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Finite Element Matrix and Mass Balance Computational Schemes for Transport in Variably Saturated Porous Media
Author(s) -
Huyakorn Peter S.,
Mercer James W.,
Ward David S.
Publication year - 1985
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/wr021i003p00346
Subject(s) - computation , finite element method , porous medium , residual , matrix (chemical analysis) , mathematics , mathematical optimization , computer science , numerical analysis , computer simulation , material balance , upstream (networking) , algorithm , porosity , mathematical analysis , simulation , engineering , geotechnical engineering , structural engineering , materials science , composite material , computer network , process engineering
An upstream‐weighted residual finite element formulation is developed for the numerical simulation of solute transport in variably saturated porous media. Included in this formulation is an influence coefficient scheme for element matrix evaluation and a mass balance computation scheme. These schemes are not only simple to implement but also cost effective. Three examples are provided to verify the numerical techniques and demonstrate the utility of the computer model. These examples indicate that mass balance information serves a useful purpose as a screening device for examining the numerical solution. They also show certain behavior of the mass balance error as well as numerical difficulties associated with the manner in which the finite element formulation of the transport equation is performed. Finally, information on the CPU time and cost required to solve the three example problems is provided to show the cost effectiveness of the present transport model. Although the present analysis considers only two dimensions, the schemes described can be extended to three dimensions, where the time and cost savings are more significant.