Rw. Healy et Tf. Russell, A FINITE-VOLUME EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR SOLUTION OF THE ADVECTION-DISPERSION EQUATION, Water resources research, 29(7), 1993, pp. 2399-2413
A new mass-conservative method for solution of the one-dimensional adv
ection-dispersion equation is derived and discussed. Test results demo
nstrate that the finite-volume Eulerian-Lagrangian localized adjoint m
ethod (FVELLAM) outperforms standard finite-difference methods, in ter
ms of accuracy and efficiency, for solute transport problems that are
dominated by advection. For dispersion-dominated problems, the perform
ance of the method is similar to that of standard methods. Like previo
us ELLAM formulations, FVELLAM systematically conserves mass globally
with all types of boundary conditions. FVELLAM differs from other ELLA
M approaches in that integrated finite differences, instead of finite
elements, are used to approximate the governing equation. This approac
h, in conjunction with a forward tracking scheme, greatly facilitates
mass conservation. The mass storage integral is numerically evaluated
at the current time level, and quadrature points are then tracked forw
ard in time to the next level. Forward tracking permits straightforwar
d treatment of inflow boundaries, thus avoiding the inherent problem i
n backtracking, as used by most characteristic methods, of characteris
tic lines intersecting inflow boundaries. FVELLAM extends previous ELL
AM results by obtaining mass conservation locally on Lagrangian space-
time elements. Details of the integration, tracking, and boundary algo
rithms are presented. Test results are given for problems in Cartesian
and radial coordinates.