A FINITE-VOLUME EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR SOLUTION OF THE ADVECTION-DISPERSION EQUATION

Citation
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
Citations number
29
Categorie Soggetti
Limnology,"Environmental Sciences","Water Resources
Journal title
ISSN journal
00431397
Volume
29
Issue
7
Year of publication
1993
Pages
2399 - 2413
Database
ISI
SICI code
0043-1397(1993)29:7<2399:AFELAM>2.0.ZU;2-X
Abstract
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.