A new approach to avoid excessive numerical diffusion in Eulerian–Lagrangian methods

Lumping is often used to avoid non-physical oscillations for advection–dispersion equations but is known to add numerical diffusion. A new approach is detailed in order to avoid excessive numerical diffusion in Eulerian–Lagrangian methods when several time steps are used. The basic idea of this approach is to keep the same characteristics during all time steps and to interpolate only the concentration variations due to the dispersion process. In this way, numerical diffusion due to the lumping is removed at the end of each time step. The method is combined with the Eulerian–Lagrangian localized adjoint method (ELLAM) which is a mass conservative characteristic method for solving the advection–dispersion equation. Two test problems are modelled to compare the proposed method to the consistent, the full and the selective lumping approaches for linear and non-linear transport equations. Copyright © 2007 John Wiley & Sons, Ltd.