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A finite‐volume Eulerian‐Lagrangian Localized Adjoint Method for solution of the advection‐dispersion equation
Author(s) -
Healy R. W.,
Russell T. F.
Publication year - 1993
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/93wr00403
Subject(s) - finite volume method , advection , conservation of mass , mathematics , eulerian path , inflow , adjoint equation , quadrature (astronomy) , boundary value problem , finite difference , mathematical analysis , lagrangian and eulerian specification of the flow field , boundary (topology) , mechanics , physics , partial differential equation , lagrangian , optics , thermodynamics
A new mass‐conservative method for solution of the one‐dimensional advection‐dispersion equation is derived and discussed. Test results demonstrate that the finite‐volume Eulerian‐Lagrangian localized adjoint method (FVELLAM) outperforms standard finite‐difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion‐dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM formulations, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, 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 forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on Lagrangian space‐time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.