THE THIRD-ORDER TVD (total-variational diminishing) METHOD in MT3D is a major improvement over the previous MT3D

It is implemented with the ULTIMATE algorithm (Universal Limiter for Transient Interpolation Modeling of the Advective Transport Equations)

The interface concentrations are determined through a third-order polynomial interpolation of nodal concentrations, supplemented by a universal flux limiting procedure to minimize overshoot/undershoot and numerical dispersion preseving sharp concentration fronts.

This third-order ULTIMATE scheme is mass conservative, without excessive numerical dispersion, and essentially free of overshoot/undershoot.

TVD schemes are not problem free, requiring more computational effort than finite difference and not being completely free of numerical dispersion. They are not AS effective as Langragian methods for eliminating numerical dispersion.

Read the MT3D manual for more specifics.