On the advective-diffusive transport in porous media in the presence of time-dependent velocities

摘要

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 advectiondiffusion 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. INDEX TERMS: 3210 Mathematical Geophysics: Modeling; 1832 Hydrology: Groundwater transport; 1829 Hydrology: Groundwater hydrology; 1842 Hydrology: Irrigation; 9805 General or Miscellaneous: Instruments useful in three or more fields.