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Additional resources for Mathematical Methods for Surface and Subsurface Hydrosystems (Series in Contemporary Applied Mathematics ? Vol. 7) (Series in Contemporary Applied Mathematics)

Example text

K(x). (94) 3. Equivalence with the non-conforming approximation of the primal formulation: $; can be evaluated by solving sequentially in time the following problems: For n 2 1, ( Seek $: E Piclanl such that [ 6t J, Hhf$h = + s, Iw($;-l))$h, Proof. Similar to that of Proposition 5 . - W hE P&,anl . 4 Water-tableground interact ion and the obstacle problem To investigate water-tableground interaction, we consider a simplified problem: the domain R is a quadrangle, no-flux conditions are imposed 42 Alesandre Ern on the le&, bottom, and right boundaries, and the top boundary, aQ,, is exposed to a constant rainfall with velocity v, = -ie, where i > 0 is the rainfall intensity; see Figure 3.

The right plot in Figure 6 displays simulation results. The agreement with the analytical solution is excellent. 5 Figure 6 Stationary infiltration test case. Top: relative hydraulic conductivity kT versus matrix potential for the three soils. Bottom: simulated and analytical profiles of capillary tension, &+(-$-), for the three soils. 2 Unstationary test case The following test case is discussed in Barry et al. [21]; see also [20]. Assume that the relative hydraulic conductivity is defined by the BrooksCorey model, equation (82), with parameters qSand @.

2 Soil hydrodynamic functions To close (71) or (72), two algebraic relations between 8, IC,, and must be specified. In soils, the volumetric water content does not vary between 0 and 1,but between a minimum value 8, called the residual volumetric water content and a maximum value Bs called the saturated volumetric water content. Define the reduced volumetric water content $J which, by definition, varies between 0 and 1. A model often considered in the engineering literature to specify the soil water retention curve is that derived by van Genuchten in 1980 [lo] i.

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