achieved here by removing the truncation error associated with advection–dispersion equation with first-order reaction and sink/source (ADERS). This chapter presents theoretical and numerical truncation error associated with ADERS for the first time. The truncation errors associated with the FD models of the ADERS are formulated from Taylor series analysis. The error expressions are based on a general form of the corresponding FD equation. A temporally and spatially weighted parametric approach is applied to differentiate among the various FD models. The study revealed that all the FD models (explicit, Crank–Nicolson, implicit) suffer from truncation errors and formulated an expression for error from sink/source term for the first time. The effects of these truncation errors on the solution of ADERS are demonstrated by comparison of numerical solution from different FD models with the analytical solution. The results revealed that these errors are not negligible and correcting the FD schemes for truncation error can result in a more accurate solution in groundwater transport models which are applied for environmental management as well as hydrological investigations.