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 Peclet 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.