Physics – Geophysics
Scientific paper
Jul 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004georl..3113505s&link_type=abstract
Geophysical Research Letters, Volume 31, Issue 13, CiteID L13505
Physics
Geophysics
3
Mathematical Geophysics: Modeling, Hydrology: Groundwater Transport, Hydrology: Groundwater Hydrology, Hydrology: Irrigation, General Or Miscellaneous: Instruments Useful In Three Or More Fields
Scientific paper
This paper develops certain exact closed form solutions to one-dimensional problems involving both advective and advective-diffusive transport in a porous medium, particularly in the presence of a Darcy velocity field that is time-dependent. Such situations can occur when the boundary potential inducing flow in the porous medium is time-dependent. A particular form chosen is an exponentially decaying time-dependency in the flow velocity, resulting from a non-replenishing source. The value of the one-dimensional solution stems not only from its potential applicability for the calibration of computational schemes used to examine the advection-diffusion equation in general, but also for the study of the purely advective flow problem with time-dependent velocity that requires sophisticated adaptive computational schemes to ensure numerical stability at a leading front in the form a discontinuity.
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