Front solutions of Richards' equation

Caputo, Jean-Guy and Stepanyants, Yury ORCID: (2008) Front solutions of Richards' equation. Transport in Porous Media, 74 (1). pp. 1-20. ISSN 0169-3913


Front solutions of the one-dimensional Richards' equation used to describe groundwater flow are studied systematically for the three soil retention models known as
Brooks–Corey, Mualem–Van Genuchten and Storm–Fujita. Both the infiltration problem when water percolates from the surface into the ground under the influence of gravity and
the imbibition (absorption) problem when groundwater diffuses in the horizontal direction without the gravity effect are considered. In general, self-similar solutions of the first kind in the form of front exist only for the imbibition case; such solutions are stable against small perturbations. In the particular case of the Brooks–Corey model, self-similar solutions of the second kind in the form of a decaying pulse also exist both for the imbibition and infiltration cases. Steady-state solutions in the form of travelling fronts exist for the infiltration case only.
The existence of such solutions does not depend on the specifics of the soil retention model. It is shown numerically that these solutions are stable against small perturbations.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Author's version not available.
Faculty/School / Institute/Centre: Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Faculty/School / Institute/Centre: Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Date Deposited: 22 Nov 2009 06:05
Last Modified: 15 Feb 2021 23:33
Uncontrolled Keywords: convection–diffusion equation; Burgers equation; front solutions; soil physics; infiltration; imbibition; porous media; groundwater flow; Richards' equation; self-similar solution; steady-state solution; water front stability
Fields of Research (2008): 04 Earth Sciences > 0404 Geophysics > 040499 Geophysics not elsewhere classified
05 Environmental Sciences > 0503 Soil Sciences > 050305 Soil Physics
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Fields of Research (2020): 37 EARTH SCIENCES > 3706 Geophysics > 370699 Geophysics not elsewhere classified
41 ENVIRONMENTAL SCIENCES > 4106 Soil sciences > 410605 Soil physics
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490109 Theoretical and applied mechanics
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences
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