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Extension of the Method of Characteristics for Simulation of Solute Transport in Three Dimensions
Author(s) -
Zheng C.
Publication year - 1993
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.1993.tb01848.x
Subject(s) - advection , interpolation (computer graphics) , tracking (education) , computer science , mechanics , particle (ecology) , flow (mathematics) , simulation , field (mathematics) , mathematical optimization , mathematics , physics , geology , thermodynamics , pure mathematics , animation , psychology , pedagogy , oceanography , computer graphics (images)
The method of characteristics (e.g., Garder et al., 1964; Konikow and Bredehoeft, 1978) has been widely used in the simulation of solute transport in ground‐water systems because of its effectiveness for handling advection‐dominated problems. However, the method requires a large amount of computer memory and execution time when it is necessary to track a large number of moving particles, especially in three dimensions. The method can also lead to large mass balance discrepancies under certain circumstances. This paper describes a number of changes which may be made in the traditional method of characteristics approach to mitigate these difficulties. These changes include a dynamic particle allocation procedure, which often reduces dramatically the total number of moving particles needed in a simulation; and a consistent velocity interpolation scheme and higher‐order particle tracking techniques, which, coupled with effective handling of particle insertion and deletion at sources and sinks, can provide improved mass balance results. The accuracy of a method‐of‐characteristics model incorporating these changes is evaluated by comparison with analytical solutions for (1) three‐dimensional advection and dispersion in a spherical flow field, and (2) concentration change in a well during an injection/pumping cycle.