SOLUTION OF THE ADVECTION-DISPERSION EQUATION IN 2 DIMENSIONS BY A FINITE-VOLUME EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD

We extend the finite-volume Eulerian-Lagrangian localized adjoint meth od (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited b y restrictions on the size of the grid Peclet or Courant number. There fore, it is well suited for solution of advection-dominated ground-wat er solute transport problems. In test problem comparisons with standar d finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable, A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mas s globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. B oundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunctio n with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow o r outflow boundaries. Published by Elsevier Science Ltd.