A New Total Variation Diminishing Scheme for the Solution of Advective-Dominant Solute Transport

It is well known that the use of standard numerical techniques can lead to numerical oscillations in the solution of the advective‐dominant case of solute transport in groundwater systems. In this work a class of numerical schemes commonly employed in aeronautical engineering called total variation diminishing (TVD) schemes is investigated. A new, formally third‐order accurate, TVD algorithm is developed in one dimension for purely advective transport and applied to a variety of problems with large mesh Peclét numbers. The one‐dimensional approach is then extended to the two‐dimensional case. In both one and two dimensions the numerical results compare favorably with their respective analytic solutions.