Qualitative Effects of Hydraulic Conductivity Distribution on Groundwater Flow in Heterogeneous Soils

• Main Authors: Alexey Beliaev, Gennady Krichevets
• Format: Article
• Language: English
• Published: MDPI AG 2018-12-01
• Series: Fluids
• Subjects: n/a
• Online Access: https://www.mdpi.com/2311-5521/3/4/102

One of the most significant difficulties in subsurface hydrology is the considerable uncertainty in hydraulic conductivity values in the medium. This stimulates qualitative analysis of the effect of conductivity distribution on the solutions or on some components of the solutions of groundwater flow equations. This work is an attempt to develop a rigorous basis for deciding whether the solutions are monotonous with respect to hydraulic conductivity. Such monotonicity is analogous to the well-known comparison principles with respect to variations of initial data or external supplies. Some example problems are given in this paper, including a problem with a free boundary, in which the monotonous dependence of the solution on the conductivity distribution is proved rigorously. Examples are also given, in which monotonicity assumptions, despite being apparently obvious, are proved to be invalid.