NUMERICAL ADVECTIVE FLUX IN HIGHLY VARIABLE VELOCITY-FIELDS EXEMPLIFIED BY SALTWATER INTRUSION

Numerical simulation of advective solute transport requires approximat ion of two vectors: the concentration gradient and the velocity. Estim ation of the concentration gradient by Eulerian solution techniques gi ves rise to classical 'numerical dispersion' since the truncation erro r is of the form del(2)C. Truncation of the velocity vector has escape d close scrutiny because the velocity field generally varies slowly in space in most groundwater environments. However, in many problems, in cluding saltwater intrusion, the velocity field is highly variable and error associated with velocity approximation strongly affects the sol ution. particle-tracking (Lagrangian) algorithms create a non-uniform error vector within each numerical block. The non-uniform error gives rise to differential advective flux that mimics the effects of classic al numerical dispersion. Since the velocity truncation error vector de pends on the size of a numerical block, Lagrangian methods may require extremely fine discretization of the underlying pressure grid. A fini te-difference Lagrangian variable-density flow and transport code show s slow convergence to a 'correct' solution of Henry's and related prob lems of saltwater intrusion as the grid density is changed. On the oth er hand, an Eulerian finite element code is shown to have a uniform ve locity error vector within each element and the solution converges qui ckly as the grid density is changed. This suggests that the usual comp utational advantage that Lagrangian transport algorithms gain by using coarse grids is lost when modeling transport within highly variable v elocity fields. (C) 1998 Published by Elsevier Science B.V. All rights reserved.