Steady saturated-unsaturated low in irregular porous domains

Tritscher, P., Read, W.W., Broadbridge, P., and Knight, J.H. (2001) Steady saturated-unsaturated low in irregular porous domains. Mathematical and Computer Modelling, 34 (1-2). pp. 177-194.

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We present a largely analytic series-based approach for steady saturated-unsaturated flow problems in irregular shaped porous domains. We consider a porous medium with irregulat shaped boundary, both at the surface and at the base. Over the ground surface is steady rainfall with any excess allowed to freely run off without ponding. We provide a variational formulation which has explicit dependence on the position of the saturated-unsaturated interface (phreatic surface) and derive a series solution for the integrand of the penalty functional. A simple direct numerical method may then be applied to minimize the functional. This approach has several advantages. It affords a realistic description of the water distribution in both zones and an accurate location of the phreatic surface. The exact separated solutions as basis functions remove much of the arbitrariness that applies to spectral methods. No spatial discretisations are necessary and the global solution errors are readily estimated from maximum principles. We apply the solution to a canonical hillslope geometry, viz. an inclined permeable region whose cross-section is a long, thin parallelogram. We find that the height of the phreatic surface is relatively independent of the sorptive number. We prove that the phreatic surface is tangential to the soil surface at the point where the phreatic surface meets the soil surface.

Item ID: 13330
Item Type: Article (Research - C1)
ISSN: 1872-9479
Keywords: arbitrary domain; fourier series; free surface; quasilinear; saturated-unsaturated flow
Date Deposited: 30 Aug 2012 22:38
FoR Codes: 01 MATHEMATICAL SCIENCES > 0199 Other Mathematical Sciences > 019999 Mathematical Sciences not elsewhere classified @ 51%
04 EARTH SCIENCES > 0406 Physical Geography and Environmental Geoscience > 040603 Hydrogeology @ 49%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 100%
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