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Mass balance errors when solving the convective form of the transport equation in transient flow problems
Author(s) -
Saaltink Maarten W.,
Carrera Jesús,
Olivella Sebastià
Publication year - 2004
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 - 10.1029/2003wr002866
Subject(s) - weighting , transient (computer programming) , eulerian path , divergence (linguistics) , convection , flow (mathematics) , mechanics , convection–diffusion equation , mass transport , mathematics , transient flow , groundwater , environmental science , lagrangian , computer science , chemistry , steady state (chemistry) , physics , engineering , geotechnical engineering , operating system , linguistics , philosophy , engineering physics , acoustics
The original (divergence) form of the solute transport equation expresses the mass balance of solutes in groundwater. The alternative (convective) form can be obtained by subtracting the flow equation, multiplied by concentration, from the original form. Many investigators prefer the latter because it facilitates the use of Lagrangian or mixed Eulerian‐Lagrangian numerical methods for solution. However, it performs very poorly in transient contaminant transport problems with large temporal variations in water content. We propose an alternative to overcome this difficulty. It consists of evaluating the water content at time level k + 1 − η if concentration in the convective term is evaluated at time level k + η. For this reason we have called it reverse time weighting, whereas we call an evaluation of the water content at time level k + η straight time weighting. We show that reverse time weighting improves significantly over straight time weighting not only in terms of mass balance errors, but also in terms of concentration errors.