Theme 2-14-Analysis of numerical dispersion in finite difference approximation of solute transport equation

Abstract

Numerical solution of the ADE by traditional finite difference/finite element techniques poses serious difficulties, which stem from the truncation of Taylor’s series while approximating both the spatial and temporal first-order derivatives occurring in the ADE. In a pure advection problem, this truncation error manifests as an additional term, described as numerical dispersion. Presence of this term renders the finite difference solution of the pure advection problem mathematically equivalent to that of an advection-dispersion problem. The paper analyzes and looks into the mathematical quantification of numerical dispersion originating from the truncation of Taylor’s series. Techniques that have been adopted by researchers to remedy this problem to various degrees are also briefly discussed highlighting their advantages and limitations